Lucie Finez

Sophie Berjot

Elisabeth Rosnet

Finez

Do Athletes Claim Handicaps in Low Ego-Threatening Conditions? Re-Examining the Effect of Ego-Threat on Claimed Self-Handicapping

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

or physical pain) rather than to their lack of abilities. Conversely, if they succeed despite these handicaps their success may be more linked to their physical abilities. During the last five years, claimed self-handicapping has received a large amount of interest, particularly in the field of sports (e.g., [START_REF] Elliot | Achievement goals, self-handicapping, and performance attainment: A mediational analysis[END_REF][START_REF] Greenlees | The effects of self-handicapping on attributions and perceived judo competence[END_REF][START_REF] Kuczka | Self-handicapping in competitive sport: Influence of the motivational climate, self-efficacy, and perceived importance[END_REF]. Indeed, this strategy is used quite frequently in sports (for a review see [START_REF] Prapavessis | Self-presentational issues in competition and sport[END_REF]) and can negatively affect athletes' social relationships, self-image and performance (see e.g., [START_REF] Elliot | Achievement goals, self-handicapping, and performance attainment: A mediational analysis[END_REF][START_REF] Martin | Self-handicapping in sport and physical activity: An elusive concept[END_REF]. It would be useful for coaches, sport psychologists and sport teachers to use techniques to prevent self-handicapping [START_REF] Kuczka | Self-handicapping in competitive sport: Influence of the motivational climate, self-efficacy, and perceived importance[END_REF]. To accomplish this, one would need to accurately predict which athletes are most likely to engage in claimed self-handicapping and when they are most likely to do so.

To reach this goal, we need to explore both the personal characteristics of individuals that are more likely to engage in claimed self-handicapping (personal determinants) and the situations in which this strategy may appear (situational determinants).While several dispositional determinants of claimed self-handicappingnamely, self-handicapping tendency and self-esteem-have been identified (e.g., [START_REF] Carron | Group effects and self-handicapping[END_REF][START_REF] Greenlees | The effects of self-handicapping on attributions and perceived judo competence[END_REF][START_REF] Prapavessis | Self-handicapping and self-esteem[END_REF], the situational determinants of claimed self-handicapping, have received less empirical examination. Studies that invested the situational determinants of this strategy mostly focused on variables linked to the climate of a group (e.g., motivation and cohesion, [START_REF] Carron | Group effects and self-handicapping[END_REF][START_REF] Kuczka | Self-handicapping in competitive sport: Influence of the motivational climate, self-efficacy, and perceived importance[END_REF] and less on the nature of the task itself or more specifically on the threat generated by a task. In addition, the situational and dispositional determinants of claimed self-handicapping have almost never been studied simultaneously, that is to say by considering the interaction of situational and dispositional factors on self-handicapping (interactionist point of view, [START_REF] Kimble | Self-focus, gender, and habitual self-handicapping: Do they make a difference in behavioral self-handicapping?[END_REF]. Consequently, two major questions remain. First, it remains unclear whether athletes use claimed self-handicapping in low ego-threatening conditions. The literature clearly indicates that athletes engage in this strategy in high ego-threatening situations such as competitions or physical tests (e.g., [START_REF] Ferrand | Relations between female students' personality traits and reported handicaps to rhythmic gymnastics performance[END_REF][START_REF] Kuczka | Self-handicapping in competitive sport: Influence of the motivational climate, self-efficacy, and perceived importance[END_REF]. However, to our knowledge, no research addresses whether athletes also use this strategy during low ego-threatening situations (e.g., conditioning training exercises or techniques training exercises without any salient evaluative components) 1 . Second, while it is evident that high self-handicappers and low self-esteem athletes can engage in claimed self-handicapping [START_REF] Carron | Group effects and self-handicapping[END_REF][START_REF] Coudevylle | Determinants of self-handicapping strategies in sport and their effects on athletic performance[END_REF][START_REF] Greenlees | The effects of self-handicapping on attributions and perceived judo competence[END_REF], whether low self-handicappers and high self-esteem athletes also engage in this strategy remains unclear. The present work uses the interactionist approach to investigate the effect of self-handicapping tendency and self-esteem level on the emergence of claimed self-handicapping in two conditions (high and low ego-threatening situations).

Claimed Self-Handicapping in Low Ego-Threatening Situations

Given that self-handicapping was initially defined as a strategy used "to shape the implications of performance feedback" to protect (or enhance) one's competence image (Jones & Berglas, 1978, p. 202), this strategy has generally been studied in evaluative situations. In most experiments on claimed self-handicapping participants were placed in high ego-threatening situations; athletes completed competitions or physical tests [START_REF] Carron | Group effects and self-handicapping[END_REF][START_REF] Ferrand | Relations between female students' personality traits and reported handicaps to rhythmic gymnastics performance[END_REF][START_REF] Greenlees | The effects of self-handicapping on attributions and perceived judo competence[END_REF] and students completed exams or intelligence tests [START_REF] Feick | The double-edged sword of self-handicapping: Discounting, augmentation, and the protection and enhancement of self-esteem[END_REF][START_REF] Hirt | Self-reported versus behavioral selfhandicapping: Empirical evidence for a theoretical distinction[END_REF][START_REF] Strube | An analysis of the Self-Handicapping Scale[END_REF]. These studies have shown that claimed self-handicapping strategies are particularly likely to emerge during high ego-threatening situations. However, up to this point, no study has investigated whether claimed self-handicapping strategies are also likely to emerge during low ego-threatening situations. Nevertheless, general research can shed light on this topic.

On the one hand, we can reference research outside of the field of sports in which ego-threat was manipulated (high vs. low), and claimed self-handicapping subsequently measured [START_REF] Degree | Adler's psychology (of use) today: Personal history of traumatic life events as a self-handicapping strategy[END_REF][START_REF] Smith | The self-serving function of hypochondriacal complaints: Physical symptoms as self-handicapping strategies[END_REF]. In these studies, the high and low ego-threatening conditions were respectively operationalized by an intelligence test and a nonevaluative cognitive task that would generate pretesting data for an upcoming study. In both of these experiments, participants engaged more in claimed self-handicapping in the high ego-threatening condition than in the low ego-threatening condition.

On the other hand, still outside of the field of sports, we can reference research in which ego-threat (high vs. low) and difficulty of the task (high vs. low) were manipulated [START_REF] Rhodewalt | Claimed self-handicaps and the self-handicappers: The relation of reduction in intended effort to performance[END_REF], studies 1 and 2). High self-handicappers who anticipated a difficult test reported lower intention of effort (more self-handicapping) than low self-handicappers both in the high and low ego-threatening conditions. These findings only partially support the authors' predictions that selfhandicapping would only emerge in the difficult, high ego-threatening condition. Rather, they suggest that high self-handicappers may engage in behavioral selfhandicapping even in low ego-threatening situations. Further, in an other study that was designed to investigate the consequences of self-handicapping on performance, [START_REF] Deppe | Self-Handicapping and intrinsic motivation: Buffering intrinsic motivation from the threat of failure[END_REF] observed that high self-handicappers engaged in more behavioral self-handicapping compared with low self-handicappers before participating in a pinball game both in a competitive condition (that included a high evaluative component) and in a noncompetitive condition (that lacked an evaluative component).

Although the experiments of [START_REF] Rhodewalt | Claimed self-handicaps and the self-handicappers: The relation of reduction in intended effort to performance[END_REF] and [START_REF] Deppe | Self-Handicapping and intrinsic motivation: Buffering intrinsic motivation from the threat of failure[END_REF] were not designed to test the emergence of self-handicapping in low ego-threatening conditions, they suggest that high self-handicappers may engage in this strategy even when they are faced with low evaluative situations-and which should be, by nature, low ego-threatening. Surprisingly, these findings were not highlighted and have received little attention in the literature even though they are inconsistent with the initial [START_REF] Jones | Control of attributions about the self through self-handicapping strategies: The appeal of alcohol and the role of underachievement[END_REF] and most defended position (see e.g., [START_REF] Self | Situational influences on self-handicapping[END_REF]) that self-handicapping emerges to shape the implication of performance feedback.

On the basis of these results, we hypothesize that self-handicapping strategies can emerge in situations with and without performance feedback. More specifically, while applying this hypothesis to the emergence of claimed self-handicapping in the field of sport, we proposed that some athletes, and particularly those who present a high self-handicapping tendency, may engage in claimed self-handicapping strategies not only in high ego-threatening situations such as competitions or physical tests but also in low ego-threatening situations.

In the same manner, other athletes, and particularly those with low self-esteem, may also engage in claimed self-handicapping in low ego-threatening situations.

Low self-esteem individuals are indeed known to engage in strategies to protect their self (for a review see [START_REF] Baumeister | Self-presentational motivations and personality differences in self-esteem[END_REF]. In this sense, two studies suggest that in comparison with high self-esteem athletes, low self-esteem athletes engage in more self-handicapping before participating in a physical test [START_REF] Coudevylle | Determinants of self-handicapping strategies in sport and their effects on athletic performance[END_REF][START_REF] Martin | Self-handicapping in physical achievement settings: The contributions of self-esteem and self-efficacy[END_REF]. It is possible that low selfesteem athletes differ from high self-esteem athletes not only by their tendency to engage more in claimed self-handicapping in high ego-threatening situations, but also by their tendency to engage in this strategy in a wider range of situations.

Claimed Self-Handicapping Among Low Self-Handicappers and High Self-Esteem Athletes

Several studies indicate that high self-handicappers claim more handicaps than low self-handicappers [START_REF] Carron | Group effects and self-handicapping[END_REF][START_REF] Finez | Comprendre et prédire les stratégies d'auto-handicap revendiqué dans le domaine du sport: une approche interactionniste[END_REF][START_REF] Greenlees | The effects of self-handicapping on attributions and perceived judo competence[END_REF]; while low self-esteem athletes claim more handicaps than high self-esteem athletes [START_REF] Coudevylle | Determinants of self-handicapping strategies in sport and their effects on athletic performance[END_REF][START_REF] Martin | Self-handicapping in physical achievement settings: The contributions of self-esteem and self-efficacy[END_REF] when they are faced with high ego-threatening events like a competition or a physical test. But the data from these studies, do not address whether low self-handicappers and high self-esteem athletes do or do not engage in claimed self-handicapping because there was only one condition (a high ego-threatening condition). Two studies focusing on self-handicapping in its behavioral form suggest that high self-esteem individuals engage in behavioral self-handicapping and that they do so to enhance their image of competence [START_REF] Newman | When stakes are higher: Self-esteem instability and self-handicapping[END_REF][START_REF] Tice | Esteem protection or enhancement? Self-handicapping motives and attributions differ by trait self-esteem[END_REF]. To our knowledge, no study has investigated whether high self-esteem individuals engage in claimed self-handicapping or whether low self-handicappers engage in this strategy.

The present study attempted to address two main issues. First, we tested whether high self-handicappers and low self-esteem athletes engage in claimed self-handicapping in low ego-threatening sports situations. Secondly, we observed whether low self-handicappers and high self-esteem athletes engage in claimed self-handicapping strategies when they are faced with high ego-threatening sports situations.

Overview

Method

The design was a 2 (Self-handicapping tendency: High vs. Low) × 2 (Self-esteem: High vs. Low) × 2 (Ego-threatening situation: High vs. Low) factorial design. The study was conducted in two phases. In phase 1, participants were asked to complete a questionnaire packet including self-handicapping and self-esteem scales. Consistent with previous researchers, we constituted the groups of low and high self-handicappers by selecting participants in the bottom and top thirds of the score distribution (respectively, CSHS-S scores < 24 and > 32; see e.g., [START_REF] Rhodewalt | Claimed self-handicaps and the self-handicappers: The relation of reduction in intended effort to performance[END_REF][START_REF] Thompson | Self-handicapping status, claimed self-handicaps and reduced practice effort following success and failure feedback[END_REF]. Participants with scores in the middle third of the score distribution were not invited to participate in second phase of the experiment. This selection criterion enabled researchers to detect an effect of self-handicapping tendency on self-handicapping. However, due to the fact that self-handicapping tendency and self-esteem level were not correlated, using the same selection criterion to create the groups of high and low self-esteem participants would imply to exclude many participants 2 . As such, to avoid losing too many participants, and because it is not necessary to exclude the participants with scores in the middle third of the score distribution on the self-esteem dimension to observe an effect of self-esteem on self-handicapping (see e.g., [START_REF] Strube | Self-enhancement, self-assessment, and selfevaluative task choice[END_REF][START_REF] Tice | Esteem protection or enhancement? Self-handicapping motives and attributions differ by trait self-esteem[END_REF][START_REF] Tice | Self-esteem, self-handicapping, and self-presentation: The strategy of inadequate practice[END_REF], the groups of low and high self-esteem athletes were distinguished a posteriori on the basis of median splits (scores below and above 24 for physical self-esteem, and score below and above 37 for global self-esteem).

The aim of phase 2 was to manipulate ego-threat and to assess athletes' engagement in claimed self-handicapping. Three weeks after phase 1, in an ostensibly unrelated setting, selected participants were contacted to participate in a physiological experiment ostensibly conducted by the physiological laboratory of their university. Participants were randomly assigned to the high (n = 51) and low (n = 52) ego-threatening conditions while controlling the sex-ratio. Approval of the study protocol was obtained from the ethics committee of the university.

Participants

Volunteer students of the Kinesiology University of Amiens (France) who practice sport competition at a level ranging from regional to international were recruited to participate in this study. In total 195 athletes participated in phase 1, from which 103 participated in phase 2. They were 73 males and 30 females (M age = 19.5; SD = 1.5) from a variety (n = 30) of team and individual sports. They trained an average of 7.1 hr per week.

Material and Procedure

Phase 1 During regular university courses, participants completed a questionnaire presented to them as part of a study on athletes' strategies.

Self-Handicapping Tendency. The self-handicapping tendency was assessed with the Claimed Self-Handicapping Scale in Sport (CSHS-S, [START_REF] Finez | Comprendre et prédire les stratégies d'auto-handicap revendiqué dans le domaine du sport: une approche interactionniste[END_REF]. This scale is composed of eight items associated with a seven-point Likert scale ranging from 1 (strongly disagree) to 7 (strongly agree). Four items assess the self-handicapping tendency for self-protective motives (e.g., "When I feel bad physically (lack of sleep, pain, etc.), I tell the others before starting the competition so that if I fail, the others will think that I have failed, in part, because of this obstacle"). Four items assess the self-handicapping tendency for self-enhancing motives (e.g., "When I'm not prepared enough for a competition, I tell the others before starting the competition, so that if I succeed despite of this obstacle, the others will think that I'm more competent). The CSHS-S has been found to have satisfying validity and reliability for athletes (Finez, 2008, studies 1, 2 and 4). This scale has demonstrated high internal consistency (Cronbach's alphas range from .86 to .88 in three different studies) and the examination of its construct validity indicated that its score correlates positively with constructs that are theoretically linked to self-handicapping such as ego goal orientation (r = .31), entity theory of ability (r = .26), public self-consciousness (r = .33), social perfectionism (r = .42) or self-esteem instability (r = .25). In addition, it has demonstrated high test-retest reliability (Pearson's r = .82) at a four weeks interval. Further, the confirmatory factor analysis confirmed the existence of the two factors: Self-protection and self-enhancing motives (GFI = .98; CFI = 1.00; RMSEA <.001). Finally, the CSHS-S has demonstrated its ability to predict athletes' engagement in claimed self-handicapping both in natural and experimental settings.

The CSHS-S was used rather than the Self-Handicapping Scale (SHS, [START_REF] Jones | The Self-Handicapping Scale[END_REF] which is generally used to assess self-handicapping tendency (e.g., [START_REF] Deppe | Self-Handicapping and intrinsic motivation: Buffering intrinsic motivation from the threat of failure[END_REF][START_REF] Rhodewalt | Claimed self-handicaps and the self-handicappers: The relation of reduction in intended effort to performance[END_REF][START_REF] Thompson | Self-handicapping status, claimed self-handicaps and reduced practice effort following success and failure feedback[END_REF] because it specifically measures claimed self-handicapping. Further, unlike the CSHS-S, the SHS assesses both self-protective and selfenhancing motives of self-handicapping, which is essential to measure all aspects of self-handicapping, not simply its self-protective motives [START_REF] Tice | Esteem protection or enhancement? Self-handicapping motives and attributions differ by trait self-esteem[END_REF]. Finally, this scale was especially developed for the population of athletes, which is necessary to study self-handicapping in the field of sports [START_REF] Martin | Is the Self-Handicapping Scale reliable in non-academic achievement domains?[END_REF].

Self-Esteem. Self-esteem level was assessed with the French version [START_REF] Berjot | Validation française de la version révisée de l'échelle de "Sentiment d'Inadéquation[END_REF] of [START_REF] Fleming | The dimensionality of self-esteem: II. Hierarchical facet model for revised measurement scales[END_REF] adaptation of the Feelings of Inadequacy Scale. The Self-Regard and Physical Abilities subscales were used to assess respectively global and physical self-esteem 3 . Responses to all questions were made on a seven-point Likert scale ranging from 1 (strongly disagree) to 7 (strongly agree).

Perceived Importance of Physical Abilities.

Previous research suggest that the perceived importance of an event plays an important role in ego-threat (e.g., [START_REF] Schultheiss | Choice of difficult tasks as a strategy of compensating for identity-relevant failure[END_REF]. Individuals may only feel threatened by a task if it assesses central components of their self [START_REF] Self | Situational influences on self-handicapping[END_REF]. As such, athletes may feel threatened by a physical ability test only if the possession of high physical abilities is central for them. Participants were asked to indicate on a Likert scale ranging from 1 (strongly disagree) to 7 (strongly agree) their agreement with four statements such as: "It is important for me to have . . . 1-high physical abilities; 2high qualities of force; 3-high qualities of speed; 4-high qualities of coordination" (α = .59). Participants who reported placing little importance on the possession of high physical abilities (score under the midpoint of the Likert scale; n = 6) were dropped from the study before phase 2 because they may not have felt threatened by the motor task.

Phase 2 Selected athletes were contacted to participate in a physiological experiment; the purpose of the experiment was not specified. To avoid strategic absences in phase 2, participants were not informed of the bogus purpose of the physiological experiment before arriving at the laboratory. The anonymous code they had reported on the questionnaire of phase 1 was used to locate and contact them.

Upon each participant's arrival, a female experimenter (the first author of this study)-who was unaware of participants' scores on the self-esteem and selfhandicapping scales-informed them that they would individually complete four successive tasks and that she would supervise only the motor task (task 4).

Manipulation of Ego-Threat (Task 1).

The first task was used to manipulate ego-threat. All participants were asked to read a notice describing the focus of the (alleged) experimental study, and then watched a video presentation of the motor task they would complete. Instructions in the video tape were presented by an actor pretending to be a coach of the National Olympic Committee. The video was used to increase the credibility and stability of instructions. During the video, participants were also presented with illustrations of the motor task that they would complete (the same illustrations were presented to participants in all conditions). The manipulation of ego-threat was adapted from one used in previous studies (see e.g., DeGree & Snyder, 1985;[START_REF] Rhodewalt | Claimed self-handicaps and the self-handicappers: The relation of reduction in intended effort to performance[END_REF][START_REF] Smith | The self-serving function of hypochondriacal complaints: Physical symptoms as self-handicapping strategies[END_REF] to fit with the population of athletes.

Participants in the high ego-threatening condition were told that they would participate in a study designed to test the relationship between physical abilities and athletics performance and that they would participate in a test on a force plate to measure their physical abilities. A force plate is an instrument used to measure the ground reaction forces generated by a body standing on or moving across it. They were informed that the results of their tests would be used by a computer program to calculate their level of physical ability and that the experimenter would send them their results within 10 days. To increase the credibility of these instructions, participants were asked to indicate their sex, date of birth, sport and best performances during the last two seasons on a questionnaire which was supposed to be used by the experimenter to report their future results on the test. They were told the following:

To ensure a reliable measure of your physical abilities, we use a physical ability test designed by the National Olympic Committee for the preparation of the London 2012 Olympic Games. This test was specially developed to evaluate the physical abilities that are essential to high performance in Olympics sports. Its ability to accurately predict the future performances in individual and collective sports have been proven [. . . ].

In contrast, participants in the low ego-threatening condition were told that they would participate in a pilot study and that they would execute a motor task on a force plate to calibrate it, and thus help to prepare the device for an upcoming study. They were told:

You will take part in a task aimed only at calibrating the material. [ . . . ] your performance on this task will not enable us to evaluate your physical abilities. You will not receive any feedback on your performance. However, we ask that you put forth your best effort on this task.

Unlike participants in the high ego-threatening condition, participants in the low ego-threatening condition were not asked to record their identity, demographic information or performance history.

Measure of Claimed Self-Handicapping (Task 2).

The second task was aimed at assessing athlete's engagement in claimed self-handicapping. Participants first read instructions about the effect of momentary physical and psychological state on task performance. These instructions were adapted from those used by [START_REF] Smith | On the self-serving function of an academic wooden leg: Test anxiety as a self-handicapping strategy[END_REF]. Participants of the high ego-threatening condition read the following:

The results of this test could be affected by the participants' state of mind at the moment of the test. Athletes who are tired, ill, anxious or who encounter any other problem, usually get results significantly below their true level of ability. Therefore we would like you to fill out a questionnaire about your current state.

In the low ego-threatening condition the same instructions were proposed, preceded by: "So as to reliably calibrate the material, we would like you to fill out a questionnaire assessing your present state of mind."

Then, participants rated the extent to which potential handicaps were likely to interfere with their execution on the task. They responded to the statement "My result to the test might be disrupted by . . . " associated with a list of 15 potential handicaps and a seven-point Likert scale ranging from 1 (strongly disagree) to 7 (strongly agree). The list of potential handicaps was adapted from [START_REF] Kuczka | Self-handicapping in competitive sport: Influence of the motivational climate, self-efficacy, and perceived importance[END_REF] and included handicaps such as "injury," "anxiety," or "academic worries." Similarly to the procedure used by [START_REF] Kuczka | Self-handicapping in competitive sport: Influence of the motivational climate, self-efficacy, and perceived importance[END_REF], participants could report additional handicaps. Only the participants of the high ego-threatening condition were invited to report their name on this questionnaire. Claimed self-handicapping was assessed by calculating the mean of disruption reported such that higher scores indicated more self-handicapping (see [START_REF] Kuczka | Self-handicapping in competitive sport: Influence of the motivational climate, self-efficacy, and perceived importance[END_REF][START_REF] Smith | On the self-serving function of an academic wooden leg: Test anxiety as a self-handicapping strategy[END_REF].

Manipulation Checks (Task 3).

To test whether participants had carefully read the instructions about the effect of state of mind on performance, participants were asked: "Do you think that a negative physical or psychological state could decrease your performance on the test?" This question was associated with a five-point Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree).

Motor Task and Debriefing (Task 4).

Finally, participants took part in a motor task which consisted of performing a series of coordinated movements and jumps shown by a computer program on a fake force plate. The experimenter debriefed participants collectively when they had all completed phase 2 of the experiment (about one week after).

Analytical Strategy

Results

Data were analyzed with multiple regressions to test the main effects and interactions between the independent variables (self-handicapping tendency, self-esteem and condition) on the amount of handicaps reported. Before conducting the regression analyses, the dichotomized independent variable (ego-threatening condition) was transformed into contrast codes (low ego-threatening, -1; high ego-threatening, 1) and the continuous independent variables (self-handicapping tendency and selfesteem level) were centered. Furthermore, to better satisfy the conditions of the application of the linear model and the normality of residuals [START_REF] Mosteller | Data analysis and regressions: A second course in statistics[END_REF], the dependent variable (mean of disruption reported) was logarithmically transformed (i.e., log 10).

Because the results were quite similar while using the measures of physical and global self-esteem, only the results obtained with the physical self-esteem are presented here. The results obtained with the global self-esteem are summarized in footnotes (see footnote n°4).

With regard to sex differences, women reported lower physical self-esteem compared with men (t(101) = 6,14, p < .01). However, no sex effect was observed on claimed self-handicapping, thus the data from males and females were analyzed together.

Manipulation Checks and Control Measures.

Participants reported that a low physical or psychological state could decrease their performance on the test (mean above the midpoint of the five-point scale; M = 3.78; SD = 1.13). They also reported placing high importance on the possession of high physical abilities (M = 5.70; SD = .89). Cronbach's alpha of the three items used to assess this measure was rather low (α = .59). This could be explained by the fact that participants were recruited from a wide range of sports, each requiring very different physical qualities. Thus, depending on his/her sport, an individual may place varying levels of importance on possessing force, speed and/or coordination abilities.

Descriptive Statistics and Preliminary Analysis.

Claimed self-handicapping (assessed by the mean of disruption reported by participants) ranged from 1 to 5.60 (M = 2.77; SD = .97). The means of claimed self-handicapping tendency, physical self-esteem and global self-esteem were respectively 26.28 (SD = 11.13, range from 8 to 56; α = .91); 24.48 (SD = 5.53, range from 5 to 35; α = .75) and 35.83 (SD = 6.55, range from 7 to 49; α = .71). The scores of global and physical self-esteem were significantly correlated (r = .47; p < .05).

Preliminary analysis indicated that the scores of self-handicapping tendency and self-esteem level were not significantly correlated (r = .10 for global self-esteem; p > .05 and r = -.09 for physical self-esteem; p > .05) and that the groups of high and low self-handicappers did not differ in their level of self-esteem; t(99) = .26, ns, for physical self-esteem and t(99)=1.40, ns for global self-esteem. Preliminary analysis also revealed that the means of self-handicapping tendency, physical selfesteem and global self-esteem of participants in the low and the high ego-threatening conditions were not significantly different which suggests that the distribution of participants in each condition was successfully randomized; respectively t(101) = .68; p > .05; t(99) = .17; p > .05 and t(99) = .47; p > .05.

Claimed Handicaps as a Function of Self-Handicapping Tendency, Physical

Self-Esteem and Condition. All the effects (main and simple interaction) were significantly related to the mean of disruption reported by participants, F(5,95) = 16.63; R 2 adjusted = .44; p < .01. The condition (ß = .52), the self-handicapping tendency (ß = .19), their interaction (ß = -.20), the physical self-esteem (ß = -.21) and its interaction with the condition (ß = .20) significantly affected claimed handicaps (see Table 1). The three-way interaction (condition × self-handicapping tendency × physical self-esteem) that was not significant was removed from the model 4 .

In the low ego-threatening condition, high self-handicappers claimed more disruptions than low self-handicappers (respectively, M = 2.60 and M = 2.00; see Table 2) and low physical self-esteem participants claimed more disruptions than high physical self-esteem participants (respectively, M = 2.61 and M = 1.94; see Table 2). These results suggest that high self-handicappers and low physical selfesteem athletes do use claimed self-handicapping when they are faced with a low ego-threatening situation. In addition, both low self-handicappers and high self-esteem athletes claimed more handicaps in the high ego-threatening condition than in the low ego-threatening condition (respectively, M = 3.16 and M = 2.00 for the low self-handicappers) and (respectively, M 3.15 and M = 1.94 for the high self-esteem athletes). These results suggest that low self-handicappers and high self-esteem athletes do use claimed self-handicapping when they are confronted with a high ego-threatening situation.

Interestingly, the results also reveal that together, self-handicapping tendency, physical self-esteem and condition, better predict claimed handicaps (R 2 adjusted = .44) than self-handicapping tendency and condition alone (R 2 adjusted = .36). This increase of explained variance of the amount of disruption reported after the addition of physical self-esteem in the predictors was statistically significant, F(2,95) = 8.11; p < .01. In other words, self-handicapping tendency and physical self-esteem complement each other to predict athletes' claimed handicaps.

Discussion

The first objective of the present work was to determine whether athletes engage in claimed self-handicapping when they are faced with low ego-threatening situations. Our results revealed that, in the low ego-threatening condition, high selfhandicappers claimed more handicaps than low self-handicappers, and low selfesteem athletes claimed more handicaps than high self-esteem athletes. These data suggest that athletes with high self-handicapping tendency and/or low self-esteem do use claimed self-handicapping in some low ego-threatening situations 5 . Before discussing these results, it is worth noting that, consistent with previous claimed self-handicapping studies, the methodology we used does not prevent athletes from engaging in sandbagging strategies in addition to self-handicapping strategies. Sandbagging is a false claim or feigned demonstration of inability used to lower observers' expectations for one's performance (see [START_REF] Gibson | Sandbagging as a self-presentational strategy: Claiming to be less than you are[END_REF]. Thus, in the current study, athletes may have claimed handicaps, not only to have an anticipative excuse (claimed self-handicapping), but also to decrease observers' expectations regarding their performances (sandbagging).

The position defended and observed in the current study expands on the notion that self-handicapping strategies emerge to shape the implications of performance feedback [START_REF] Jones | Control of attributions about the self through self-handicapping strategies: The appeal of alcohol and the role of underachievement[END_REF][START_REF] Self | Situational influences on self-handicapping[END_REF]. We propose that self-handicapping strategies can emerge in situations with and without expected performance feedback. Indeed, in the current study some athletes engaged in claimed self-handicapping in the low ego-threatening condition, a condition without an evaluative component and in which they were clearly informed that they would not receive feedback.

Our results are consistent with the findings of previous research in which high self-handicappers students engaged in self-handicapping in a situations with low evaluative components [START_REF] Rhodewalt | Claimed self-handicaps and the self-handicappers: The relation of reduction in intended effort to performance[END_REF], studies 1 and 2) or in a noncompetitive task [START_REF] Deppe | Self-Handicapping and intrinsic motivation: Buffering intrinsic motivation from the threat of failure[END_REF]. Our findings, however, differ from these studies on three points. First, our results concern not only high self-handicappers but also low self-esteem participants. Second, our results focus on claimed self-handicapping. Third, we examined a different kind of population: Athletes. Further, the previous studies were not specifically designed to test the emergence of self-handicapping in low ego-threatening situations but rather to investigate the consequences of this strategy. Thus, the emergence of behavioral self-handicapping in low ego-threatening conditions was not hypothesized nor formally tested.

It is also necessary to point out that, consistent with previous work (DeGree & Snyder, 1985;[START_REF] Smith | The self-serving function of hypochondriacal complaints: Physical symptoms as self-handicapping strategies[END_REF][START_REF] Snyder | On the self-serving function of social anxiety: Shyness as a self-handicapping strategy[END_REF] our results suggest that claimed self-handicapping is more prevalent in high egothreatening situations than in low ego-threatening situations. Indeed, we observed a positive effect of ego-threat on the amount of handicaps reported by participants: high self-handicappers and low self-esteem athletes claimed more handicaps in the high than in the low ego-threatening condition. Despite the fact that claimed self-handicapping is more prevalent in high ego-threatening situations, its potential emergence in low ego-threatening situations should not be neglected. This is particularly noteworthy because athletes are routinely faced with low ego-threatening situations such as technical or tactical exercises during training. In addition, it was in the low ego-threatening condition that claimed self-handicapping was better predicted by self-handicapping tendency and self-esteem level. Indeed, while in the low ego-threatening condition, high self-handicappers claimed more handicaps than low self-handicappers, and low self-esteem athletes claimed more handicaps than high self-esteem athletes; in the high ego-threatening condition this difference disappeared. This finding is consistent with several studies in which the effects of self-handicapping tendency [START_REF] Rhodewalt | Self-handicapping among competitive athletes: The role of practice in self-esteem protection[END_REF] and selfesteem [START_REF] Ferrand | Relations between female students' personality traits and reported handicaps to rhythmic gymnastics performance[END_REF] on the amount of handicaps reported by participants in a high ego-threatening situation was not significant. This finding is also consistent with the position of [START_REF] Kimble | Self-focus, gender, and habitual self-handicapping: Do they make a difference in behavioral self-handicapping?[END_REF] that there are many situations in which a situational factor overrides individual differences in self-handicapping tendency and that it is necessary to use an interactionist approach to understand the conditions of emergence of self-handicapping strategies.

Further investigation should focus on determining why high self-handicappers and low self-esteem athletes engage in claimed self-handicapping in low egothreatening situations. One hypothesis is that they feel threatened by any motor task, even those without any salient evaluative component. We can indeed assume that high self-handicappers and low self-esteem athletes perceive threats in most sport situations because they believe that any situation could inform them (or others) on their physical abilities. When self-handicappers and low self-esteem individuals care a great deal about a domain, they could try to evaluate themselves, thus making any situations related to this domain high evaluative and high ego-threatening. It is also possible that, for high self-handicappers and low self-esteem athletes, simply anticipating a failure leads to feelings of threat, regardless of whether the situation is related to central components of the self. [START_REF] Rhodewalt | Claimed self-handicaps and the self-handicappers: The relation of reduction in intended effort to performance[END_REF] relied on this explanation when discussing why some students behaviorally self-handicapped in their low ego-threatening condition. This explanation could also be applied to low self-esteem athletes since low self-esteem individuals are particularly concerned about failure (for a review see [START_REF] Baumeister | Self-presentational motivations and personality differences in self-esteem[END_REF].

Another hypothesis that deserves further investigation is that these athletes did not feel threatened by the low ego-threatening condition but reported handicaps because they had incorporated these handicaps. Indeed, [START_REF] Snyder | From making to being the excuse: An analysis of deception and verbal/nonverbal issues[END_REF]p. 249) hypothesized that individuals who are regularly confronted with evaluative situations construct an always-available excuse ("incorporated excuse") they use in all situations. They explained that, unlike the anticipatory excuse which is strategically invoked before a probable bad performance, "the incorporated excuse is simply "there" and available for most failure experiences." We can imagine that high self-handicappers and/or low self-esteem athletes put forward handicaps whenever they are faced with motor tasks, even if they do not perceive them as threatening, because they have incorporated excuses.

To test these two main hypotheses (perception of threat in the low ego-threatening condition versus incorporated excuses) it would be necessary to investigate the threat that is experienced by participants who engage in claimed self-handicapping. This task is difficult and has not yet been attempted. New implicit measures such as the patterns of cardiovascular responses proposed by Blascovich and his colleagues (e.g., [START_REF] Blascovich | Challenge and threat appraisals: The role of affective cues[END_REF][START_REF] Blascovich | Predicting athletic performance from cardiovascular indexes of challenge and threat[END_REF] would provide a means of accomplishing this task. Their biopsychosocial model describes a method that used patterns of cardiovascular responses to accurately and implicitly estimate the threat that individuals experience.

The second objective of the current study was to test whether low self-handicappers and high self-esteem athletes do engage in claimed self-handicapping. Our results revealed that they did so in the high ego-threatening condition. To our knowledge, no study has provided evidence that low self-handicappers or high self-esteem individuals do engage in claimed self-handicapping. These findings are however consistent with those of [START_REF] Tice | Esteem protection or enhancement? Self-handicapping motives and attributions differ by trait self-esteem[END_REF] or [START_REF] Newman | When stakes are higher: Self-esteem instability and self-handicapping[END_REF] who observed that high self-esteem individuals engaged in behavioral self-handicapping (the other expression of self-handicapping) to enhance their image of intellectual ability. We believe that, in the same manner, high self-esteem athletes claim handicaps to enhance their image of physical abilities.

The present study suggests applications for coaches, sport psychologists or sport teachers. First, it reveals that claimed self-handicapping tendency and the self-esteem level accurately predict claimed self-handicapping emergence among athletes. The prediction is even more accurate when using these two variables together than when using either variable alone. Previous research has reached similar conclusions for claimed [START_REF] Finez | Comprendre et prédire les stratégies d'auto-handicap revendiqué dans le domaine du sport: une approche interactionniste[END_REF] or behavioral [START_REF] Richards | Predictive ability of self-handicapping and self-esteem in physical activity achievement context[END_REF] self-handicapping. As [START_REF] Finez | Comprendre et prédire les stratégies d'auto-handicap revendiqué dans le domaine du sport: une approche interactionniste[END_REF] proposed, self-esteem level may enable researchers and practitioners to estimate athletes' motivation to protect and/or enhance their self, while claimed self-handicapping tendency may enable researchers and practitioners to estimate the extent to which athletes are likely to engage in claimed self-handicapping to do so. In the present experiment, self-esteem and self-handicapping tendency appeared particularly pertinent to predict claimed self-handicapping in the low ego-threatening condition, where they explained together 33% of the amount of handicaps reported by athletes (or 30% with the measure of global self-esteem) 6 . Note that our groups of high and low self-handicappers were created by excluding participants whose scores were in the middle third of the distribution, thus the prediction might have been slightly lower if we had used a median split to create groups.

Further, our results suggest that coaches who plan to implement interventions to reduce claimed self-handicapping should consider all their athletes rather than focusing only on athletes identified as having a high propensity to engage in claimed self-handicapping and/or a low level of self-esteem. All athletes are susceptible to engage in this strategy, particularly when they participate in high ego-threatening tasks such as competitions or physical tests. In addition, coaches should be aware that some athletes, notably those with a high propensity to engage in claimed self-handicapping and/or those with a low self-esteem level, are susceptible to use this strategy in any kind of sport situation even those that lack a salient evaluative component, such as technical, tactical or physical conditioning training exercises. We also believe that these findings can be generalized to a population of students. Findings from the academic field are indeed generally consistent with those observed in the sport field (see e.g., [START_REF] Prapavessis | Self-presentational issues in competition and sport[END_REF]. Then, it seems likely that high and low self-handicappers as well as high and low self-esteem students do engage in claimed self-handicapping before their exams; and that high self-handicappers and low self-esteem students engage in this strategy, not only before their exams but also in non evaluative circumstances.

To prevent self-handicapping, coaches, psychologists and teachers can use different techniques (see e.g., [START_REF] Kuczka | Self-handicapping in competitive sport: Influence of the motivational climate, self-efficacy, and perceived importance[END_REF][START_REF] Siegel | Reducing the tendency to self-handicap: The effect of self-affirmation[END_REF]. For example, they can change the motivational climate of their group, focus athletes' attention away from the implication of performance, promote athletes' self-esteem or alter the specific responses athletes use to protect their self. However, these techniques are probably not suitable for all individuals in all situations and should be applied specifically to particular individuals in particular contexts. Thus, it is necessary to consider both the dispositional and situational determinants of claimed self-handicapping and apply techniques accordingly.

Notes

1. Theoretically, low ego-threatening situations (also called low ego-relevance, or non evaluative settings) refers to situations that do not assess central components of the self; whereas high ego-threatening situations refers to situations that assess relevant components of the self and that have an uncertain issue (e.g., [START_REF] Degree | Adler's psychology (of use) today: Personal history of traumatic life events as a self-handicapping strategy[END_REF][START_REF] Rhodewalt | Claimed self-handicaps and the self-handicappers: The relation of reduction in intended effort to performance[END_REF]. Then, competitions or physical tests which inform athletes on their physical abilities are generally considered as highly threatening for their self (e.g., [START_REF] Martin | Self-handicapping in physical achievement settings: The contributions of self-esteem and self-efficacy[END_REF], while sports situations without any salient evaluative components can be considered as minimally threatening.

2. If one excludes the participants who are in the middle third of the score distribution on the self-handicapping dimension, and excludes the participants who are in the middle third of the score distribution on the self-esteem dimension, one could potentially exclude approximately half of the participants of the study. Further, we preferred to exclude participants whose self-handicapping score was in the middle third of the distribution before phase 2 as opposed to after phase 2. We did this with the goal of reducing the number of participants that took part in phase 2.

3. In previous work, both, the FIS and the Rosenberg Self-esteem Scale (SES, 1965) have been used to predict self-handicapping (e.g., [START_REF] Newman | When stakes are higher: Self-esteem instability and self-handicapping[END_REF][START_REF] Prapavessis | Self-handicapping and self-esteem[END_REF]. We opted for the FIS because it is multidimensional, and it enabled us to assess both global and domain-specific self-esteem, such as physical self-esteem. 4. Quite similarly, the regression conducted while using the measure of global self-esteem reveals a significant effect of the condition (ß = .54), the self-handicapping tendency (ß = .25), the interaction between the condition and the self-handicapping tendency (ß = -.24), the global self-esteem (ß = -.26) and a marginal effect of the interaction between the condition and the global self-esteem (ß = .13; p = .09); F(5,95) = 16. 13; R 2 adjusted = .43; p < .01. The three-way interaction (condition x self-handicapping tendency x global self-esteem) was not significant. 5. Note that the similarity observed here between the results of high self-handicappers and the results of low self-esteem athletes cannot be due to the fact that high self-handicappers participants have a particularly low self-esteem level because the scores of self-handicapping and self-esteem were not correlated. The absence of correlation observed between the scores of the CSHS-S and the level of self-esteem is consistent with previous findings [START_REF] Finez | Comprendre et prédire les stratégies d'auto-handicap revendiqué dans le domaine du sport: une approche interactionniste[END_REF], studies 1 and 4) and coherent given that both low and high self-esteem individuals may engage in self-handicapping (see e.g., [START_REF] Newman | When stakes are higher: Self-esteem instability and self-handicapping[END_REF][START_REF] Tice | Esteem protection or enhancement? Self-handicapping motives and attributions differ by trait self-esteem[END_REF]. 6. Supplementary analyses led separately by conditions reveal a positive effect of selfhandicapping tendency and a negative effect of self-esteem in the low ego-threatening condition; F(2,48) = 13.01; R 2 adjusted = .33; p < .001 while using the measure of physical self-esteem; and F(2,48) = 11.94; R 2 adjusted =.30; p < .001 while using the measure of global self-esteem.

Table 1 Effect of Self-Handicapping Tendency, Physical Self- Esteem and Condition, on the Mean of Disruption Reported by Participants

 1

			Std.
	Variables	B	Error		t	p
	Intercept	.41	.01		34.20 < .001
	Condition	.08	.01	.52	6.90	< .001
	SH Tendency (SH)	< .01	< .01	.19	2.48	.015
	Condition × SH	< .01	< .01	-.20	-2.60	.011
	Physical Self-Esteem (PSE)	-.01	< .01	-.21	-2.71	.008
	Condition × PSE	.01	< .01	.20	2.66	.009

Note: Condition × SH = interaction between condition and self-handicapping tendency; Condition × PSE = interaction between condition and physical self-esteem.

Table 2 Means of Disruption Reported by Low and High Self- Handicappers, and Low and High Self-Esteem Athletes in Each Experimental Condition

 2

		Conditions
		Low	High
		Ego-Threatening	Ego-Threatening
	Low Self-Handicappers	2.00 (.72)	3.16 (.64)
	High Self-Handicappers	2.60 (.99)	3.21 (.71)
	Low Physical Self-Esteem Athletes	2.61 (.83)	3.19 (.67)
	High Physical Self-Esteem Athletes	1.94 (.90)	3.15 (.68)

Note. n = 24, 26 or 27 per cell. Numbers represent the means of disruption reported by participants. Numbers in parentheses represent the standard deviation of the mean of disruption reported.


Sylvain Saïghi
email: saighi@ixl.fr

Yannick Bornat

Jean Tomas

Sylvie Renaud

Neuromimetic ICs and System for Parameters Extraction in Biological Neuron Models

This paper presents an analog neuromimetic integrated circuit and an associated system dedicated for experiments of parameters extraction in biological neuron models. The IC based on Hodgkin-Huxley (HH) formalism computes in real-time and continuous mode. The dedicated system is a PCI board that is able to program dynamically the neuron model parameters in the IC. The full system, which includes the IC and the PCI board, is used to build a new hardware/software technique to extract biophysics parameters from biological neuron. This technique could be helpful for the neuroscientists proposing an alternative to voltage-clamp technique. For that, the new technique will use optimization algorithms to be efficient.

I. INTRODUCTION

Since the first silicon neuron from M. Mahowald and R. Douglas [START_REF] Mahowald | A silicon neuron[END_REF], research groups have designed and used analog integrated circuits to integrate neuromorphic systems. Among those neuromorphic items, we can isolate two groups. The first one consists in bio-inspired systems, designed to develop new solutions for engineering questions. The designers use biological principles to build new and more efficient systems about vision [START_REF] Boahen | A Retinomorphic Vision System[END_REF] [START_REF] Culurciello | A Biomorphic Digital Image Sensor[END_REF], attention [START_REF] Indiveri | Neuromorphic selective attention systems[END_REF] and learning [START_REF] Dioro | Adaptive CMOS: From Biological Inspiration to System-on-a-Chip[END_REF]. The second type are neuromimetic systems that use engineering means and tools; those systems are developed to address neurosciences questions, like the comprehension of central pattern generator [START_REF] Simoni | A Multiconductance Silicon Neuron With Biologically Matched Dynamics[END_REF], rhythmic motor control [START_REF] Calabrese | Half-Center Oscillators Underlying Rhythmic Movements[END_REF], learning [START_REF] Zou | Real-time simulations of networks of Hodgking-Huxley neurons using analog circuits[END_REF] or vision processing [START_REF] Delbrück | A silicon early visual system as a model animal[END_REF].

Neuromimetic systems can also be helpful tools for neurophysiology experiments. For example, to specify a biological neuron, neuroscientists use the voltage-clamp technique [START_REF] Hodgkin | Ionic currents underlyong activity in the giant axon of the squid[END_REF]. This is a long process, where the in-vitro cell activity is measured in a way that it fits one by one ionic channel while measuring the cell surface area and the membrane capacitance. Another technique is to use optimization algorithms to identify the electrical behavior of the observed cell to a mathematical model. When the neuron model is based on the Hodgkin-Huxley formalism, as many as fifteen parameter values have to be fitted for a simple three conductances neuron. If optimization algorithms are computed using a software solution, the computation power of the system [START_REF] Masson | Stabilité fonctionnelle des réseaux de neurones: Etude expérimentale et théorique dans le cas d'un réseau simple[END_REF] becomes quickly a key issue when handling so many parameters. Hardware computation using VLSI ASICs is a solution in such a case. We have already designed analog neuromimetic integrated circuits based on Hodgkin-Huxley formalism, including the description of calcium-dependent channels [START_REF] Saïghi | A Neuromimetic Integrated Circuit for Interactive Real-Time Simulation[END_REF]. One of the last neuromimetic integrated circuit (IC) that we have designed is a mixed analog-digital chip. Its main features are: it simulates in biological real-time the neuron activity (membrane potential); it is able to process models with onchip dynamically programmable parameters. The ICs are hosted in a custom system, and communicate via a PCI interface with user interface software that controls the neuron models parameters and the simulation progress [START_REF] Saïghi | A Conductance-Based Silicon Neuron with Dynamically Tunable Model Parameters[END_REF]. In such a system, where the neural activity is computed by dedicated ICs, the host computer is available during the simulation for calculating optimization algorithms.

We will present in this paper the design of analog neuromimetic ICs; results will be shown where analog IC neurons achieve neural simulations in biological real-time but also faster than the biological real-time. This configuration will increase the efficiency of our hardware/software system when identifying a biological neuron. We will end up by the presentation of the complete system developed to process the optimization technique.

II. THE MODEL IMPLEMENTATION

A. The Hodgkin-Huxley formalism

To design neuromimetic IC (in contrast to bio-inspired IC), we chose the Hodgkin-Huxley formalism. The main advantage of this formalism is that it relies on parameters, which are biophysically realistic, by the way of a conductance-based expression of the neural activity (see detailed description of the Hodgkin-Huxley formalism in [START_REF] Hodgkin | A quantitative description of membrane current and its appication to conduction and excitation in nerve[END_REF]). We will express here the conductance-based principle and find out generic expressions for these conductance phenomena.

The Hodgkin-Huxley formalism provides a set of equations and an electrical equivalent circuit (Fig. 1) that describe the behavior of separate conductances. Each conductance represents the dynamics of an ionic specie (sodium, potassium or calcium) flowing through the neural membrane. All these ionic currents are integrated on the membrane capacitance following the electrical equation ( 1),

C mem . dV mem / dt = -Σ I ion + I s (1)
where V mem is the membrane potential, C mem the membrane capacitance and Is an eventual stimulation or synaptic current. The generic mathematical expression (2) for each ionic current is:

Ι ion = g max . m p . h q . (V mem -V equi ) (2)
where g max is the maximal conductance value, m and h are respectively the activation and inactivation function and V equi the ion-specific reverse potential. We will for our implementation integrate current generators that follow expression [START_REF] Boahen | A Retinomorphic Vision System[END_REF]. Synaptic current are based on similar conductance-based model.

B. The implemented analog computation core

Figure 2 describes the organization of the integrated IC gathering ionic current generators as described earlier. To cover the widest possible range of models, while limiting the design complexity, we retained five channel types: leakage, sodium, potassium, calcium and calcium-dependent potassium. A neuron model will be possibly described by any combination of these channel types; associated to the chosen set of conductances, 8 input synapses and one stimulation current generator. The analog computation core is configurable through two internal buses. The first one, which is analog, defines the parameter values in the mathematical expression given in [START_REF] Boahen | A Retinomorphic Vision System[END_REF]. The second one is a digital bus used to specify which ionic current generators are active for the simulation. The membrane voltage (via the "Vmem buffered" output) and any ionic current generator switched to the "Display output" can be displayed in real time on an oscilloscope.

III. FROM ANALOG COMPUTATION CORE TO SYSTEM

A. Design principle

We integrated a circuit including two analog computation cores (Fig. 3). The 158 analog parameters that are necessary for the 2 analog cores are stored on-chip, using dynamic analog memories, based on integrated capacitors. The memory cells array receives data from an external ADC, which sequentially refreshes the analog parameters values. This technique allows external modifications of one or more parameters, even during the running of the simulation. Due to internal protocol, one modification necessitates three refreshing cycles (≤ 5 ms), which is compatible with the V mem dynamics in biological real time. To program the parameter memories we use a 3 bits bus (Clock, Reset and Data) and an analog bus (Parameter values). The experimenter chooses a topology before the simulation starts, to define which channels are activated to compute the electrical activity. This topology is stored on built-in dynamic digital memories and programmed by another 3 bits bus (Clock, Reset and Data).

B. The Chip Pamina

The chip was designed in full-custom mode with a BiCMOS SiGe 0.35µm technology process from austriamicrosystems (AMS) under Cadence environment. Figure 4 is a microphotograph of the ASIC called Pamina. The ionic current generators have been designed in current mode [START_REF] Toumazou | Analogue IC Design: the current mode approach[END_REF], which means that the internal variables in the model expressions are physically represented by currents. Topology and analog memory cells can also be identified on the figure. Pamina contains around 19,000 MOS transistors,

C. The system

A complete computer-based system was built to exploit the designed ASICs (see Fig. 5). The experimenter defines the neurons model parameters, using interface software. Theses characteristics include the ionic channels choice between sodium, potassium, leakage, calcium and calciumdependent potassium and the parameters values for each channel. These data are sent to the IC through the analog and digital buses described in the previous paragraph. The analog computation core simulates in real-time the membrane potential, which is digitized through an analog digital converter and sent to the computer for display, storage or further processing.

IV. TOWARDS OPTIMIZATION TECHNIQUE

With the neuromimetic IC called Pamina and the communication via PCI-bus with the host computer, we have all components to build a system to determine the set of parameters from a biological neuron, as mentioned in the introduction paragraph.

The parameters extraction by optimization algorithms necessitates to minimize an error function between a reference activity and a current activity. More specifically, this error function compares two membrane potentials, one measured from a biological cell (the reference), and the other from the simulation (the model which parameters are examined). Optimization algorithms do the error function minimization. An error function in temporal domain would have to deal with the arbitrary phase difference that exists between the 2 signals. Synchronizing the reference and simulated activity by adjusting for example the stimulations is not a simple case. We chose to define an error function that compares the membrane potentials evolution in time rather than their static values. Considering the definition of the mathematical expression (1) and ( 2) for the membrane potentials, we will calculate the phase diagram (3), which specifies the membrane voltage activity on a single period, regardless of the absolute phase. This approach is possible only because we consider periodic activities.

dV mem / dt = f(V mem ) (3)
Figure 6 illustrates plots such a phase diagram in the case of a three conductances neuron model [START_REF] Connors | Intrinsic firing patterns of diverse neocortical neurons[END_REF]. We plot the phase diagram of the reference activity and the simulated activity, which simulates a set of parameters arbitrary chosen. In that demonstration case, the reference activity is from an already known model card, obtained from voltageclamp experiments, and is software simulated. This plot points out the difference between the two electrical activities, and the "error" is clearly visible. This means that the IC parameters are not well tuned to fit the reference model. The optimization technique will minimize the error function to obtain closer trajectories in the phase diagram. The error function definition and the optimization algorithms choice are discussed in [START_REF] Le Masson | Introduction to Eqaution Solving arameter Fiting[END_REF].

The main advantages of this technique are that it helps reducing neurophysiology experiments, while giving the opportunity to explore systematically the parameters space of the studied model. With this technique, the neuroscientists need to measure only the membrane voltage, which is easier than the ionic channels dynamic with the voltage-clamp technique. The set of parameters exploration will give to the neuroscientists the mathematically possible solutions (possibly more than one). Neuroscientists will then retain the most realistic model card.

V. THE COMPUTATION SPEED

The analog neuromimetic IC present a great advantage over the digital implementations: we can increase the computational speed, and run simulations at a fixed time scale that will be more than the biological real-time. Looking at expression (1), if we arbitrarily divide the membrane capacitor value by a α term, and divide all the kinetics of the activation and inactivation variables by the same α term, we immediately divide the simulation time by the α term (t in the expression is replaced by t/α). We show in fig. 7 test measurements on the ASIC Pamina in the cases α = 1, 10 and 100. Each simulation is drawn with its own time scale t/α. This property is limited by the circuit electronic performances, as it was not designed to process higher kinetics than the real-time ones. When α = 10, the action potential shape is almost identical to the reference one (α = 1), and the activity frequency slightly increases. When α = 100, we can observe noise during the depolarizing phase of the spike, before the action potential. These results show us that, although the IC Pamina was not designed for increasing the computation speed, we can find an optimum factor to speed up the simulation while keeping an activity identical to the reference one. Applying that property to the software/hardware optimization technique will reduce the simulation time; this can be a key issue when exploring large set of parameters in the Hodgkin-Huxley models.

VI. CONCLUSION

We presented in this paper a custom experimental setup, which includes analog neuromimetic IC modeling the Hodgkin-Huxley formalism, and a PCI interface to dynamically control the IC. The proposed hardware/software technique using this system is an alternative to voltage-clamp experiments for parameters extraction in biological neuron models. We demonstrated that the analog neuromimetic IC can compute neural activity faster than biological time. Additional results including the software implementation of optimization algorithms implementation will be presented during the conference.

Fig. 3 :

 3 Fig. 1: Neuron electrical equivalent circuit

Fig. 4 :Fig. 5 :Fig. 6 :

 456 Fig. 4: Microphotograph of the chip Pamina

Fig. 7 :

 7 Fig. 7: IC simulation speed increasing for a 3-conductances neuron model

ACKNOWLEDGMENT

The authors thank Pr. G. Le Masson (INSERM E 358 -France) for his help on model specifications. This work was supported by E.U. Grant SenseMaker (IST-2001-34712) and E.U. Grant NeuroBit (IST-2001-33564).