List of Figures

List of Tables

Context

The safety of French nuclear reactors is based essentially on a deterministic approach. Probabilistic safety assessment (PSA) supplement the conventional deterministic analyses. A PSA is a systematic and comprehensive methodology to evaluate risks associated with a complex engineering technology entity (such as airlines or a nuclear power plant). It provides an overall view of safety including both equipment and operators behavior. The development of PSA consist of:

 Identifying accidental scenarios leading to undesired consequences  Assessing these scenarios in terms of frequency

In the year 1995 NRC has recommended in its final policy statement to increase the use of PSA in nuclear regulatory activities to the extent supported by the state of the art [START_REF]Use of probabilistc Risk Assessment Methods in Nucear Regulatory Activities[END_REF]. The current PSA models for plants in operation are built to estimate the risk for unit. The initiating events in PSA models may be classified in different hazard groups:  So-called internal events.  Internal hazards (fire, internal flooding).  External hazards (external flood, earthquake, strong winds, etc.).

PSA model was developed over many years for internal events, but specific models have recently been developed for each hazard. The level of conservatism of the models is based on the origin of the initiating events. In particular, for external hazards, due to the lack of data (testing, physical models, etc.) conservative assumptions can be made regarding the impact of the hazards on the installation. The fact that the development of PSA it became a point of interest comes from the importance of these aspects in risk-informed decision making process.

"There is too much focus on the letter P 1 in the PSA". It has been said once that in PSA we tend to focus only on the probability and the consequences, and we ignore a lot of other important factors that plays a big role in the total risk and risk analysis process. Actually a lot of researches proved that there are a lot of other factors beside the risk (probability × consequences) that might affect the result of total risk aggregation. Through the operation of US nuclear power plant, fire has been considered as a great contributor of the total risk, which might be due to the importance of the fire risk or/and due to that it is characterized as immature and less realistic compared to some other initiating events; such as the internal events. As it is indicated in one of NRC"s technical reports that was published earlier this year (2015) about the maturity of fire analysis, the fire analysis might be conservative compared to other hazards [START_REF] (n.D | FIRE PRA MATURITY AND REALISM: A DISCUSSION AND SUGGESTIONS FOR IMPROVEMENT[END_REF]. It is illustrated using the radar charts in Figure 2 that represents CDF (core damage frequency) [START_REF]NUREG-1855 (Guidance on the Treatment of Uncertainties Associated with PRAs in Risk-Informed Decision Making)[END_REF].

In the other hand there are many other key aspects that it is believed to influence the risk informed decision making process, such as the interpretation of uncertainty 1 Here P stands for probability Actually understand these aspects and their impact on PSA (probabilistic safety analysis), and providing a pragmatic approach of addressing these aspects is a critical point in development of the risk-informed decision making process [START_REF]EPRI Technical Update, Practical Guidance on the Use of Probabilistic Risk Assessment in Risk-Informed Applications with a Focus on the treatment of Uncertanity[END_REF], [START_REF]Addressing multi-hazards risk aggregation for nuclear power plants through response surface and risk visualization[END_REF]. Similarly, for the evaluation of the frequency of these hazard, studied at extreme levels of intensity, it is often difficult to establish a result in which we can have a great confidence.

Figure 2

Risk informed decision making process, factors influencing decision making, and RIDM weaknesses

Definition of the Problem

In order to make decision we need to have a global comprehensive view of the risk, for example when we have to assess the benefits of a specific modification of the plant (ex: after Fukushima"s accident design modifications as shown in Figure 3). The risk might be evaluated taking into account the different origins and natures of the hazard groups; the following figure illustrates the different contributions of the different hazard groups before and after the modifications. Risk Informed Decision making (RDIM) was defined by NASA in risk informed decision making handbook [START_REF]NASA Risk-Informed Decision MakingHnadbook[END_REF], as being "a deliberative process that uses a diverse set of performance measures, along with other considerations, to inform decision making. The RIDM process acknowledges the role that human judgment plays in decisions, and that technical information cannot be the sole basis for decision making. This is not only because of inevitable gaps in the technical information, but also because decision making is an inherently subjective, valuesbased enterprise. In the face of complex decision making involving multiple competing objectives, the cumulative wisdom provided by experienced personnel is essential for integrating technical and nontechnical factors to produce sound decisions."

In Figure 4 which was taken from (NASA Risk-Informed Decision MakingHnadbook, 2010) the part deliberation is referred to as the communication gate between different parties and stages including the risk analysis and the decision making. Actually it is necessary to ensure the completeness, integrity, and comprehension of the information that is needed to be delivered and interpreted into a decision [START_REF]NASA Risk-Informed Decision MakingHnadbook[END_REF]. Aven also referred to the risk analysis as a decision supporting tool in which by, the decision maker should be able to balance the cost and the risk [START_REF]On the use of risk and decision analysis to support decision making[END_REF].

We agree that the risk analysis is part and parcel of decision making process, and that the analyst should understand the context of decision making, but still at the current stage we believe that the way we are using the risk analysis result in decision making is not enough, due to the different types of knowledge of those two processes, where one of them might be on the level of the implicit knowledge and the other is on the level of explicit knowledge that cannot be directly connected. So in order to make the right decision we need to know the risk, understand it, and of course to be able to acknowledge it in order to help the decision maker to comprehend it [START_REF]On how to Understand and acknowledge risk[END_REF]. In a philosophic way we can say that both decision maker and analysts speak a slightly different technical languages, because the decision maker decision is based more on the experience, sense, and wisdom even though that he uses the result of the analyst to make his decision. In the other hand the analysts rely more on data, facts, and numbers, which create a kind of technical gap between both of the analyst and the decision maker. It might be a real misleading issue for taking the right decision. The question is: are we able to translate the implicit knowledge into an explicit one, in order to come out with a new simplified technical language that is spoken by both parties?

In risk-informed decision making, risk aggregation is required to give an overall characterization of the risk, by combining different information on the risk from different contributors. The traditional approach of MHRA (multi hazard risk aggregation), which consists in simply summing risks from different hazard groups (risk contributors) as illustrated in Figure 5, in order to come out with a final metric that should be used in order to evaluate the acceptance of the risk. This is not mathematically consistent nor physically meaningful, because of highly heterogeneous levels of parameter uncertainties, uncertainties for initiating event frequencies, modeling details and approximations, conservatisms in PSA models, and etc. Another problem arises from the fact that the classical approach does not address the issue of the potential interactions between risk factors that might increase the overall risk, and that some of PRA"s methods are more conservative than the others, as well as that there are different natures of risks. The normal summation of the risk is going to give a mathematical result, but it won"t give a physical meaning which might be sometimes meaningless and misleading [START_REF]Addressing multi-hazards risk aggregation for nuclear power plants through response surface and risk visualization[END_REF], [START_REF]An Approach to Risk Aggregation for RisK-Informed Decision-Making[END_REF]. As it is explained before, this issue becomes a real concern when the results of PRA is to be used in risk informed decision making, due to the different levels of PSA"s maturity [START_REF]Addressing multi-hazards risk aggregation for nuclear power plants through response surface and risk visualization[END_REF], [START_REF]An Approach to Risk Aggregation for RisK-Informed Decision-Making[END_REF].

Existing Methods and Drawbacks

The aggregation of risks is defined in the EPRI document ( [START_REF]An Approach to Risk Aggregation for RisK-Informed Decision-Making[END_REF], EPRI Technical Update, 2014) as a process that combines the information on the risk from different contributors in order to characterize risk and inform a decision. Given that in most of the "risk Informed" applications, it is necessary to compare a particular metric (e.g core damage frequency, large early release frequency, risk increase, etc.) to a threshold value or goal (e.g. RG 1.174 [START_REF] (n.D | FIRE PRA MATURITY AND REALISM: A DISCUSSION AND SUGGESTIONS FOR IMPROVEMENT[END_REF]), it is really tempting to do this aggregation through a "simple summation" of the different contributions to the metric studied. This summation may however present difficulties in terms of interpretation of the results, given the current limitations of PSA including hazards. The EPRI document (an Approach to Risk Aggregation for Risk-Informed Decision-Making) firstly explains the reasons why a direct summation can be dangerous in terms of decision making, and proposes an approach to overcome these difficulties within the RG.1174 context [START_REF] (n.D | FIRE PRA MATURITY AND REALISM: A DISCUSSION AND SUGGESTIONS FOR IMPROVEMENT[END_REF]. Actually, in an application informed risk decisions should be made by integrating several components. Figure 6 below summarizes the aspects to be taken into account. This decision making context is taken from the RG 1.174 [START_REF] (n.D | FIRE PRA MATURITY AND REALISM: A DISCUSSION AND SUGGESTIONS FOR IMPROVEMENT[END_REF]. However it is noted that the INSAG 25 of IAEA [START_REF]NUREG-1855 (Guidance on the Treatment of Uncertainties Associated with PRAs in Risk-Informed Decision Making)[END_REF], offers the same type of approach. The use of quantitative result of PSA is clearly presented but is only one factor that enlightens the decision. However, it must include the uncertainty analysis that affect quantitative results ( [START_REF]An Approach to Risk Aggregation for RisK-Informed Decision-Making[END_REF], EPRI Technical Update, 2014).

The approach proposed by EPRI can be summed up as in the following flowcharts (Figure 7, Figure 9, and Figure 8).

Task 2 aims to identify the main contributors to the baseline risk. Then, the analyst "disaggregates" the base model to establish how much credibility or confidence there is in the assessment. Important contributors should be reviewed in order to clearly understand the implications of departures from realism included in the PRA model. Figure 9 outlines the basic process. Figure 8 shows how to apply these tasks in the context of a risk-informed application that requires the evaluation of a risk metric, such as CDF or ΔCDF, by aggregating the results from PRAs for a number of different hazard groups. The EPRI document ( [START_REF]An Approach to Risk Aggregation for RisK-Informed Decision-Making[END_REF], EPRI Technical Update, 2014) gives a good industrial view of the problem and propose an approach that fits very well to the "Risk Informed" philosophy. However, this document does not provide guidance on how the level of realism of a PSA model can be measured (see the marked area in the Figure 9). Moreover, the presentation of the results of the assessment seems to be proposed without any reference to the decision making process. An illustration of possible tools to be used to implement the process presented in Figure 8, is given in the document (Addressing multi-hazards risk aggregation for nuclear power plants). This document proposes a new consistent approach to the quantifiable aspects of MHRA with a focus on relative rather than absolute risk metrics, using response surfaces based on arbitrary polynomial chaos expansion in combination with radar chart visualization of overall risk and associated uncertainties. Using the response surface, we can identify major contributors to overall plant risk, both on individual and aggregate bases, as well as cliff edge regions. While using arbitrary polynomial chaos (aPC). This method provides the mathematical tool to enable the investigations of MHRA, and it is capable of handling models with a very large number of input parameters (aPC feature), and any form of probability distribution, only knowing low-order statistical moments of these distributions. In other language, this method relies on quantifying the response surface rather than the complex original model itself. Radar charts provide the analysis and communication tool to represent the multi-dimensional elements of the optimization process. Using the radar chart visualization tool, contributors of many different natures to selected metrics, are readily compared to regulatory safety guidelines. Ultimately, plant PSA models, response surfaces and radar charts can be combined into an iterative process (see Figure 10), to support the process related to aggregate riskinformed decision making. The iterative process using together PSA, RSM and radar charts is proposed as a process to aggregate the results from different hazard groups. But actually, the use of RSM only does not really allow to identify all the significant contributors. It does not take into account the "hidden" uncertainties which lie, for example, in the assumptions we make when we lack of knowledge. And radar charts do not really allow the aggregation of the hazards from different hazard groups. They only make decision makers able to compare the relative result of each hazard group (associated with its uncertainty) to a given threshold. There is an implicit rule for decision making with this type of representation which may not be applicable in every application.

Goal of the research

Figure 11 gives a brief illustration of the main goal and its benefits, where we are seeking to introduce a way and creating a comprehensive model that represents the communication gate in the figure below, which is able to assess the level of heterogeneity of risk assessment for each hazard group (given the lego consisting parts of the final metrics, the uncertainty, the available knowledge, the model and methods used, etc.), which should give a sense of realism of the risk prediction, and to be easily understandable and accessible by the decision makers, in order to help improving the decision making process. In other language we should create a common frame for both the analysts and the decision maker that covers the risk and guarantees the proper decision, which should lead to safer practice of the technology.

Figure 11

Risk informed decision making process with and without level of maturity model.

First developments

As we explained before, our goal is to create a model that should cover all the drawbacks of the usual techniques that is used for risk aggregation in risk-informed decision making, in which it is able to unify all the bases of different hazard group, and overcome the heterogeneity whenever we proceed to make the aggregation, as well as building a common base which is understood by both the analysts and the decision maker. Actually we thought about introducing what we call the level of maturity, which can be defined as the level of analysis, knowledge, capability and trustworthiness of the model taking into account different elements that assess the reliability of the model and its capability of prediction; in other words the assessment of how much we can trust our model and analysis. Actually a similar idea was introduced and explained in a paper regarding the predictive capability maturity model for computational modeling and simulation [START_REF]Predictive Capability Maturity Model for Computational Modeling and Simulation[END_REF], which aims to cover the following:

 The model should be able to assess the usefulness of the analysis in order to better inform and improve decision making  It should help in increasing the adequacy of prediction to meet accuracy requirement for system response of interest.

In this model they have addressed six different criteria (contributors) to the level of maturity, where from their point of view they believe that those different criteria affects the level of maturity of the model, as illustrated in Table 1.

̂[ ∑ ], (1)
In this way a set of three scores are computed and presented to the user (decision maker). It represents the minimum, the average, and the maximum of the aggregation of the elements. An example that was presented by the same paper:

[ ] [ ] [ ] [ ] (2)
And using equations 1 and 2 they computed the PCMM aggregate triple:

̂[ ] (3)
In a similar way we are thinking about looking for the different criteria that we believe they can affect the level of maturity. The idea comprises of finding these criteria and giving a score for each depending on previous definition and classification, and then aggregation of the scores according to a mathematical model that we choose similarly to what was shown before in the PCMM model, to come out with a final result that represents a score of the level of maturity. This level of maturity must help the decision maker or the analyst to understand what should be the next step, whether through doing further analysis if needed, or through taking the decision relying on these data. The maturity model can be aggregated in different methods, one of them is the suggested previous method to give triple results. Another method suggests the direct aggregation of each score from each criteria of each hazard group, similarly to what mentioned before but giving an average or a final summation of scores, which represents a level of satisfactory in terms of level of maturity. Each element (criteria) is to be given a specific score for each system in the hazard group, which results in a total sub-maturity model that can be aggregated of different hazard groups.

∑ ∑ (4) Or using the average aggregation method:

∑ ∑ (5)
Where : is the level of maturity of each hazard group, represent different criteria for different systems within each hazard group Furthermore the total level of maturity of the total analysis can be obtained by summing the different sub-maturity of each hazard group as illustrated in the following. ∑

Or using the average aggregation method: ∑

The problem with this type of aggregation that it might be misleading for the decision maker in some cases if it is needed to know the causes of low level of maturity. A better way is to represent this kind of aggregation in matrices, and representing a final matrix of maturity that represents the scores of each criteria as illustrated in equation 6, which could be better informing for the decision maker, or it could be achieved by making the aggregation while keeping a symbol referring to each criteria as illustrated in equations 9 and 10.

∑ [ ] ( [ ] ) ( [ ] ) (8) ∑ ∑ (9)
And in vectors:

(10) Or using the average aggregation method:

∑ ∑ (11)
Where represents the scores in numbers and represents the criteria in symbols which helps the analyst in reviewing the analysis easily, as well as giving the decision maker the indication of the real meaning of the final score. This method is based on similar ideas of MCDM (multiple criteria decision making) methodologies, where in MCDM methodology you need to measure and rate different options regarding a number of different criteria in order to compare them. Actually this method can be really very helpful in decision making process, where it can be used to rank different decision regarding the different criteria that have been set by both the decision maker and the analyst. This leads us to think about some tools such as ELECTRE TRI. ELECTRE TRI approach is concerned by multiple criteria decision making problems that are designed to address different problem sorting and segmentation, by assigning categories to pre-defined categories (criteria) [START_REF]A user-oriented implementation of the ELECTRE-TRI method integrating preference elicitation support[END_REF]. Actually our future goal is to try to connect and integrate both the Maturity model approach and ELECTRE TRI approach into a comprehensive new methodology in order to enhance the decision making process.

So now and in order to judge the trustworthiness and the sensitivity of our analysis and as illustrated before, we should take into account different perspectives and approaches (criteria and element) that we believe it influences the risks aggregation"s result a great deal. Some of these criteria that affect the trustworthiness and what we call the maturity level of the model are: the degree of our knowledge about this specific problem and model, the degree to which the models are being extrapolated from the real case to the condition of the application of interest; approximations made by the model and on the model, degree of precision and accuracy of our analysis, the degree to which we perform the analysis, and many other factors and criteria that will be illustrated in the following section. Terje Aven pointed to the importance of some criteria and their link with risk in his article "conceptual framework for linking risk and the elements of the data-information-knowledgewisdom (DIKW) hierarchy" [START_REF]A conceptual framework for linking risk and the elements of the datainformation-knowledge-wisdom (DIKW) hierarchy[END_REF], where he discussed how the risk is (which calculated only by multiplying the consequences by the frequency of occurrence) and those perspectives are linked to the knowledge and its different features. Other points might be of interest in evaluating the risk analysis models and their capability of predication through different metrics for evaluation of prognostic performance [START_REF]Metrics for Offline Evaluation of Prognostic Performance[END_REF]. Based on different papers, we listed the model"s elements that we believe it influences a lot the result as the following:

1. Certainty: it refers to the knowledge perfection, where through this criteria we should able to give a score regarding the uncertainty analysis that might be done quantitatively at the beginning and then qualitatively by giving it a rank or a score.

2. Level of importance of each consisting element of the hazard group: the importance analysis of the system"s components, such as the importance analysis that is related reliability and availability requirements; ex: Birnbaum importance measures, and Fussell-Vesely importance measures [START_REF]Computational Methods for Reliability and Risk Analysis[END_REF].

3. Level of conservatism in the analysis: this criterion is a measure of the tendency of caution during the risk analysis that arises from concerns regarding the lack of data and knowledge about the nature and magnitude of the hazard.

4. The sensitivity of the analysis: sensitivity analysis is generally used to determine how a dependent variable can be changed and affected by the change of the input independent variable. This criterion is a measure of how the uncertainty in the output of a model can be affected or propagated regarding different sources of uncertainty in the input [START_REF]Global Sensitivity Analysis[END_REF].This analysis can be done using response surface and cliff edges analysis [START_REF]Addressing multi-hazards risk aggregation for nuclear power plants through response surface and risk visualization[END_REF].

5. Dependency: it is a rank of the dependency of one criterion on the other.

6. The type (criteria) and the level of trustworthiness in the analysis tool: it gives a score regarding the suitability of a specific model or risk analysis tool in a specific problem, and the previous feedback of the trustworthiness of this tool.

7. The state of knowledge regarding each specific hazard group, (can refer to the previous experience and our knowledge regarding a specific subject)

8. The level of analysis: ranking of the level of the details that are taken into account during the analysis. 9. Other algorithmic prognostics prediction assessment features (Accuracy and Precision): it measures and ranks the quality of data, and the characteristic of features.

Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model.

Actually Figure 12 sums up the total work that has been done so far, where it is seen that usually in order to make a decision or to assess the benefits of a specific modification of the plant a final change on the metric is studied (such as metric). The total metric or the total change on the metric is calculated with the assumption of different scenarios which leads the decision maker to make a specific decision regarding the final metric score. Actually the problem becomes more complicated and challenging regarding the risk informed decision making when the analyst needs to aggregate the total risk from different hazard groups, which is usually the case.

As the risk aggregation is needed to compare the final metric to a specific threshold value, the risk analysts usually do that using a simple summation which in the other hand presents difficulties in terms of interpretation of the results, given the current limitations of PSA including hazards. The figure above illustrates that using the level of maturity model the analysis should be better informing for the decision maker, as well as creating a proper communication gate between the decision makers and the analysts.

Criteria (elements) Definition and Scaling

Definition and scaling of the model"s criteria, as well as establishing a guide for the analysts and the decision makers are essential to allows them to understand what are those criteria, how to give the scores for the different hazard groups, what is needed during the model building, and even during decision making process. Such a mission requires giving first definition and scaling with the help of the experts, and to benefit from their experience and common of sense regarding the different important details of the assessment that was developed during their work practice. Obtaining complete, accurate, and comprehensive definitions requires as well giving feedback during the primary test of the model on some examples, regarding the problem and the challenges that faces the analysts while giving the scores from the point of view of the precision of the definition.

As a first step the following points should be considered before giving the definitions:

1. The score is given quantitatively or qualitatively.

2. Scores are giving relative to each other.

It is suggested to give different relative scores for each one of these elements (ex; scores 1-5 for the uncertainty, depending on the level of the uncertainty), by giving a relative definition and description for each level and score

Rough classification of the levels of the model's elements

At the current moment we are going to give a brief rough classifications of each element of the maturity model, taking into account that these classification might vary from problem to another. Actually a good classification of each of these elements needs a deep study of these elements generally and the problem itself. Later on we will try to choose the best classification of the scores of each of these elements, making sure that no important information would be lost between these giving scores.

So as a starting point we choose to focus on 3 different elements (criteria) which are the knowledge, the level of conservatism, and the uncertainty. As a first step working on these 3 different elements, and relying on previous scaling and definition of these criteria we tried to give a clear definition and description for each element as it is illustrated in the following section, in order to help the analyst to in evaluating each level.

a. The uncertainty is defined by US EPA [START_REF]Draft Hazardous Waste Combustion Protocols -Risk Characterization[END_REF] as "the imperfect knowledge of the true value of a particular variable, or its real variability in an individual or a group". The uncertainty can be classified into different levels relatively, depending on the degree of knowledge perfection. What distinguishes the uncertainty in particular that it can be analyzed using different models, and obtain a final mathematical results that is sensed more easily due to its explicit nature, which can make the mission even easier when it is required to give a relative qualitative score of the degree of uncertainty.

Actually Hauke Riesch discussed the uncertainty level in one of the books regarding risk theories [START_REF]Essentials of Risk Theory[END_REF], where he gave a different scales for the uncertainty through a general definition of these levels as the following|:

 Level 1 of uncertainty (level 5 of certainty): Uncertainty about the outcome, where the model is known, the parameters are known, and it predicts a certain outcome with a probability P. (The traditional mathematical and philosophical problems of probability theory are most concerned with level 1.

 Level 2 of uncertainty (level 4 of certainty): Uncertainty about the parameters, where the model is known, but its parameters are not known, once the parameters fixed then model predicts an outcome with parameters with probability P. (lack of empirical information, (ex. large break in primary circuit which has never happened).

 Level 3 of uncertainty (level 3 of certainty): Uncertainty about the model, where there are several models to choose from, and we have an idea of how likely each competing model is to reflect reality. (which model is more suitable for our problem)

 Level 4 of uncertainty (level 2 of certainty): Uncertainty about acknowledged inadequacies and our implicitly made assumptions. Unmolded uncertainty, and their estimation of their uncertainty will be different according to background knowledge and assumptions.

 Level 5 of uncertainty (level 1 of certainty): Uncertainty about unknown inadequacies and it is corresponding to unforeseen events, non-modeled and nonmodable risks. In other language it is the uncertainty when we do not even know what we don"t know (unknown unknowns).These limitations could arise because some aspects that we know of have been omitted, or because of extrapolations from data or limitations in the computations, or a host of other possible reasons. A slightly more formal way of responding to unforeseen events is the introduction of ""fudge factors,"" b. Knowledge: refers to the amount and the type of data, the suitability and the applicability of this data corresponding to the problem, the ability to apply and utilize these data, the sources and the origins of these data and its relation with the suitability and trustworthy, the type of models used to obtain or use these data, the cognition regarding the type of the technology and each specific system, the experience in this technology, the level of the experience of the analyst, the type of knowledge (explicit, implicit, tacit), the background knowledge. 1. The degree to which data/information and are available and reliable/relevant 2. The degree to which the assumptions are reasonable/realistic 3. The degree to which there is agreement among experts 4. The degree to which the phenomenon involved are understood and accurate models exist.

Actually as it is known that the knowledge itself has so many aspects to be considered when it is needed to give the score, it is better to give the score of the level of the knowledge relying on previous questions imposed. The imposed questions can have multiple answers that is defined previously and each one of these answers refers to a specific score. Table 2 gives an example on of some questions that can be imposed. The match between the reality and the (gap between) how realistic the analysis are

The analysis are not realistic at all

There is only few realistic points in the analysis

The analysis are partially realistic The analysis are realistic but do not match all real cases that took place before

The analysis are so realistic and matches a lot most of the real cases that took place

The conservatism arises from the fact that it is "Better safe than sorry" Samuel Lover"s Rory O"More (1837). Some has referred to the conservatism in risk management as the desire for caution that rises from different consideration and reasons such as the concerns regarding the lack of knowledge about the nature and magnitude of the hazard [START_REF]Conservative versus Mean Risk Assessments: Implications for Superfund Policies[END_REF]. Others refer to the conservatism as a preference to make a mistake in the side of overestimating the risk rather than understanding it under conditions of uncertainty that might be underestimating of it. This tendency is manifested when risk estimation exceeds the mean value of risk probability distribution (that is neither underestimating, not overestimating the risk); where conservatism might involve selecting a risk estimate at for example 95th percentile, or 99 th percentile, meaning there is a 99% probability that the risk is over estimated and 1% is underestimated [START_REF]comment on: Does Risk Aversion Make a Case for Conservatism?[END_REF].

Actually at the beginning we thought about classifying the levels of conservatism as the following:

1. Extremely conservative: the level of knowledge is very low and we have a high level of uncertainty.

2. Conservative : we need to be conservative due to the lack of knowledge and the high level of uncertainty 3. Modest conservatism : we have a very good level of knowledge, with quite low uncertainty, quite good reliability 4. Very modest conservatism: when we have a high level of knowledge, the uncertainty is quite low, the reliability is very good, and the importance is low.

5.

No conservatism: the knowledge is absolute and there is no uncertainty, the reliability is high, and the importance (the criticality of the rule of the part or the detriment in case of the fail) is low, so we do not need to be conservative

According to the previous we can see the dependency of this element (conservatism) with other criteria such as the uncertainty and importance.

Actually we tried to enhance the definition of the levels as we have found that it is not fitting with the different hazard groups. 1. I"m sure to be conservative in a way that covers even the unknown unknowns 2. I"m conservative and I know it 3. I think I"m conservative but I"m not sure 4. I think I"m not conservative 5. I"m sure that I"m not conservative.

Final Mathematical Model of the Level of Maturity

As we discussed before the final model of maturity is a function of several criteria that affect the analysis and the degree of trustworthiness of the model. Integrating the different maturity criteria into the maturity model results in the following:

Maturity level model = {uncertainty, importance, conservatism, sensitivity, dependency, trustworthiness of the analysis tool, state of knowledge, level of analysis, accuracy, precision}

In symbols: m j = {(sc) 1 u j , (sc) 2 i j , (sc) 3 c j , (sc) 4 s j , (sc) 5 d j , (sc) 6 t j , (sc) 7 k j , (sc) 8 a j , (sc) 9 ac j , (sc) 10 p j }

M = {(SC) 1 U, (SC) 2 I, (SC) 3 C, (SC) 4 S, (SC) 5 D, (SC) 6 T, (SC) 7 K, (SC) 8 A, (SC) 9 Ac, (SC) 10 P}

ex; m internal fire = {3u, 3i, 4c, … … … . . } means that the internal fire hazard group scores uncertainty of level 3, importance of level 3, and conservatism of level, which can be also represented in matrices as previously. Actually we kept the symbol of each element of the maturity model, in order to keep a sense of the meaning of these number before the final step of scalar aggregation, which would be better informing for the decision maker. ] in average aggregation method.

Another suggestion is to introduce the risk as well in the same model, which might at the hazard group level or at the sub-hazard group (consisting elements of each hazard group)

Hazard group level: m j = Risk × {(sc) 1 u j , (sc) 2 i j , (sc) 3 c j , (sc) 4 s j , (sc) 5 d j , (sc) 6 t j , (sc) 7 k j , (sc) / a j , (sc) 9 ac j , (sc) 10 p, }

Suggestion:

 In this type of model it is suggested to keep the symbols to give a clue about the scores meaning.

Conclusion

As discussed through this report, the risk aggregation is a very important process in risk informed decision making, as it is needed to compare a final metric of risk; (core damage frequency, early large release) to a reference or a threshold value. In fact risk aggregation using classic methods might be misleading for the decision maker, as it is usually achieved using a simple summation of the risk from different hazard groups which is not mathematically consistent nor physically meaningful due to the heterogeneity of different hazard groups.

Our idea was to create what we called the level of maturity model, which should be able to overcome the problem of hazard group heterogeneity. The model consists of different criteria (elements) that are believed to affect the level of maturity of each hazard group such as: the level of uncertainty, the level of conservatism, the level of knowledge, and etc.

As a start the model was applied on a basic example (look at table A.1 in appendix A) using only 3 criteria, and as it is believed that that the score (rank) won't be precise unless so many aspects of each single criteria are taken into account, we have started by dividing the level of knowledge into different other sub-criterion, and the final score of the level of the knowledge was given by averaging the different scores of each sub-criterion. Actually giving a precise definition and sub-criterion for criteria is what we are planning to do in the near future for the PhD purposes, especially that we noticed the need to give a more specific and precise definition or even to change the way of scaling during the application of the model on some hazard groups to make more compatible.

The application of this model on a basic example, has opened the eyes on other important and challenging point. In fact It is not really convincing to use all the criteria of the model in the same way, because it is believed that each criteria contributes in different way and percentage in the level of maturity, which is usually done in multiple criteria decision making MCDM process, as well as in ELECTRE TRI approach with the help of the management. In the other hand for maturity level model, the weighting of each criterion should be accomplished with the help of the experts (the analysts and the decision maker), using their experience and common sense to give an estimation of their contribution, where each criterion is then weighted, according to how important it is in the overall picture, relative to all the rest.

The model of maturity is not complete yet, and it still needs a lot of developments regarding the mathematical model, the different perspectives of the definition of each criterion and their contribution, as well as trying to integrate known multi criteria decision making approaches (ex. ELECTRE TRI approach in order to use it in ranking the different possible combination of scores) with our model to enhance it, and finally to make a guideline for both the analysts and the decision maker to help them understand and apply better the model, which are believed to be our goals for the PhD thesis.

Figure 1

 1 Figure 1 Example of radar chart representing CDF distribution of different hazard groups ....Figure 2 Risk informed decision making process, factors influencing decision making, and RIDM weaknesses ......................................................................................................................Figure 3: Risk contributions from different hazard groups before and after modifications .....Figure 4: Functional Roles and Information Flow in RIDM (Notional) ...................................Figure 5 Risk aggregation from different hazard groups. .........................................................Figure 6: Risk Informed decision making process within RG 1.174 framework ..................... Figure 7 Proposed general approach ......................................................................................... Figure 8 Process to assess realism of the PSA model ...............................................................Figure 9: Process to aggregate ..................................................................................................Figure 10 Iterative process to "aggregate" ................................................................................ Figure 11 Risk informed decision making process with and without level of maturity model.Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model. ...........................................................................................................

Figure 2

 2 Figure 1 Example of radar chart representing CDF distribution of different hazard groups ....Figure 2 Risk informed decision making process, factors influencing decision making, and RIDM weaknesses ......................................................................................................................Figure 3: Risk contributions from different hazard groups before and after modifications .....Figure 4: Functional Roles and Information Flow in RIDM (Notional) ...................................Figure 5 Risk aggregation from different hazard groups. .........................................................Figure 6: Risk Informed decision making process within RG 1.174 framework ..................... Figure 7 Proposed general approach ......................................................................................... Figure 8 Process to assess realism of the PSA model ...............................................................Figure 9: Process to aggregate ..................................................................................................Figure 10 Iterative process to "aggregate" ................................................................................ Figure 11 Risk informed decision making process with and without level of maturity model.Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model. ...........................................................................................................

Figure 3 :

 3 Figure 1 Example of radar chart representing CDF distribution of different hazard groups ....Figure 2 Risk informed decision making process, factors influencing decision making, and RIDM weaknesses ......................................................................................................................Figure 3: Risk contributions from different hazard groups before and after modifications .....Figure 4: Functional Roles and Information Flow in RIDM (Notional) ...................................Figure 5 Risk aggregation from different hazard groups. .........................................................Figure 6: Risk Informed decision making process within RG 1.174 framework ..................... Figure 7 Proposed general approach ......................................................................................... Figure 8 Process to assess realism of the PSA model ...............................................................Figure 9: Process to aggregate ..................................................................................................Figure 10 Iterative process to "aggregate" ................................................................................ Figure 11 Risk informed decision making process with and without level of maturity model.Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model. ...........................................................................................................

Figure 4 :

 4 Figure 1 Example of radar chart representing CDF distribution of different hazard groups ....Figure 2 Risk informed decision making process, factors influencing decision making, and RIDM weaknesses ......................................................................................................................Figure 3: Risk contributions from different hazard groups before and after modifications .....Figure 4: Functional Roles and Information Flow in RIDM (Notional) ...................................Figure 5 Risk aggregation from different hazard groups. .........................................................Figure 6: Risk Informed decision making process within RG 1.174 framework ..................... Figure 7 Proposed general approach ......................................................................................... Figure 8 Process to assess realism of the PSA model ...............................................................Figure 9: Process to aggregate ..................................................................................................Figure 10 Iterative process to "aggregate" ................................................................................ Figure 11 Risk informed decision making process with and without level of maturity model.Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model. ...........................................................................................................

Figure 5

 5 Figure 1 Example of radar chart representing CDF distribution of different hazard groups ....Figure 2 Risk informed decision making process, factors influencing decision making, and RIDM weaknesses ......................................................................................................................Figure 3: Risk contributions from different hazard groups before and after modifications .....Figure 4: Functional Roles and Information Flow in RIDM (Notional) ...................................Figure 5 Risk aggregation from different hazard groups. .........................................................Figure 6: Risk Informed decision making process within RG 1.174 framework ..................... Figure 7 Proposed general approach ......................................................................................... Figure 8 Process to assess realism of the PSA model ...............................................................Figure 9: Process to aggregate ..................................................................................................Figure 10 Iterative process to "aggregate" ................................................................................ Figure 11 Risk informed decision making process with and without level of maturity model.Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model. ...........................................................................................................

Figure 6 :Figure 7 Figure 8

 678 Figure 1 Example of radar chart representing CDF distribution of different hazard groups ....Figure 2 Risk informed decision making process, factors influencing decision making, and RIDM weaknesses ......................................................................................................................Figure 3: Risk contributions from different hazard groups before and after modifications .....Figure 4: Functional Roles and Information Flow in RIDM (Notional) ...................................Figure 5 Risk aggregation from different hazard groups. .........................................................Figure 6: Risk Informed decision making process within RG 1.174 framework ..................... Figure 7 Proposed general approach ......................................................................................... Figure 8 Process to assess realism of the PSA model ...............................................................Figure 9: Process to aggregate ..................................................................................................Figure 10 Iterative process to "aggregate" ................................................................................ Figure 11 Risk informed decision making process with and without level of maturity model.Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model. ...........................................................................................................

Figure 9 :

 9 Figure 1 Example of radar chart representing CDF distribution of different hazard groups ....Figure 2 Risk informed decision making process, factors influencing decision making, and RIDM weaknesses ......................................................................................................................Figure 3: Risk contributions from different hazard groups before and after modifications .....Figure 4: Functional Roles and Information Flow in RIDM (Notional) ...................................Figure 5 Risk aggregation from different hazard groups. .........................................................Figure 6: Risk Informed decision making process within RG 1.174 framework ..................... Figure 7 Proposed general approach ......................................................................................... Figure 8 Process to assess realism of the PSA model ...............................................................Figure 9: Process to aggregate ..................................................................................................Figure 10 Iterative process to "aggregate" ................................................................................ Figure 11 Risk informed decision making process with and without level of maturity model.Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model. ...........................................................................................................

Figure 10 Figure 11

 1011 Figure 1 Example of radar chart representing CDF distribution of different hazard groups ....Figure 2 Risk informed decision making process, factors influencing decision making, and RIDM weaknesses ......................................................................................................................Figure 3: Risk contributions from different hazard groups before and after modifications .....Figure 4: Functional Roles and Information Flow in RIDM (Notional) ...................................Figure 5 Risk aggregation from different hazard groups. .........................................................Figure 6: Risk Informed decision making process within RG 1.174 framework ..................... Figure 7 Proposed general approach ......................................................................................... Figure 8 Process to assess realism of the PSA model ...............................................................Figure 9: Process to aggregate ..................................................................................................Figure 10 Iterative process to "aggregate" ................................................................................ Figure 11 Risk informed decision making process with and without level of maturity model.Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model. ...........................................................................................................

Figure 12

 12 Figure 1 Example of radar chart representing CDF distribution of different hazard groups ....Figure 2 Risk informed decision making process, factors influencing decision making, and RIDM weaknesses ......................................................................................................................Figure 3: Risk contributions from different hazard groups before and after modifications .....Figure 4: Functional Roles and Information Flow in RIDM (Notional) ...................................Figure 5 Risk aggregation from different hazard groups. .........................................................Figure 6: Risk Informed decision making process within RG 1.174 framework ..................... Figure 7 Proposed general approach ......................................................................................... Figure 8 Process to assess realism of the PSA model ...............................................................Figure 9: Process to aggregate ..................................................................................................Figure 10 Iterative process to "aggregate" ................................................................................ Figure 11 Risk informed decision making process with and without level of maturity model.Figure 12 Risk analysis progression and steps with risk informed decision making with and without maturity model. ...........................................................................................................

Figure 1

 1 Figure 1 Example of radar chart representing CDF distribution of different hazard groups

Figure 3 :

 3 Figure 3: Risk contributions from different hazard groups before and after modifications

Figure 4 :

 4 Figure 4: Functional Roles and Information Flow in RIDM (Notional)

Figure 5

 5 Figure 5 Risk aggregation from different hazard groups.

Figure 6 :

 6 Figure 6: Risk Informed decision making process within RG 1.174 framework

Figure 8 :

 8 Figure 8: Process to aggregate

Figure 9

 9 Figure 9 Process to assess realism of the PSA model

Figure 10

 10 Figure 10 Iterative process to "aggregate"

M

  = m internal fire + m internal flooding + m external flooding + ⋯.

Table 1

 1 Example of PCMMTable Assessment and Project Maturity Requirements . .............

Table 2

 2 Knowledge Criteria levels definition and description ................................................

Table 1

 1 Example

of PCMM Table Assessment and Project Maturity Requirements

[START_REF]Predictive Capability Maturity Model for Computational Modeling and Simulation[END_REF]

.

They gave different colors for each element to address if they meet the requirement of maturity or not, you can notice that the scores of the different criteria are [1,2,1,0,1,1] while what is required is [2,2,1,2,2,3]. The next step which might be more challenging is the aggregation, especially that it is known that collecting information for decision maker can be really challenging and difficult. For this model they have suggested a very simple way of aggregation in order to help maintaining the key information in the different individual scores as the following (

[START_REF]Predictive Capability Maturity Model for Computational Modeling and Simulation[END_REF]

):

Table 2

 2 Knowledge Criteria levels definition and description

	Level 5	The data are Available	in abundance and can be	extracted or gotten	easily from so many	sources and places	world wide	Specific to your plant			Own plant			The data are perfectly	suitable and applicable	to our case		The data are measured	precisely and	accurately, and then	modeled		This event is quite	common and we have a	wide experience inn
	Level 4	The data are available in	all kinds of power plants					Specific for types of	reactors, (PWR, BWR,	CANDUM….)	Other nuclear power	plants of the same type	and technology	The data are applicable	for our NPP, but not	perfectly applicable to	our case	Data are gotten using	computer mathematical	and physical models			Experienced this event	in the same nuclear	power plant
	Level 3	The data are available	and can be extracted	from any other	nuclear power plant			Specific for nuclear	power plant		Other nuclear power	plants		Applicable and	suitable for NPP	generally		Data are both	assumed and	calculated using	computer physical	and mathematical	models	Experienced such an	event in nuclear	power plants industry
	Level 1 Level 2	No data The data are so	limited and can be	extracted only from	the same type of	nuclear power	plants	General and can be General for all kind	extracted from any of power plants	place	Other sources that is Other power plants	not related directly and other	to the technology	Not really applicable Applicable and	and suitable for the suitable for power	NPP plants		Assumption of data Data are calculated	using statistical	models			No experience at all Experienced such	an event in other	industries
	Knowledge criteria	Amount of data sources,	references					Type of needed data			Source of data			Applicability and	suitability for the case	study		Quality of the data and	the models				Experience in the	initiating event

APPENDICES APPENDIX A


Sandrine Sorlin

Person deixis and impersonation in Iain Banks's Complicity

belongs to the category of the thriller novels. It is in the vein of the author's first novel, The Wasp Factory (1984), also depicting a vicious serial killer. But Complicity is stylistically remarkable 1 for its alternation of narratives featuring two different protagonists: a journalist for the Caledonian newspaper, Cameron Colley, investigating murders, whose narrative is in the first person, and a murderer relating his crimes with graphic details in the second person. 2 Presented as widely apart at the beginning, the threads of the two protagonists--narrators' lives start to interlace as the novel enfolds. Without prior warning, there is a continuous shift between the protagonists' narratives from one chapter to the other and even within the same chapter. The readers have then no other choice than to turn into 'forensic linguists', leaning on textual fingerprints to determine which frame of mind they are in. Combined with other linguistic markers, the personal pronouns are of course particularly helpful, except when, at one point in the novel, one of the narrators stages what I call stylistic impersonation, bringing about confusion regarding the identity of the protagonists. At the end of the novel, adding to the mirror--effects created by the I/you dyad, the 'I' protagonist--narrator switches to the second--person pronoun that has so far been the stylistic preserve of the assaulter.

. It will more specifically determine the reason why Iain Banks uses the second person pronoun in his novel and, compared with other potential personal pronouns, what position it pragmatically constructs for the reader. Drawing on the psycholinguistic--oriented approach of text processing adopted by Sanford and Emmott in their 'Rhetorical Processing Framework' (2012), I will also delve into how readers tend to mentally process Complicity, by trying to exhibit the mental representations they are led to build from the stylistic devices finely chosen by the writer.

The pragmatic paradoxes of the second person pronoun

In his 1993 book on language and point of view, Paul Simpson left it to the reader to decide whether there should be added, besides his category A (novels written in the first person) and Category B (novels written in the third person), a category C that would gather what is called odd pronominal narratives (Simpson, 1993: 78--9). If Category C is used, it can display the positive, negative and neutral

modal shading that Simpson elaborates in his modal grammar of point of view. As a matter of fact, if the focus is on 'you' narratives, they do show these three types of shading, as can easily be evidenced (see [START_REF] Sorlin | La Stylistique anglaise. Théories & pratiques[END_REF]. The only problem facing Category C, if it is to be considered along the same lines as the other categories, is that generally the second person pronoun can hardly be said to have a stable reference. 3 Indeed as opposed to the first person singular for instance, 4 the reference of the second person can be multiple (see [START_REF] Fludernik | Second--person fiction. Narrative You as addressee and/or protagonist[END_REF][START_REF] Fludernik | Introduction: Second--person narrative and related issues[END_REF][START_REF] Fludernik | Towards a 'Natural' Narratology[END_REF]: it could refer to the reader, an internal addressee, people in general, it can denote a fictional protagonist and/or can be a form of self--address.

If, as Gérard Genette indicates, every third--person narrative always implies the presence of an 'I' that is at the origin of the enunciative act (Genette, 1972: 252), the same can often be said of first--person narratives where the 'I' can be construed as a 's/he': under the speaking 'I' saying 'I', there is someone about whom something is said, that is to say a 'self' that is me and that can be considered as a third person (Joly, 1990: 21). This disguised similarity between first and third person seems to leave the second person aside-for Genette (1983/1988: 133), second person narratives are 'a rare but very simple case' that he integrates in his heterodiegetic category. If, on the plane of enunciation, 'I' and 's/he' can be considered similar, where can the second--person pronoun be situated? In novels where the second person notionally corresponds to a first person, 5 operating what Uri Margolin (1986: 190--9) calls a 'deictic transfer', can second--person narratives be said to be part of Simpson's category A (novels written in the first person)? Yet if this particular case is melted in the broader category A, what can be said about novels like Banks's Complicity which present alternative use of 'I' and 'you' referring to two different persons? Here especially, the play on the I/you dyad turns out to be at the very heart of the plot. Rather than embodying discursive intersubjectivity as described by Benveniste (1974: 82), the I/you dyad in Complicity indeed exhibits, as I shall demonstrate, complex psychological (dis)connections between 'self' and 'other'. 6

Depersonalised persona: the neutralisation of subjectivity

The passages figuring 'you' in the novel are written in a 'neutral' mode that seems to near writing degree zero. Grammatically, they are marked by a quasi absence of modality, privileging confident grammatical assertions. Here is an extract chosen at random from the very beginning:

Then the door closes and they are there in front of you and in that instant you see him turned slightly away, putting his briefcase down on the table beside the answer-machine. The girl-blond, tan, mid--twenties, holding a slim briefcase-glances at you. She does a double--take. You are smiling behind the mask, putting one finger up to your lips. She hesitates. You hear the answer--machine spin back, squeaking. As the girl starts to open her mouth, you step forward, behind him.

You swing the cosh and hit him very hard across the back of the head, a hand's width above his jacket collar. He collapses instantly, falling against the wall and down over the table, dislodging the answer--machine as you turn to the girl. (Banks, 1994: 6) The cold, detached style is produced by specific linguistic choices made by the narrator, in terms of tense (the present tense, evincing a minimum characterisation of the process, creating a moment--to--moment description) and processes (concrete material processes referring to the actions performed, relational processes describing the physical surroundings and perception processes involving bodily senses). Apart from non--finite nominal subordinate clauses, the syntax makes mostly use of parataxis and coordination-in the first 'you' passage for instance (3--9), only five subordinate clauses can be found introduced by the conjunction 'as' and 'though'. All the 'you' passages in the book are written in the same type of style, often producing a binary hypnotic rhythm: 'you put a ten--centimetre strip across her mouth and leave the kitchen, putting the light out and closing the door' (8), 'The hotel is dark and very quiet' (176).

In her analysis of personal pronouns in English, Katie Wales insists on the inherently 'egocentric' orientation of 'you', even in its most impersonal uses. For her indeed even generic 'you' is inherently subjective: 'a speaker's observations on life will invariably be coloured by their subjective attitudes and experience' (Wales, 1996: 78). Yet in this novel the 'you' protagonist--narrator precisely sees to it that no subjective clues about himself transpire in his narrative. Just as he is careful not to leave any fingerprints on his crime scenes, his narrative tends to erase any linguistic fingerprints that might reveal something about his (social and geographical) identity, his motivations or his emotions. The second person pronoun seems a means to adopt a 'persona' behind which the criminal can hide himself. The 'you mask' is somehow the grammatical equivalent of the real mask he is wearing in order not to be identified. To use Collins and Postal's term in Imposters. A Study of Pronominal Agreement (2012), 'you' is here definitely an 'imposter': it is notionally a first person and grammatically a second one. 7 But there is a sense in which this grammatical imposture mirrors a more psychological camouflage. The pronoun 'you' operates here a distancing effect which allows the protagonist not to put too much of himself in the narrative. What he performs are controlled 'acts of identity' 8 in his desire to project the image of the rational assaulter who perfectly knows what he's doing: 'you decide to stick to the plan. It's important; it shows that you are not just some nutter, and the extra risk lifts you onto another plane of chance and luck' (58--9). 1.2. Between distance and complicity: the defamiliarising familiarity of 'you'

A high level of construction marks the narrator's very controlled narrative. Indeed although the 'you' passages can be said to be, narratologically speaking, interior monologues, they can hardly be compared with stream of consciousness novels where intimate thought is expressed without any addressee in mind or prior construction. In novels like Joyce's Ulysses where Molly's monologue can be said to be the epitome of the genre, the fragmented syntax mirrors the irrational meanders of thought, flowing at the whim of the narrator's memories or associations of ideas. In Complicity, the second person sections are too self-conscious to be mere records of irrational thoughts. Besides, they share the high degree of artificiality pointed out long ago by Dorrit Cohn about first--person narrators of interior monologues: 'forced to describe the actions they perform while they perform them, they tend to sound like gymnastics teachers vocally demonstrating an exercise' (Cohn, 1978: 222). 9 In Banks's novel, the protagonist describes the performance of his crimes, as if narration and action could coincide. He is describing and commenting on his actions, using what could be called 'metaperformatives': 'you hesitate for a second, then walk normally to the stairs and go down them with a fairly quick, heavy tread, whistling', 'you already know what you're going to do, how you're going to play this' (35).

But the interior monologues that Cohn's comment above refers to are first-person narratives, like Dujardin's Les Lauriers sont coupés for instance. Is the effect the same with second--person narratives? It seems that the uncommon, surprising choice of the second person accentuates the high artificiality of such an unnatural narrative technique. For the Free Indirect Speech specialist, Monique de Mattia--Viviès, the 'I' of interior monologues is in fact a disguised third person:

It is as if we were dealing with a masked temporal back--shifting that does not appear in the tense used but that shows in the construction, through the self-description, of an 'object--of--discourse I' out of touch with the 'I' describing her own acts. The protagonist looks at herself, as if she was watching again the film of which she is the main actress. (de Mattia--Viviès, 2006: 211, my translation) So the 'I' of interior monologues introduces a distance between the 'I' who describes the acts and the 'I' who is the object of discourse, making the latter akin to a third person. It could be illustrated thus: I → he. As said earlier, 'you' tends to put the self (I) at a distance through the deictic transfer it effects: I → you. As a consequence, in second person interior monologues, 'you' seems to occupy a position in between traditional first and third person pronouns. To recap, the intermediary position of 'you' can be thus illustrated: I → he ('I' as third person in interior monologues) I → you (the deictic transfer of self--address) Hence: I → [you] → he ('you' in interior monologues) It could be argued indeed that the second person pronoun adds here another link to the chain that separates further the enunciator from the acting protagonist.

However, the distance created by 'you' between narrating self and narrated self is counterbalanced by an effect of proximity with the reader produced by the second person. Indeed as Wales points out, 10 'you' (like 'we') 'has a strong inter-personal base, speaker--or addressee--oriented, reflecting we and you's origins' (Wales, 1996: 59). In some sort of pragmatic paradox, the readers cannot help feeling addressed while knowing perfectly well they are not (directly). In the staging of his crimes, the protagonist--narrator seems indeed to give advice to the reader on 'how to do this…' and 'what to avoid…' in order to obtain a high degree of perfection in crime: 11 'you go into the bedroom, checking the position of the mirrors; none of them ought to show you to anybody in the bathroom' (163). 'Spirited' into the narrative through the second person pronoun, readers are placed as 'in--siders', in the heat of the action, watching the scene from behind the protagonist's mask. His extremely precise descriptions, saturated with specific geographical and physical details, enable the readers to visualise everything as if they were there. 'You' does not directly interpellate them and yet it seems to require their complicity-in echo of the title of the book-since a form of intimacy is inevitably forced upon them: they are indeed the only ones who have access to the mind(style) of the assaulter while the others (journalists and policemen) arrive after the crime has been committed.

Textual 'You' seems here to pertain to the last of the five functional types identified by David Herman (1994: 378--411): what with the total agreement between the grammatical form and its deictic function ('you' addressing a narratee or the reader in a direct apostrophe, first and second type) 12 and total disagreement (when 'you' embodies a deictic transfer or has a generic meaning close to 'one', third and fourth types), Herman theorizes yet another intermediary type ('doubly deictic you') that would evince neither complete agreement between form and function nor complete discord between them. In this case, the reader is clearly not the referent of the second person and yet he/she 13 paradoxically is. In Collins and Postal's terms, it could be said that 'you' 'obtains its 2 nd person value from ADDRESSEE functioning as a secondary source' (Collins & Postal, 2012: 223). In Complicity, the readers are both excluded from narration while at the same time being included into it, whether they like it or not. The reader is summoned to occupy the impossible double posture of exterior observer and addressee captured into the narrative [START_REF] Herman | Textual "You" and double deixis in Edna O'Brien's A Pagan Place[END_REF].

Where Herman speaks of 'double deixis' I would rather speak of 'metaphorical you', basing myself on Ricoeur's definition of metaphor as what 'is and isn't' at the very same time 14 : 'you' clearly isn't the reader and yet it metaphorically is-this ties in with Wales's remark that every personal pronoun should be interpreted 'rather in the same way as we interpret metaphors' (Wales, 1996: 83), especially in case of imposture where the 'literal', morphological reference is at odds with the notional, semantic one [START_REF] Collins | Imposters. A Study of Pronominal Agreement[END_REF]. The same second person pronoun manages to perform two contrary effects in Complicity, that of distancing on the one hand and of bringing closer on the other: the protagonist--narrator is distancing himself from the subject that commits these crimes as if to get himself off the hook and shifting the blame onto some other 'you persona' and there is at the same time some kind of metaphoric transfer onto the reader. The distancing from the narrating 'I' is indeed commensurate with the rapprochement with the reader that the second pronoun inevitably initiates. The metaphorical encroaching upon the 'zone of the reader' is what is particularly defamiliarising when reading. This getting closer to the readers is also what makes possible the rhetorical manipulation of their emotions.

Manipulating emotions

This staged complicity predisposes the reader to adopt a certain point of view. In the suspense created by the narration, with some events not going the way the protagonist predicted, the readers can surprise themselves wanting him to succeed as if the forced complicity was working on them: this 'participatory response' [START_REF] Allbritton | Participatory responses in text understanding[END_REF] is for me elicited by the 'you' construction. In addition, despite the obvious unlawful actions of the 'you' protagonist, the reader gets a sense that the victims deserve their plight as they are powerful people implicitly described as involved in amoral issues and getting away with them because of their high social status. In fact the reader's reactions to the text are rhetorically manipulated. For instance, the victims' pain is always reported in a very 'cold' mode: never is the reader brought to vicariously experience the pain of the other, through what Sanford & Emmott (2012: 201) call 'hot cognition'. 15 By contrast, the description of the victims' painful response to violence is interspersed with technical or poetic comments, as in this long passage on the specific syringe used:

The syringe is a big mother; not like those dinky little disposable plastic things medics and junkies use. This device is made from stainless steel and glass; it has two

Scenario mappings and mental processes

In Complicity, the narration switches narrators without warning. In order to understand which 'footing' [START_REF] Goffman | Footing. In: Forms of Talk[END_REF] they are on, the readers must look for references to time, place and movement and other linguistic footprints like personal pronouns, or sociolinguistic markers like register, dialect and idiolect. For in these respects, the two protagonists--narrators' mindstyles could not be further apart. Cameron's style is unmistakable with its colloquial register and journalese jargon. His lexicon is also sprinkled with terms appertaining to the world of the video game he is particularly fond of:

No waste! No fat! Just exactly the right, most elegantly eco--optimum system-as near to state--of--the--art as I could afford at the time, barely a year ago and I'm still paying the now quite superseded bastard off-to run this stunningly Machiavellian turbo--screamer of a game; an instant classic, easily a year ahead of its time and just possibly better than sex. ( 52)

Compared to the 'you' narrator, Cameron gives a profusion of details about his emotions, his sex life and his addiction to drugs, cigarettes and alcohol: 'I have another whisky and a bowl of Coco Pops with lots of milk. My hand keeps reaching for the place where the cigarette packet would normally be, but I'm coping with the cravings and surviving so far. I really want some speed but I know if I have any I'll want a cigarette afterwards, so I leave it alone' (55). So the readers know which 'frame' they are in thanks to lexical and sociolinguistic elements that construct a particular mental space.

Style impersonation and deception

However, at one point in the narrative, a passage in the first person is recognizably written in the neutral mode of the 'you' narrator, as it describes the spatial surroundings of someone about to commit a crime in the same moment--to-moment description that the reader has become used to associating with the aggressor:

The wind is loud in the leaf--bare branches overhead. I head down the track to the road, then look back to the car; it's almost fully hidden. I cross the tarmac and climb a fence, than take the ski--mask from my trouser--pocket and pull it over my head. I follow the line of the hedge along the side of the road, ducking once as a car drives past on the road; its headlights sweep along the hedge above me. The car carries on into the night. I start breathing again. (125--126) In addition, some elements are recognizable from previous 'you' passages, like the gloves, the mask and interjections like 'shit!' that the 'you' protagonist often uses when something goes wrong. As Emmott (2003: 145--146) indicates, there are several types of knowledge that the reader relies on in order to build mental representations of the text: general knowledge, knowledge of typical text structures, text--specific knowledge of a particular fictional world and knowledge of the style of a particular text. Here it seems that the writer wants the reader to focus on text--(and style)--specific knowledge as what is being described seems to fit in the Text World [START_REF] Werth | Text Worlds: Representing Conceptual Space in Discourse[END_REF][START_REF] Gavins | Text World Theory: An Introduction[END_REF]) constructed in the reader's mind from the accumulated contextual information. The reader is made to believe that the actions performed are those of the assaulter.

Sanford and Emmott's 'Rhetorical Processing Framework' is of help here to grasp how the reader's attention is psychologically controlled (Sanford & Emmott, 2012: 5). 16 In an automatic psychological process, the readers relate the mental representation of the discourse they are reading to something that they already know; this is the principle of the Scenario--Mapping Theory (Sanford & Emmott 18): 'The strongest processing assumption of the Scenario--Mapping Theory is that the reader automatically seeks out a known situation (scenario) to which a text is referring, what Sanford andGarrod [1981, 1998] termed primary processing, leading to basic understanding. Wherever possible, text is mapped onto the scenario' (Sanford & Emmott, 2012: 20--21). The 'mental models' the reader has formed are brought up whenever similar contexts come up: 'The basic suggestion was that mental representations of a discourse are formed by relating what is being read to a situation that the reader knows something about already' (Sanford & Emmott, 2012: 21). In the passage quoted above, the writer seems to want the reader to map the passage onto the familiar scenario of a (future) crime scene. Within Sanford and Emmott's psycho--linguistic framework, this corresponds to what they call the Rhetorical Focussing Principle, that is to say 'the idea that writers aim to focus attention on selective aspects of a text, causing some parts of the text to be processed more thoroughly than others' (Sanford & Emmott, 2012: 101).

Given the known scenario and its characteristic style, we may expect the reader's attention to focus on 'selective aspects' of the text and to overlook certain anomalies in the picture: the first--person pronoun for one thing, the fact that the narrator--protagonist uses a car and not a bike as the murderer usually does. Even more surprising is the fact that he finds a key to open the back door ('I feel the putty, then the embedded key and its short length of string. I take hold of the string and pull gently. The key comes out, clinking quietly once. I put my glove back on', 127). The protagonist's taking off his muddy shoes before going to the bedroom where a woman is sleeping might, on re--reading, sound like a clear anomaly for a his own house. The way Iain Banks has constructed his narrative often brings the reader to 'wait and see', as primordial information comes up sparingly. Indeed as Sanford and Emmott underline, when the information given in a novel cannot be mapped onto an appropriate scenario, 'secondary processing occurs'. This can take several forms 17 like 'putting unresolvable input on a "wait and see" list' (Sanford & Emmott, 2012: 38).

Slowly Andy's personality gains in psychological complexity leading the reader to understand that the way Cameron has presented his friend Andy ('my old soul--mate, my surrogate brother, my other me', 29) is a far cry from the way the latter has lived out his relationship with Cameron: the linguistic and pragmatic reciprocity of the I/you dyad put forward by Benveniste in canonical situations of interlocution gives way here to a marked psychological dissymmetry between the ways the characters have respectively perceived their alter ego. What has been repressed by Cameron (the 'ice incident', Andy falling in an ice hole and Cameron being too shocked to go and rescue him) along with the psychological impact of Andy's sister's death and other painful shared events, are slowly coming up to the surface and ultimately lead Cameron, and the reader as well, to realise that Andy is the one who set him up. Disguised, Andy manages to kidnap Cameron after sabotaging his car. Andy offers Cameron two options: call the police right away with the phone Andy has left him or choose not to betray him once again and let him go. Cameron calls his doctor instead.

'You' and depth of processing

'You' returns in the last chapter of the novel (chapter 13) but this time with Cameron as protagonist--narrator. In Banks's characteristically misleading style, the 'sentence fragment' 18 ('tennis ball'), in the paragraphs quoted below, may lead the readers down some garden--path reasoning (they might think of something playful) that needs to be 'repaired' 19 in the following sentence:

A tennis ball. They say it's about the size of a tennis ball. You slide your hand inside your coat and jacket and press up under the floating rib on your left side. Pain. You're not sure whether you can feel it, the thing, the growth itself or not; you cough a bit as you press, and the pain gets worse. You stop pressing and the pain eases. (310--311) Here as well, the second person pronoun seems to bring about some distancing effect between the self and the topic, that is a painful, depressing one here (Andy later learns he has cancer). It seems that 'you' creates a specific zone where emotions are put at a safe distance from the character and reader alike. As the self-address pronoun communicates here on a personal situation (Cameron's) but one that could be shared by the reader at a more generic level on the mode 'imagine you...', the paradoxical final effect seems to be a more intense rendering of emotions that are paradoxically put at a farther distance.

When using the second--person pronoun, Cameron sounds as if he does not belong to his former self any more, the 'I' of the past has given way to a more lucid 'you' apprehending things from a different light, seeing the world in an alien, antagonistic way. This switch from 'I' to 'you' thus reflects this psychological estrangement that tends, in the end, to bring him closer to his former soul--mate Andy and to the latter's bitterness about the world gone mad. As Leslie Jeffries points out in her analysis of pronouns and point of view in contemporary poetry, 'you' seems to be particularly appropriate for depressed and anxious narrators: 'It would be premature to assume that all such uses of "you" as the sole deictic centre of poems were equally anxious or depressed, though my data does bear out this interpretation' (Jeffries, 2013: 188). 20 Here, in the last words of the novel, the disease brings Cameron to a new emotional detachment, as he gives up on medical restrictions on tobacco in an ironical laugh:

You put the tin away, sniffing. You tap the other packet in your jacket, then shrug, take it out and open it. You bought these last night, too. What the fuck. Screw the world, bugger reality. Saint Hunter would understand; Uncle Warren wrote a song about it.

You light a cigarette, shake your head as you look out over the grey-enthroned city, and laugh. (313) Perhaps because it is a narratological form that is less used than other more traditional modes, the 'you' narrative tends to attract attention. This is in part borne out by psychological research which assumes that readers tend to remember such passages better because they process them more deeply: 'there is a need for further exploration, but one possibility is that readers may become more attentive if they encounter such a form of address' (Sanford & Emmott, 2012: 173). This extra processing on the part of the reader can account for the extra involvement induced by the pronoun. With the second--person pronoun, it is as though the reader was always already involved. Crossing the conventional fictional borders, 'you' explicitly and continuously solicits the reader's complicit presence.

The ambiguities generated by the second person pronoun can also be measured if the readers choose to consider the relation between the narrator(s) and the protagonist(s), rather than the one between the protagonists--narrators and the reader, which has been my main focus here. 'You' being an address pronoun, not only may the interpretation according to which Cameron is the narrator in the 'you sections' emphatically addressing the murderer in an after--the--event narrative be validated, but it could also be defended that in the last 'you' chapter Cameron is only the protagonist--referent whose post--traumatic life is related by a narrator addressing him with 'you'. Hence the versatility of the pronoun that can generate different readings depending on who it can refer to. I thus leave it open to the readers to decide on how they feel interpellated (or not) by the subtle use of person deixis in Complicity. 21

Apart from William McIlvanney's Laidlaw (1977) using some aspects of the second--person technique, there seem to be very few crime novels, if any, featuring a 'you narrator' who is also the criminal. Many thanks to Christiana Gregoriou for helping me to find this out.

The novel inspired a film in 2000 called 'Complicity' ('Retribution' in the USA).

hook--shaped finger--grips on either side of the barrel and it holds a fifth of litre. You hold the medicine bottle sealed with cling--film upside down and slip the slanted tip of the big syringe needle into the clotted--cream--coloured liquid inside the bottle. Mr Oliver is still screaming behind the gag. (89) The positive connotations of some poetic descriptions divert the reader's attention from the terrible deed just committed as if nothing happened:

It's sunset when you leave, locking the quiet house securely behind you. The sun flames orange and pink behind the trees above the house, the breeze is cool rather than cold, scented with flowers, the sea, and you think what a pleasant if rather bland place this could be to settle down. ( 168 Furthermore, the narrator's very detailed descriptions tend to uglify the bodies of the victims the aggressor is either sodomizing or infecting with AIDS, which deprives them of all dignity. Here, for instance, the victim's fart brings an implicit element of disgust or irony that deflates the horror being performed: 'He moans and farts at the same time. You have to turn your head away from the smell, but you push the vibrator in further. You can hear seagulls crying outside, beyond the closed curtains' (38). With the repeated crimes, like in Burgess's A Clockwork Orange, the reader seems to get familiarized with highly unsettling descriptions. The pronoun 'you' sometimes seems to address the reader directly as a reading accomplice that should by now be familiar with pain and screams: 'He moans, then his eyes open slowly and he sees you and tries to move but he can't. He screams down his nose. You are becoming familiar with men making this noise now' (103).

What clearly evinces the degree of manipulation undergone by the reader through the protagonist--narrator's rhetoric is the fact that when the criminal's acts are shown or described to the other narrator of this novel, Cameron Colley (the 'I' protagonist--narrator), he can't help vomiting and being haunted by the gorilla mask for days on end. This is unlikely to be the perlocutionary effect produced on the reader by the 'you' narrative. The discrepancy between the responses is rhetorically managed, the use of the second person pronoun contributing highly to the double contradictory effects evidenced above: the effect of emotional detachment from the acts on the one hand, enabling the protagonist to coldly put his acts at a distance, and that of 'conative solicitude' [START_REF] Bonheim | Conative solicitude and the anaphoric pronoun in the Canadian short story[END_REF] on the other, with the 'decidedly involving quality' of the pronoun (Fludernik, 1994: 286). murderer but at this stage the reader is likely to be ready to find alternative explanations that fit in the familiar scenario: he took off his shoes to reduce potential noise for instance. The research carried out by psychologists to explain the difficulty in detecting anomalies evinces that readers fail to detect them when they seem to 'fit the global context well' (Sanford & Emmott, 2012: 107). The 'shallow processing' of the information that is clearly anomalous at the 'local level' is due to the fact that it seems to fit already known text structures and general context: 'the outcome of shallow processing is an underspecified mental representation of the text that is shallow processed' (Sanford & Emmott, 2012: 104).

At the sudden appearance of the inclusive first person plural pronoun (we), the reader is led to infer that the rapist and the woman in fact know each other: She comes screaming; I don't think I'm going to but then I do. We collapse together onto the bed, breathing in time. I pull myself out of her. There is a faint smell of shit. I undo the handcuffs and lie there, holding her. She pulls the ski--mask from my head.

'Where are your shoes?' She whispers after a while. 'In the kitchen,' I tell her. 'They were muddy. Didn't want to make a mess.' She laughs quietly in the darkness. ( 130)

All along Cameron has impersonated a rapist to fulfil one of his mistress's sex fantasies. What is unsettling for the reader is that the first--person narrator has usurped the writing degree zero of the 'you' narrator. At this point in the narration, the stylistic imposture has the effect of planting seeds of doubt as to the identity of the 'you' character: is the 'I' and 'you' protagonists one and the same character after all? As reading goes on, the criminal's identity takes shape: suspicion is likely to crystallise around Cameron's childhood friend, Andy, presented as a reformed capitalist that has gone from huge wealth to a very modest life. When the reader is quite convinced about this deduction, the 'you protagonist' enters Andy's house describing it as if he was seeing it for the first time. He approaches a sleeping person and kills him with a log. Of course in these circumstances, the reader is led to believe the victim is Andy. The policeman confirms Andy's death to Cameron who is in prison, accused of the aggressor's crimes. The reader is at this point unlikely to take in the hints dropped by the 'you' narrator: 'You bring the log down with all your might. It hits his head and you don't hear the noise it makes because you cry out at the same time, as though it's you in the bed, you being attacked, you being killed' (177, my emphasis). In order to get away with his crimes, Andy has faked his own death, killing a friend he had put up for the night and setting fire to