Chloé Rolos
email: chloe.rolos@total.com

Guy A Boy
email: g.boy@estia.fr

Dimitri H Masson

Operations room design for the control of a fleet of robots Ontology-based function identification and allocation

Keywords: Oil and gas, control room, ontology, human centered design, fleet of robots

In this research work we focuses on the elicitation of concepts for the design of an oil and gas complex system involving a fleet of robots. We are using expertise and an experience-based approach to formalize existing control rooms and extending them to include robots. We are building a structural and functional ontology to identify and allocate current and emergent functions. The approach leads to the development of a software simulator that includes structures and functions of an oil and gas platform and its operations room.

INTRODUCTION

Offshore platform infrastructures are risk-adverse and costeffective. This is the reason why oil and gas companies are looking for a new type of platforms. They project to developed unmanned infrastructures. In order to reach this goal, we propose a new way to operate a site remotely using a fleet of robots and specially design an operations room. Developing a fleet of robots that can take humanlydangerous activities require a deep understanding of human activities on an offshore site. We deliberately chose a human centered design approach that dictates to identify and allocate appropriate functions among robots and human operators in the operations room. Results of this cognitive functions analysis will be used to define the specifications of the operations room. These encompass guidelines for human computer interfaces, scheduling rules for autonomous robots, workflow between the different control entities (e.g, control room, SMART room, operations room) and between robots (e.g, several robots executing a common task).

COLLABORATIVE WORK ENVIRONMENT

Running an oil platform requires maintenance operations. Most of them involve the management of daily events. These infrastructures be seen as complex and unstable systems. Control rooms are directly implemented on site to maintain platform in good conditions. These control rooms are designed to manage operations in real time on the field (e.g coordination of day to day operational tasks).

Every operation generates a large quantity of data. The oil and gas companies collect and exploit these data. For that purpose they developed a few years ago Support and Monitoring of Assets in Real Time (SMART) rooms which aim to analyze and capitalize all the data from platform [START_REF] Couture | Etude de réflexion stratégique sur les Smart Rooms[END_REF].

These rooms were created with the will to be a collaborative work space.

Current SMART rooms are equipped with communication tools such as screen walls, smartboards, computers. SMART rooms have been installed in different oil and gas companies' subsidiaries. The main objectives of this collaborative work environment are:  A better prevention of critical failures which lead to important shortfalls by a closer monitoring.  An improved planning taking into account a maximum of information and constraints  Sharing of real time information between sites.  Reducing the need to be on or to go to the remote sites.  A better preparation of interventions on site which potentially reduces intervention duration.  An improved logistic support by sharing real time information, well defined requests and a closer followup.

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HSI2019, September 11-13, 2019, Biarritz, France. Equally collaborative work environment has been established at the headquarter to provide a tier II support to operation.

Internal reports highlight that these rooms are not used at their full potential. Ergonomics of the room has been shown to not to be always suitable to operate these rooms at their full potential. The experience shows that the occupation time is under fifty percent for the major part of the SMART rooms [START_REF] Couture | Etude de réflexion stratégique sur les Smart Rooms[END_REF]. In this work we focus on integration of robots on the platform. This change implies the design of a new area from where robot management will be performed. This operations room will bring new kinds of workflow between the different control entities. The location of these rooms is to be determined during the study. We based our research on a taxonomy of existing collaborative work environment and the identification of a lack of functions and equipments to design the future operations room which will manage the robots on the platform. Indeed, the idea is to develop the operations room using a human centered design (HCD) approach.

METHODOLOGY

Our HCD approach is based on multi-agent modeling, cognitive functions analysis and study of the tangibility of the underlying complex systems, which includes the analysis of five properties: complexity, maturity, flexibility, stability and sustainability [START_REF] Boy | Orchestrating human-centered design[END_REF]. The methodology relies on the following steps. An analyses based on domain expert knowledge, as well as on activity analysis carried out using human-in-the-loop simulations. At each stage of the development an effective and usable solution is produced. This prototype is tested through formative evaluations. This agile approach enables the adaption of the robot's functions and potentially the infrastructure of the platform.

In this HCD approach, we start by developing software architecture and related physical and cognitive functions that will need to be tested against the five tangibility criteria. In other words, we plan on developing a simulation of the operations room and platform that need to be managed remotely. The virtual prototype will use data available from oil and gas companies existing test room and platform.

Our HCD approach is also scenario-based, starting with the development of an ontology to provide declarative scenarios defining agents and their resources, and procedural scenarios defining agents' roles and functions.

ONTOLOGY DESIGN

Infrastructures such as oil and gas platforms are complex systems that need to be more explicitly describe, since they generate a large amont of data every day. Platforms requires numerous operators performing various and complex tasks. Describing such infrastructures and their operations requires a deep understanding of the interfacing of operator's tasks, as well as underlying organizations [START_REF] Boy | Human-centered design of complex systems: An experience-based approach[END_REF].

Using an ontology to describe a platform operation will enable us to decrease ambiguity in this collaborative work.

Indeed, it will provide the design team with a shared and explicit understanding of stuctures and functions (e.g,vocabulary used, constraints) usefull for operating a platform and design its related operations room [START_REF] Chum | Use case: Ontology-driven information integration and delivery: A survey of semantic web technology in the oil and gas industry[END_REF].

Functions are represented by their role, context of validity and resources that are necessary to accomplish them.

Resources are in turn represented as system (i.e structure and function) therefore the approach is recursive. The key issues will be identification of the appropriate level of granularity and recursion that fits the purpose of the study. Consequently, key functions are defined and allocated to robots and human operators in the operations room with a special focus on cooperation rules that defined the articulation between the various functions. After several iterations we expect to have emergent functions which will have to allocate on an appropriate way to the robots or the operators. This cannot be done without domain expertise and experience. This is the reason why we are intimately working with oil and gas experts in a participatory way. We expect several iterations to reach an acceptable ontology of the domain. We expect to have an ontology to be presented at HSI 2019.

DISCUSSION

To gather the data, we are currently performing a literature review on what oil and gas companies are doing on the subject, and more precisely gather current models and experimental results. This research work is carried out in collaboration with an oil and gas company using an experimental platform. This review will be complemented by subject matter expert's interviews.

Then, thanks to a better knowledge of platform operations we will be able to iterate on structural and functional ontologies in order to identify and allocate functions. We are also gathering data on the different existing digital tools inside the company. We want to create the new interface based on current tools. Indeed, to be efficient the future interface has to fit with the existing tools used by the other entities of the platform such as the current human organization. This is a guideline we want to follow in order to optimize the acceptance and the support around the future interface.

Consequently, we plan on building different scenarios. The prototype will be tested using these scenarios in normal situations as well as in abnormal and emergency situations using safety, efficiency and comfort criteria.

For example, remote control and management of a fleet of robots will be tested using a simulated platform on cases like battery autonomy or communication among the various agents (e.g, robots, human operators). We believe that going from a virtual simulator to a tangible prototype build from the ontology will improve understanding on function allocations, change management and more generally definition of the various structures and functions. Here the HCD approach will enable us to take into account human factors in our future developments. We expect each iteration of the prototype to significantly improve the overall safety.

CONCLUSION

This PhD is a part of a bigger project which aim to create a new generation of unmanned platforms. This is a radical change in the way of designing and operating these infrastructures. To better understand the structure and the functions of an offshore platform we decided to build an ontology. This is the first step of this research work. Then, over the three years we intend to design an HCD based operations room to manage the fleet of robots, but also establish the cooperation rules among the different agents.

Our goal is to investigate how the cooperation rules and emergent functions are key to the success of the robots' management. We intend to reach an automated planning to drive the fleet of robots. We will conduct experimentations, first on a virtual simulator and then on an experimental platform and as the robot's technology mature on real offshore platforms. Additionally, the result expected by the company is a technical specification on how to design an operations room and the interactions with other structures such as the control room and the SMART room.

Figure 1 :

 1 Figure 1: Relation between the different control entity in Total Eploration & Production (SMART room= tier I, HQ=tier II).

Figure 2 :

 2 Figure 2: High level structural ontology


H Lu

R Pacanowski

X Granier

Second-Order Approximation for Variance Reduction in Multiple Importance Sampling

← Light-based sampling BRDF-based sampling → Low to high glossy materials with five diffuse area light sources Glossy materials with high-frequency environment map lighting Figure 1: Our per-pixel second-order approximation of the variance leads to a new and automatic approach for balancing the number of samples between two different sampling strategies. Except for light sources, the inset images show the sample distribution for each pixel. The yellow corresponds to the default balance heuristic strategy [Vea98]. Compared to the balance heuristic, the variance is reduced by (Left) 26% and (Right) 20% in average (14% and 11% for the standard deviation).

Motivation and Previous Work

The computation of physically realistic shading [Kaj86] for a position p viewed from direction o relies mostly on the estimation of the following integral:

L( p → o) = Ω ρ(o, ω) cos θ V( p, ω) L(ω → p)dω
where Ω is the unit hemisphere, ρ(o, ω) is the reflectance function, cos θ is the cosine factor, and L(ω → p) represents † e-mail: heqi.lu@inria.fr ‡ e-mail: romain.pacanowski@institutoptique.fr § e-mail: xavier.granier@institutoptique.fr the radiance coming from direction ω. For the sake of simplicity, we denote the whole integrand by

f(p, o, ω) = ρ(o, ω) cos θ V(p, ω) L(ω → p).
The main trend to compute such integral is to use Monte Carlo methods where the estimation of a reflected radiance L(p → o) is computed from a set of N samples:

L(p → o) ≈ 1 N N n=1 f( p, o, ω n ) p(ω n ) (1)
In Equation (1), p(ω n ) is a Probability Density Function (PDF), the closer it matches the numerator of the Equation the lower the number of samples N will be required to con-verge to the solution. Although the best matching is reached when p is proportional to f(p, o, ω), it is hard to obtain an exact integrable analytical form in most cases.

A lot of work has been dedicated to derive an efficient sampling strategy for each component, or a subset, of the function f( p, o, ω) based on light [ODJ04,HSK * 05,EKÖ12], or BRDF [START_REF] Ashikhmin | Distribution-based BRDFs[END_REF] or BRDF corrected by the cosine factor [PCS * 12]. For visibility, since no analytical form exists, precomputation [GH06] is generally required. In general, a product cannot be accurately approximated with only one of its components.

A better PDF can be obtained by an approximation of the whole integrand. Bidirectional Importance Sampling techniques [BGH05, TCE05] approximate this product on a preliminary sampling (either BRDF-based or light-based): a weight is computed for each sample according to the shading functions. Then, a subset of these samples is selected by using these weights. A potential problem is due to the oversampling needed to perform the second-step (resampling): some generated samples will not be used for the final estimator. Wang Compared to these approaches, Multiple Importance Sampling (MIS) [Vea98] is still a simple and efficient way to combine different sampling techniques by first balancing the number of samples between the different strategies and second combining them into a weighted estimator (balance, power, maximum heuristics [Vea98] or α-max heuristic [START_REF] Georgiev | Importance Caching for Complex Illumination[END_REF]). Despite the average improvement over the use of a unique strategy, the optimal balancing may differ from pixel to pixel in an unpredictable way [OZ00]. To reduce this problem, Pajot et al. [PBPP11] have introduced the empirical notion of representativity that estimates the concentration information for BRDF or photon maps. Intuitively, narrow lobe-shaped PDFs will request more samples. General guidelines to develop new representativity functions are introduced, but problems may occur when multiple concentrations exist such as in environment maps. Therefore, our work differs on the following points. First, we do not need to introduce a dedicated representativity function when introducing a new sampling strategy. Second, we do not make any assumption on the shape of the PDFs, which is difficult to achieve on generic environment maps. Third, our balancing is completely done per-pixel and takes into account the local shading configuration.

Contributions In this paper, we introduce a second-order approximation for variance reduction when using MIS approaches. We demonstrate that our approach leads to a new and automatic way to distribute samples between different strategies. We show that for our test scenes and for direct lighting, our approximation also improves the average variance, validating its accuracy. We also demonstrate that we can use our approach for offline rendering with a better efficiency compared to previous balancing techniques. Its accuracy also permits to visualize what should be the dominant strategy for future investigations.

Theoretical Variance Reduction

To estimate the integral of a function L = f(ω) dω using random samples {ω i=B|L,n=1..N i } from two PDFs p B (for BRDF-based strategy to generate N B samples) and p L (for light-based strategy to generate N L samples), Veach [Vea98] has introduced the following MIS primary estimator

L N L ,N B = i=B|L 1 N i N i n=1 w i ω i,n f ω i,n p i ω i,n (2)
where w i (ω i,n ) is a weighting function. For balance heuristic,

w i ω i,n = N i p i ω i,n N B p B ω i,n + N L p L ω i,n
.

By denoting N = N B + N L (N is the total number of samples) with N B = αN, N L = (1 -α)N, α ∈ [0, 1] and as pointed by Georgiev et al. [START_REF] Georgiev | Importance Caching for Complex Illumination[END_REF], this estimator is equivalent to the secondary estimator

L N,α = 1 N N n=1 f (ω n ) α p B (ω n ) + (1 -α) p L (ω n ) . (3)
This is an estimator for the Defensive Importance Sampling strategy [START_REF] Hesterberg | Weighted Average Importance Sampling and Defensive Mixture Distributions[END_REF] where a set of N samples ω n is generated according to α p B +(1-α) p L . In this paper, we focus on minimizing the variance of this estimator to improve the sampling quality.

Second-Order Approximation of Variance

Finding the best α that minimizes the variance of L N,α (i.e., V L N,α ) is equivalent to minimize the sampling variance of the strategy (i.e., V L 1,α ) since

V L N,α = 1 N V L 1,α .
If α p B +(1-α) p L leads to an unbiased strategy for all α (this is the case when both p B and p L generate unbiased samples), the expected value of L 1,α is independent of α since, by definition of unbiased techniques, E L 1,α = L. Minimizing the sampling variance is therefore similar to

minimize E L 2 1,α since V L 1,α = E L 2 1,α -E L 1,α 2 = E L 2 1,α -L 2 .
Nonetheless, the analytical form of the minimum for such a function is too complex to obtain. Therefore, we approximate the problem using a second order Taylor expansion around α = 1/2:

E L 2 1,α f 2 p -(2α -1) f 2 ∆p p2 + (2α -1) 2 f 2 ∆p 2 p3
where p = (p B + p L )/2 and ∆p = (p Bp L )/2. We demonstrate (cf. the derivation in the supplemental material) that this quadratic objective function is minimized when

α = 1 4 2 + f 2 ∆p p2 / f 2 ∆p 2 p3 (4)
We do a Taylor expansion around α = 1/2 since it ensures that the best approximation is centered in the definition domain of α, which is [0, 1]. As discussed in Section 2.3, when the best sampling strategy is to use a unique strategy (i.e., α = 0 or α = 1), our approximation becomes less valid. However, as demonstrated in the Section 3, our estimation of α still reduces the variance compared to the default balance heuristic.

Estimation of α

Despite the fact that we have an analytical formula (cf. Equation 4) to compute what would the best α according to a second-order approximation of the sampling variance, two numerical integrations have to be computed. For this purpose, we use a MIS approach by classically selecting the same number of samples from each strategy, and combining them with balance heuristic. Then, the two integrals are estimated using M samples:

f 2 ∆p p2 1 M M m=1 f(ω m ) p(ω m ) 2 ∆p(ω m ) 1 p(ω m ) f 2 ∆p 2 p3 1 M M m=1 f(ω m ) p(ω m ) 2 ∆p 2 (ω m ) p(ω m ) 1 p(ω m ) (5)
Therefore, like Bidirectional Importance Sampling techniques and oppositely to [PBPP11], we compute and make use of the evaluated shading function on the generated samples: f(ω m ). However, instead of rejecting the samples, we use them to estimate the radiance as well.

Theoretical Accuracy and Improvement

Since our approach is based on an approximation, it has limited accuracy. We estimate its accuracy for two cases: perfect mirror BRDF where α has to be 1 and Dirac light source where α has to be 0. For highly specular cases, BRDFs are zero in almost every direction except in a small direction domain. In this domain, p B (ω) is very large, therefore, ∆p and p are well approximated by p B (ω). One can demonstrate (cf. the supplemental material) that α = 3/4 instead of α = 1. Similarly, with extremely directional light sources, α becomes equal to 1/4 for our approximation whereas α = 0 is expected. Note that 1/4 and 3/4 are not bounds of our estimation, but theoretical values for two selected cases. This demonstrates that, in these two cases, we cannot find the optimal value for α. However, our estimated α still clearly indicates the dominant strategy.

We demonstrate (cf. supplemental material) that our variance reduction is proportional to |2 α -1|:

V L 1,α -V L 1,1/2 ≤ |2 α -1| V L 1,1/2 + L 2 . ( 6
)
The closer the estimated α is to 1/2, the less efficient becomes our approach.

Numerical Validation

We have implemented our α estimation into PBRT [PH04] and tested our technique on many different scenes (cf. Figures 1 and 2 and to the supplemental material for the full set). All the results are computed using 4 camera rays per pixel. For each camera ray, we use the default PBRT approach and sample uniformly all light sources and accumulate the contribution of each light source to estimate the final radiance. In the following, we will indicate the number of samples per light source.

Variance Reduction

To demonstrate the limited accuracy of our approach, we compare (cf. Table 1) the use of a reliable estimation of α, which is computed using M = 4096 samples for each light source, against different sampling and combination strategies: only light-based importance sampling, only BRDFbased one, and the half-half strategies that use the same number of samples between the two sampling techniques, combined with balance, power, or maximum heuristics. We do not compare with the α-max heuristic [START_REF] Georgiev | Importance Caching for Complex Illumination[END_REF] since it requires additional knowledge about which strategy achieves more often a better sampling than the others.

As shown in Table 1, in most cases our technique reduces the variance compared to previous methods. As discussed in Section 2.3, since our second-order approximation is done around α = 1/2, the approximation is getting worse for α = 0 or α = 1. Therefore, we cannot guarantee to detect correctly if using only light-based or BRDF-based strategy is the best solution. For example in scene 2 only light-based sampling performs better in average, and in scene 9 only BRDF-based sampling is better. However, our approach is always better than default balance/power/maximum heuristics: this demonstrates that our second-order approximation is sufficient to improve (sometimes slightly) these strategies. The improvements may be in average since, for pixels where the best α is 1/2, our approach does not improve anything (cf. Equation 6). Moreover, selecting either lightbased or BRDF-based requires an a priori knowledge, which is unavailable in most practical cases, but our α estimation provide an indication of what may be the dominant strategy.

Convergence Speed and Clamping Interval for α

For practical reasons, the number of samples to estimate α should be as low as possible. In Figure 3 we investigate how many samples are required to bring a satisfying variance reduction. Depending on the scene, the number of samples per light source can be low (upper curve) but conservatively, at least 128 samples per light source are required for a good estimation of α that will reduce the variance of the L N,α estimator. We will use this number for the following tests.

We already know from Section 2.3 that our estimation is only an approximation of the best α. In order to investigate its limited accuracy in a more general context, we have tested (cf. supplemental material for details) the effect of clamping the estimated α. The main result of this experiment is that, for some scenes, the variance increases if the value of α is outside the interval [0.025, 0.975] (i.e., with a size of 0.95). Furthermore, this experience confirms two facts. First, the second-order approximation is not sufficient to capture some variance oscillations in the interval [0, 1] since clamping improves the results. Second, it also confirms that our estimation still provides a good hint of what is the dominant strategy. Finally, it justifies the clamping of α to [0.025, 0.975] for all the following results.

Practical Implementations and Results

Integrated α Estimation

In Section 3.1, we have demonstrated the accuracy of our α estimation with M samples. Moreover, instead of losing these M samples we would like to reuse them to compute the radiance L N,α . One solution would be to store and use them with the estimated α to compute the shading. However, this would require an extra-storage of size M per pixel. Therefore, we prefer to use a less optimal but simpler solution that reduces the memory footprint.

We first estimate α using a low number of M samples as in Equation 5. At the same time, we estimate a first radiance value L M/2,M/2 as in Equation 2 with the default balance heuristic. Once α is known, we estimate the second radiance value L α(N-M),(1-α)(N-M) and combine these two estimators:

L N = M N L M/2,M/2 + N -M N L α(N-M),(1-α)(N-M) (7)
With this formula, when α = 1/2, our estimator is exactly the same as the default balance heuristic one.

Variance Reduction The maximum expected variance reduction is the one obtained without any combination as in Section 3.1 or when N is very large compared to M (cf. the supplemental material). In most cases, the expected reduction will be lower than this maximum, but better than the default balance heuristic. Even when using M = N/2 our approach still preserves the variance reduction (cf. Table 2top). To visualize the variance reduction for each pixel, we compute the difference of variance between the default balance heuristic and our approach (cf. Figure 4). As shown ). We use N = 256 samples per light source for each method. Est. 7 refers to the estimator introduced in Equation 7where we use half of the total samples to evaluate α (M = 128) and the remaining half to evaluate the radiance with the estimated α. Efficiency [Vea98] is the inverse of the product between variance and rendering time.

by the preponderance of the red color, our method outperforms the default balance heuristic for most pixels. When our technique is worse (green pixels), the value of α oscillates around 1/2 (cf. the inset image in Figure 1-left): this illustrates where slow convergence for α-estimation takes place.

Efficiency and Computation Time

We have also investigated the overhead of the required α estimation on an Intel i7-3930K@3.2 GHz PC. This overhead takes place only during the first step and is consistently about 1% of the rendering time. This comes from the fact that most of the rendering cost is due to shading computation and PDF evaluation: the estimation of α, based on Equation 5, simply reuses these values. That is also why the fastest strategy is either lightbased or BRDF-based sampling (cf.Table 2).

We have computed the efficiency [Vea98] of the sampling strategies: as shown in supplemental material, for all tested scenes our strategy outperforms the previous ones (balance, power and max heuristics). Moreover as shown in Table 2, for some scenes (e.g., 10 and 11), our method is even better than the two extreme strategies: BRDF-based or light-based sampling. Figure 6 shows that for the same rendering time our approach is slightly better for Lab error (1.51 vs 1.57) and estimator variance V[L N,α ] (1.99 10 -4 vs 2.22 10 -4 ).

GPU Implementation

As shown in the companion video, the low overhead of our approach is suitable for a GPU implementation. It could help exploring new balancing strategies for dynamic scenes. For this purpose, we have implemented the two-step approach, described in the previous section, into a full dedicated GPU solution for dynamic environment maps [LPG13] lighting. The solution is implemented on a NVIDIA 580 GTX with 1.5 GB of memory. For one environment map and without any visibility computation, we achieve a frame rate of 67 fps with 256 samples per pixels at a 1024 × 768 resolution. Finally, Figure 5 and the companion video illustrate that our approach is perfectly suited for dynamic scenes where it is difficult to know a priori the scene characteristics. 5 Final Discussion and Future Work Accuracy of α Estimation As pointed out in Sections 2.3 and 3.2, the main limitation of our approach is due to the second-order approximation of the variance around α = 1/2. We have investigated third-order approximation but there is generally no real solution to the objective equation. In the case of forth-order approximation, the theoretical upper bound is only slightly improved to α 0.8 at the price of a larger computational cost. Finally, we have shown that the use of a non-converged estimation of α may lead to some variance improvements.

Despite these limitations and since our technique exhibits some consistent improvements for variance reduction, we believe that it might be a good framework for future studies on balancing criteria. We think that our second-order approximation provides a good trade-off between accuracy and computational cost. It may also be used to estimate α progressively using a non-linear optimization method.

More Sampling Strategies

We have experimented our approach for balancing only between two strategies that do not require a precomputation step. The same approach might be use to combine them with other strategies such as the ones based on Photon Mapping as in [PBPP11] or visibility-based ones [GH06]. For more than two strategies, the minimization of the second-order approximation will result in solving a linear system to find the strategy weights.

Since our approach reduces the sampling variance, it can also benefit to Bidirectional Importance Sampling strategies.

Default balance heuristic

Our combined estimator Reference solution (32768 samples, 9163s)

Conclusion

In this paper, we have introduced a second-order approximation of variance for Multiple Importance Sampling. This approximation leads to an automatic distribution of samples between different sampling strategies. We have demonstrated that, for all our test scenes, our balancing technique reduces (sometimes slightly) the variance compared to previous MIS approaches and outperforms them as well in terms of efficiency. Finally, we have also shown that it fits into existing MIS approaches and that it can be implemented on GPU. We believe that our approach will help further investigations on how to develop improved balancing strategies.

  et al. [WA09] improved the techniques by combining lightcuts [WFA * 05] with a BRDF-based sampling to reduce the initial bias caused by the initial distribution. Rousselle et al. [RCL * 08] have extended these techniques by taking into account visibility. More generally, precomputing conservative approximations of lighting environment and BRDF helps computing dynamically PDFs based on the product of the lighting and BRDF. For this purpose, Cline et al. [CETC06] split the environment map according to BRDF peaks computed from BRDF-based importance sampling. To be more conservative, Clarberg et al. [CAM08b] use a wavelet representation of the environment map, a wavelet approximation of the BRDF, and a fast computation of their product. These techniques require dedicated representations to support a per-pixel dynamic computation of the importance sampling structure. Although photon maps can also be used (e.g., [PBPP11]), in this paper we focus on a technique that does not required any additional storage.

  complex vis. Diffuse BRDFs, complex vis.Measured glossy BRDFs High-frequency env. map Low-frequency env. map Low-frequency env. map High-frequency env. map + 1 point and 1 directional light sources

Figure 2 :

 2 Figure 2: Subset of test scenes, ranging from diffuse (10) to mirror (8) materials including complex visibility (9-10) with different types of illumination. These images are computed using the estimator of Eq. ( 7) with N = 256 and M = 128. Since only one sample is required for point and directional light sources, their contribution are added separately and are removed from the variance computation.

Figure 3 :

 3 Figure 3: Plot of the variance V[L N=256,α ] for increasing number of samples M used to estimate α. The plot is normalized by dividing the variance value by the one obtained when estimating α with M = 4096. This illustrates the convergence of the α estimation.

Figure 4 :Figure 5 :

 45 Figure4: Per-pixel comparison for variance reduction. This figure shows the difference of variance between the default balance heuristic and our method. Red corresponds to pixels where our method is better whereas Green corresponds to those where the default balance heuristic is better. Black means that variances are equal.

Figure 6 :

 6 Figure 6: Equal time (72ms) comparisons for scene 11. Our solution is slightly smoother and also closer (1.51 vs 1.57 mean Lab error) to the reference solution than the default balance heuristic (cf. supplemental material for more comparisons). For example, Burke et al. [BGH05] use either BRDF-based or light-based strategies as initialization step. Improved sampling would certainly improve it. Similarly, our approach can serve as a support for Control Variate techniques (e.g., [CAM08a]) since they can be used on top of state-of-the-art schemes for importance sampling.

Table 1 :

 1 Comparisons, for each scene, of different balancing methods in terms of average sampling variance. The average variances are computed over all the pixels using the same number of samples N = 256 for each light source.

	Method	1	2	8	Scene 9	10	11
	BRDF	67.3 4597 2.070 0.0198 139.75 0.378
	Light	0.47 2.56 0.036 118.20 0.776 0.127
	Balanced heur. 0.90 4.76 0.043 0.250 0.402 0.055
	Power heur.	0.99 4.87 0.046 0.255 0.440 0.059
	Maximum heur. 1.24 5.11 0.061 0.256 0.618 0.075
	Preprocessed α 0.42 2.95 0.033 0.095 0.301 0.045

Table 2 :

 2 Average variance, rendering time and efficiency for different sampling stratetgies (for the full table, read the supplemental material

		Method	1	2	8	Scene	9	10	11
	Var.	Est. 7	for Light and BRDF, cf. Table 1 0.66 3.88 0.037 0.1700 0.359 0.051
	Time (s)	BRDF 158.6 138.1 Light 299.7 102.8 Est. 7 250.8 128.3	36.5 34.2 34.5	49.2 27.1 40.9	354 178 281	91.0 53.0 72.0
	Efficiency	BRDF 0.0001 0.0000 0.0132 1.0265 0.0000 0.0291 Light 0.0071 0.0038 0.8122 0.0003 0.0072 0.1486 Est. 7 0.0060 0.0020 0.7834 0.1438 0.0099 0.2723

© 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd

Acknowledgments

We would like to thank Laurent Belcour for his suggestions as well as Petrik Clarberg for sharing scene 2. Heqi Lu's PhD scholarship is funded by the Région Aquitaine. This research has been supported by the ALTA project (ANR-11-BS02-006).


Syed Muhammad

All-E-Raza Rizvi
email: allerazarizvi@gmail.com

Marie-Ange Véganzonès-Varoudakis

Catherine Araujo-Bonjean

Keywords: Conflict, Fragile States, Economic Reforms, Education, Democracy, Institutions

In this article, we use Fixed Effect Poisson Regression (FEPR) with robust standard errors, to study the economic, social, and institutional determinants of internal conflict in 58 fragile states over the period 2004 to 2017. We show that effective institutions (measured by judicial effectiveness) and higher incomes can help reduce conflict in these countries. By contrast, democracy does not seem to mitigate violence, with democratic experiences generally showing an increase in conflicts in fragile countries. It also appears that human capacity development does not contribute to conflict reduction. This implies that fragile states must first improve the social, economic, and institutional conditions of their population before they can reap the benefits of political reforms and of education. The same is true for economic reforms in the context of globalization, which also do not seem to help reduce violence in fragile countries.

Introduction

Over the past decade, the Uppsala Conflict Data Program (UCDP) has recorded an upward trend of violence in the world. The number of armed conflicts increased from 33 in 2006 to 49 in 2016. The number of terrorist actions reached a peak in 2014, with the death of more than 100,000 people that year (Allansson et al, 2017). In addition to human suffering, civil strife causes considerable damage to economies due to its negative effects on infrastructure, public spending, political stability, foreign direct investment, trade, and growth. As a result, while extreme poverty is declining worldwide, it is increasing in fragile countries affected by conflicts (World Bank, 2018). Conflicts also have a destabilizing effect on neighboring countries, with political instability in a country threatening the stability of the entire region (Teydas et al, 2011). Civil unrest in Syria, for example, has led many other states and international organizations to participate directly in the conflict. If left unchecked, nearly half of the world's poor will live in fragile countries facing conflict situations by 2030 (World Bank, 2018), and the expansion of armed conflict around the world will cause more harm to populations [START_REF] Pettersson | Organized Violence, 1989-2018 and Peace Agreements[END_REF].

Several studies have suggested that armed conflict and terrorism1 occur in fragile countries which have poor social, economic, and political conditions (World Bank, 2011 and[START_REF] George | State Failure and Transnational Terrorism: An Empirical Analysis[END_REF]. [START_REF] Collier | The Bottom Billion: Why the Poorest Countries are Failing and What Can be Done About it[END_REF] states that "seventy-three percent of people of the bottom billion have recently been through a civil war or are still in one". Stewart (2002) notes that most of the economies with the lowest level of human development have been confronted with civil wars over the last three decades. [START_REF] Ostby | Polarization, Horizontal Inequalities and Violent Civil Conflict[END_REF] shows that poverty, inequality, and dependence on natural resources are at the root of most conflicts in the world. [START_REF] Lai | Draining the Swamp": An Empirical Examination of the Production of International Terrorism, 1968-1998[END_REF] states that low income levels and high income inequality are positively associated with terrorism. Countries with fragile political conditions are also more vulnerable to domestic violence. [START_REF] Coggins | Does State Failure Cause Terrorism? An Empirical Analysis (1999-2008)[END_REF] found that political collapse has a positive correlation with terrorism. [START_REF] Newman | Weak States, State Failure, and Terrorism[END_REF] and [START_REF] Piazza | Incubators of Terror: Do Failed and Failing States Promote Transnational Terrorism[END_REF] confirm that it is easier for terrorist groups to establish their organizations in failed sates.

However, economic growth and wealth are not always a source of peace and non-violence in fragile countries, as [START_REF] Caruso | The Socio-Economic Determinants of Terrorism and Political Violence in Western Europe (1994-2007)[END_REF] explain in their theory of "immiserizing modernization". When growth changes the distribution of wealth, as described by [START_REF] Olson | Rapid Growth as a Destabilizing Force[END_REF], it can lead to social and political unrest fueled by groups of people who lose from the change. If perceived as a threat, economic reforms may lead to unrest as well, as explained by [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] for globalization. [START_REF] Gur | Why Men Rebel[END_REF] confirms that when individuals feel economically disadvantaged, they may be willing to fight to change their situation. When inequalities create grievances among the poor, recruiting them to fight the government, in the hope of a better life, becomes easy for terrorist organizations.

Rational Choice theory provides an explanation for the emergence of civil conflicts in fragile countries by suggesting that human actions are based on the "calculation of risk, cost and incentive" (Teydas et al, 2011). [START_REF] Wintrobe | Extremism, Suicide Terror, and Authoritarianism[END_REF] assumes that extremists are rational and choose the best way to achieve their goal. [START_REF] Becker | Crime and Punishment: An Economic Approach[END_REF] argues that individuals commit a crime if the expected benefits outweigh the costs. [START_REF] Caplan | Terrorism: The Relevance of the Rational Choice Model[END_REF] suggests that terrorist activities are the product of a cost-benefit analysis. The benefits derived from these activities are increased power and wealth. Similarly, the "opportunity-based approach" indicates that the most important factor in becoming a rebel is the expectation of personal gain or reward (Teydas et al, 2011). [START_REF] Collier | Greed and Grievance in Civil War[END_REF] argue that "rebellion can occur when lost income is low". [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] suggest that if the opportunity cost of terror is high, people will choose material wealth rather than mental reward.

In this study, we explore the social, economic, and institutional determinants of conflict in 58 fragile countries. The goal is to identify the explanatory factors of violence so that governments can reduce the sources of instability. The literature shows that countries with poor economic, social, and political conditions are more exposed to the risk of conflict. It may be thought that governments counter these risks by improving the standard of living of the population. [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] and [START_REF] Burgoon | On Welfare and Terror: Social Welfare Policies and Political-Economic Roots of Terrorism[END_REF] show that public spending and social protection policies reduce violence by improving people's socioeconomic conditions. [START_REF] George | State Failure and Transnational Terrorism: An Empirical Analysis[END_REF] suggests that in failed states, an effective counter-terrorism measure is to build reliable institutions. Providing better living conditions for citizens, equal opportunities to generate wealth, investing in human development, political rights, and effective institutions, could help governments to decrease the people's grievances and increase the opportunity cost and risk of violence, thus isolating the terrorists from their supporters.

In this study, we use [START_REF] Tavares | The Open Society Assesses its Enemies: Shocks, Disasters and Terrorist Attacks[END_REF] definition of terrorism -"the premeditated use, or threat of use, of extreme violence to obtain a political objective through intimidation or fear directed at large audience". We use the annual number of conflict-based incidents from the Global Terrorism Database (GTD) as a proxy for conflict. We analyze the development of violence for 8 different groups of countries from 2004 to 2017: (i) Total sample of fragile countries, (ii) Islamic fragile states, (iii) fragile countries with more than one main religion 2 , (iv) States affected by major conflicts 3 , (v) Middle East and North African (MENA) fragile countries, vi) Asian fragile countries, vii) African fragile countries, viii) Latin American fragile countries. These countries were selected from the Fund for Peace (FFP) database, which publishes annually a fragility index for 178 countries around the world. In the empirical part of the study, we show that effective institutions (measured by judicial effectiveness) and higher incomes can help to reduce conflict in the most fragile countries. However, democracy does not seem to mitigate violence, with democratic experiences generally showing an upsurge of fighting in fragile countries. It also appears that the development of human capital does not contribute to the reduction of conflicts, which implies that fragile states must first improve their social, economic and institutional conditions before they can benefit from the fruits of reforms and of education of populations. The same conclusion can be drawn for economic reforms in the context of globalization. These reforms do not seem to help reduce violence in fragile countries.

These results are important in the context of the increasing number of conflicts around the world, which undermine progress in improving living standards and reducing poverty in fragile countries. They help to understand the difficulties faced by governments in reducing violence in their country and point to ways for a progressive approach to long-term conflict resolution. The results are robust because they are tested on several panels of countries of different characteristics and based on different appropriate quantitative methods.

The rest of the article is organized as follows. Based on the literature, Section 2 summarizes our theoretical framework and the reasons that motivate violence in fragile countries. Section 3 presents our model of conflict and defines the variables used in the analysis and the data sources. Section 4 highlights 2 Countries where more than 10% of people belong to a different religious group 3 Countries which have 5 or more terrorist events in at least one year.

the methodological aspects related to our estimates of violence. Section 5 presents the results of the empirical analysis for our various samples of countries. The last section concludes with our main findings and policy recommendations.

Conflict Motivation: A Theoretical Framework

Conflict motivation can be studied using the Rational Choice Theory framework. Rational behavior implies that individuals perform a cost-benefit analysis before acting. In the case of terrorism, the expected benefits of opposition to government include a redistribution of power and wealth; the costs include a reduction in resources and sanctions (Frey and Luechinger, 2003;Harrisson, 2006).

Sanctions can be legal or military. LaFree et al (2009) state that these sanctions can have two contradictory effects on violence: a "deterrent" effect, or an "amplification" effect. Deterrence models assume that the threat or imposition of a sanction changes the behavior of individuals. According to [START_REF] Nagin | Enduring Individual Differences and Rational Choice Theories of Crime[END_REF], deterrence works when the expected benefits of illegal actions are lower than the expected costs. LaFree et al ( 2009) define two types of deterrence: "specific" deterrence which dissuades individuals from repeating their act, and "general" deterrence which discourages members of a society from opting for a given action by fear of possible sanctions. [START_REF] Dezhbakhsh | Does Capital Punishment Have a Deterrent Effect? New Evidence from Post Moratorium Panel Data[END_REF] confirm that the probability of arrest, conviction, or execution results in a significant decrease in the crime rate of a population.

On the contrary, [START_REF] Higson-Smith | A Community Psychology Perspective on Terrorism: Lessons from South Africa[END_REF] puts forward the idea that conflict may get worse as a result of government sanctions. This is the case, for example, when terrorists use the public's potential for sympathy to recruit new members, or when terrorists become more radicalized by sanctions. [START_REF] Sherman | Defiance, Deterrence, and Irrelevance: A Theory of the Criminal Sanction[END_REF] explains that deterrence or amplification effects depend on how offenders accept sanctions. If they do not consider them to be legitimate, it will create new grievances. The hostile reaction to sanctions may be "specific" when offenders view the sanctions as unfair and continue their activities, or "general" when society considers the sanctions unjustified and then supports activists. If, in a society, the legal system is ineffective and the activists consider the sentence illegitimate, they can seek support from the general public to legitimize their actions. People who have grievances, but who do not trust the legal system, may also find it legitimate to achieve justice by force.

With regard to the cost/benefit ratio of terrorist action, [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] focus on the trade-off between loss of material wealth (the opportunity cost of terrorist action) and mental reward (the benefit of terrorism). They suggest that if the opportunity cost of terror (such as the likelihood of sanctions or loss of income) outweighs the benefit, people will choose to preserve their material wealth rather than the mental reward of a terrorist action. On the other hand, in the case of poverty or a slowdown in economic activity, as the relative price of material wealth increases, citizens will opt for conflict more easily, seeing it also as a means of imposing change in addition to seeking a mental reward. This may also be the case after economic reforms. [START_REF] Caruso | The Socio-Economic Determinants of Terrorism and Political Violence in Western Europe (1994-2007)[END_REF], in their theory of "immiserizing modernization", explain that reforms can lead to a decrease in the wealth of some stakeholders, which can lead to more conflicts because of the lower opportunity cost of violence for these categories. [START_REF] Wintrobe | Extremism, Suicide Terror, and Authoritarianism[END_REF] confirms that trade reforms, and globalization in particular, can be seen as a threat of loss of income for part of the population. By limiting the economic opportunities of the affected population, in addition to reducing the opportunity cost of violence, economic reforms can create grievances against the government, thus increasing the risk of conflict [START_REF] Harrison | An Economist Looks at Suicide Terrorism[END_REF]. Violence in these cases can also be seen as a way to resist change. [START_REF] Blomberg | From (no) Butter to Guns? Understanding the Economic Role in Transnational Terrorism[END_REF] and [START_REF] Kurrild-Klitgaard | The Political Economy of Freedom, Democracy and Transnational Terrorism[END_REF], however, find an inverse relationship between trade reform and conflict, which would make reform an opportunity rather than a threat, reducing violence and promoting development. More generally, adverse socio-economic conditions can lead to violence by making conflicts more profitable because of potential positive spin-offs, particularly with regard to the redistribution of wealth, but also because of low direct costs, including the low cost of recruiting terrorists. [START_REF] Bernholz | Supreme Values as the Basis for Terror[END_REF] describes the ideological content of certain conflicts through the concept of "supreme values". These values refer to one or more objectives that are preferred above all others, and whose achievement is more important than any other value [START_REF] Wilkens | Suicide Bombers and Society: A Study on Suicide Bombers in Afghanistan and Pakistan[END_REF]. Black (2001) suggests that these extreme beliefs (e.g. religious) are based on deeply inculcated doctrines to achieve the goals of extremist groups [START_REF] Wintrobe | Extremism, Suicide Terror, and Authoritarianism[END_REF]. [START_REF] Bernholz | Supreme Values as the Basis for Terror[END_REF] states that people with supreme values, may want to implement these values by force. In this case, if the grievance concerns problems other than poverty, for instance injustice or unequal treatment of certain regions, ethnic groups, or religions 4 , an increase in wealth increases the resources for terrorist organizations and terrorist activities. [START_REF] Wintrobe | Extremism, Suicide Terror, and Authoritarianism[END_REF] adds that terrorist activities are based on a compromise between "autonomy" and "solidarity". A person can give up his beliefs (autonomy) to experience social belonging and solidarity.

Presentation of the Model and of the Variables

The Model

The equations used to study the determinants of conflict in fragile states are as follows:

Confit = α0 + α1 (GDPc it) + α2 (Edumit) + α3 (Openit) + α4 (Popit) + α5 (Contractsit) + α6 (Demoit) +Ɛt Eq (1) Confit = α0 + α1 (GDPc it) + α2 (Hit) + α3 (Openit) + α4 (Popit) + α5 (Contractsit) + α6 (Demoit) +Ɛt Eq (2)
Where Conf is the count data variable for measuring conflict, GDPc the logarithm of real GDP per capita, Edum the average years of education, H the human capital index, Open the indicator of trade openness, Pop the logarithm of population, Contracts the proxy for judicial effectiveness, and Demo the democracy variable. i is the cross sections index, t the time dimension and Ɛ the error term. α0 to α6 are the parameters to estimate.

The Variables

Annual Conflict-Based Incidents as Proxy for Internal Conflict

This study uses the annual conflict-based domestic incidents from the Global Terrorism Database (GTD, 2018) as a proxy for conflict as proposed by [START_REF] Enders | Domestic Versus Transnational Terrorism: Data, Decomposition, and Dynamics[END_REF]. The conflict-based incidents in the GTD codebook are defined as "the threatened or actual use of illegal force and violence by a non-state actor to attain a political, economic, religious, or social goal through fear, coercion, or intimidation". The time period for the annual data is from 2004 to 2017 (see descriptive statistics in Table A.1 in the Appendix).

GDP per Capita as Proxy for Income and Wealth

The empirical evidence for the impact of income and wealth on internal conflict yields mixed results. Some of the literature finds poverty and low income a cause of violence. [START_REF] Humphreys | Economics and Violent Conflict[END_REF] indicates that low resources increase the likelihood of civil wars. [START_REF] Collier | Greed and Grievance in Civil War[END_REF] show that low incomes increase conflict. By contrast, [START_REF] Caruso | The Socio-Economic Determinants of Terrorism and Political Violence in Western Europe (1994-2007)[END_REF] find a positive relationship between increased income and the number of people killed in conflict-based incidents. [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] and Shahbaz (2012) confirm that there is a positive correlation between increasing GDP per capita and increased violence. [START_REF] Piazza | Incubators of Terror: Do Failed and Failing States Promote Transnational Terrorism[END_REF] however does not find a significant association between the two variables. [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] and [START_REF] Lai | Draining the Swamp": An Empirical Examination of the Production of International Terrorism, 1968-1998[END_REF] show on their side that the use of the quadratic form of GDP per capita inverts the sign of the relation. They conclude that a country must go beyond a certain threshold of development to counter conflict by an increase in wealth. In this study, we hypothesize that economically disadvantaged people in fragile states develop grievances against their government, and that poor economic conditions make violence more likely because direct costs (including terrorist recruitment) and opportunity costs are low GDP per capita is our measure of income and wealth. The data comes from WDI (2017). For some countries, we collect data from national sources and other international institutions for missing values.

The study uses the logarithm of the variable in real terms (see the descriptive statistics in the Table A.1 in the appendix). We assume a negative influence of this variable on our variable of conflict.

Effective Judiciary as a Proxy for Deterrence

Countries with fragile institutions are vulnerable to violence (Ross 1993, Basuchoudhary and[START_REF] Basuchoudhary | On Ethnic Conflict and Origins of Transnational Terrorism[END_REF]. It is easier for terrorist groups to operate in states where institutions are weak [START_REF] Newman | Weak States, State Failure, and Terrorism[END_REF][START_REF] Piazza | Incubators of Terror: Do Failed and Failing States Promote Transnational Terrorism[END_REF]. People who have grievances and who do not trust the institutions may also find it legitimate to use force. If the justice system is effective and the penalties are perceived as just, the threat of punishment can change the behavior of individuals. [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] state that the possibility of punishment is a cost to terrorists. [START_REF] Dezhbakhsh | Does Capital Punishment Have a Deterrent Effect? New Evidence from Post Moratorium Panel Data[END_REF] confirm that the likelihood of punishment leads to a decrease in crime in a country. [START_REF] George | State Failure and Transnational Terrorism: An Empirical Analysis[END_REF] shows that in failed states building reliable institutions is a counter-terrorism measure.

We use the "Time for Enforcing Contracts" variable from the "Doing Business" database as an indirect indicator of the ineffectiveness of the judiciary. If the judiciary punishes in a timely manner, the population will be reluctant to use violence. On the other hand, if the justice system is ineffective and terrorists may not be punished, then it is easier for them to continue the conflict. If the justice system in a country is effective and citizens trust its decisions, it will deter terrorism (see descriptive statistics in Table A.1 in the Appendix). In this study, we assume a positive impact of the judicial ineffectiveness variable on conflict.

Education and Human Capital as Proxy for Human Development

Human development might be seen as a way to reduce violence. Higher human development can limit the risk of conflict by reducing people's grievances [START_REF] Bravo | An empirical analysis of terrorism: Deprivation, Islamism and Geopolitical Factors[END_REF]Kurrild-Kitgaard et al, 2006). Educated people may also be less likely to choose terrorism because they can use their own reasoning to form their own opinion. This is especially true in the case of conflicts based on supreme values where education can help develop critical thinking and reject extremism [START_REF] Ghosh | Can Education Counter Violent Religious Extremism?[END_REF]. Educated people can also use their knowledge to improve their economic and social situation [START_REF] Berrebi | Evidence About the Link Between Education, Poverty and Terrorism Among Palestinians[END_REF]. Advances in education thus increase the opportunity cost of civil conflict by providing better opportunities for people [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF].

At the empirical level, [START_REF] Hamilton | Dynamics of Terrorism[END_REF] note that illiteracy is positively correlated with terrorism. [START_REF] Collier | Greed and Grievance in Civil War[END_REF] and [START_REF] Azam | The Roles of Foreign Aid and Education in the War on Terror[END_REF] highlight the negative impact of education on conflict. However, [START_REF] Brockhoff | Great Expectations and Hard Times: The (Nontrivial) Impact of Education on Domestic Terrorism[END_REF], [START_REF] Berrebi | Evidence About the Link Between Education, Poverty and Terrorism Among Palestinians[END_REF], [START_REF] Testas | Determinants of Terrorism in the Muslim World: An Empirical Cross-Sectional Analysis[END_REF] and [START_REF] Nasir | Determinants of Terrorism: A Panel Data Analysis of Selected South Asian Countries[END_REF] show a positive relationship between education and conflict. [START_REF] Brockhoff | Great Expectations and Hard Times: The (Nontrivial) Impact of Education on Domestic Terrorism[END_REF] show that in countries where social, economic, political, and demographic conditions are unfavorable, education can exacerbate discontent. If access to education does not translate into the expected better life, it will increase frustration and conflict. People may consider joining terrorist organizations if career path returns are below expectations (Krueger, 2008). In addition, terrorist groups may have an interest in recruiting educated people, as this can increase the chances of success of their activities, as well as contribute to a better image for their propaganda in the media (Krueger and Maleckova, 2003).

We We assume that education provides people with more information and encourages them not to choose terrorism, as well as more economic opportunities which increases the opportunity cost of conflict. A negative sign in the equation is expected.

Trade Openness as Proxy for Economic Reforms

The influence of economic reforms on violence is another dimension studied in the literature. The impact of trade reforms and globalization has been the subject of discussion. Trade reforms can be a factor of growth and modernization of the economy [START_REF] Frankel | Does Trade Cause Growth?[END_REF][START_REF] Dollar | Institutions, Trade, and Growth[END_REF]. New opportunities created by trade can reduce the discontent of the population and increase the opportunity cost of violence, thus reducing the risk of conflict. [START_REF] Blomberg | From (no) Butter to Guns? Understanding the Economic Role in Transnational Terrorism[END_REF] and [START_REF] Kurrild-Klitgaard | The Political Economy of Freedom, Democracy and Transnational Terrorism[END_REF] find an inverse relationship between trade openness and conflict which would confirm that reforms can help reduce violence.

Another part of the literature, however, emphasizes the destabilizing effect of economic reforms. [START_REF] Caruso | The Socio-Economic Determinants of Terrorism and Political Violence in Western Europe (1994-2007)[END_REF] state that reforms can reduce the wealth of some stakeholders. [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] and [START_REF] Wintrobe | Extremism, Suicide Terror, and Authoritarianism[END_REF] confirm that globalization can be seen as a threat to part of the population. In this case, reforms can lead to political and social unrest fueled by groups of people who lose or fear losing because of change [START_REF] Harrison | An Economist Looks at Suicide Terrorism[END_REF][START_REF] Gaibulloev | Terrorism and Affinity of Nations[END_REF].

In this study, we assume that trade openness reduces violence and promotes a country's development. A negative relationship with conflict is expected. We use the ratio of exports plus imports to GDP (in real terms), as proxy for trade reform and globalization. The data are from National and International sources (see descriptive statistics in Table A.1 in the Appendix).

Democratic Accountability as Proxy for Democracy

The impact of the political regime on terrorism and conflict in a country is another dimension whose empirical evidence is contradictory. Some of the literature emphasizes that democratic regimes allow people to express their demands and be heard, thereby reducing the grievances they may have towards the government. This is the case of [START_REF] Eyerman | Terrorism and Democratic States: Soft Targets or Accessible Systems[END_REF] and Li (2005) who highlight a positive relationship between democracy and the absence of violence. However, other authors point out that it is easier and cheaper for extremists to engage in terrorist activities when they enjoy more civil liberties and political rights. For instance [START_REF] Li | Economic Globalization and Transnational Terrorism: A Pooled Time-Series Analysis[END_REF] and Rizvi and Véganzonès-Varoudakis (2019) note an increase of violence in fragile countries during democratic periods. [START_REF] Eubank | Terrorism and Democracy: What Recent Events Disclose?[END_REF] find that terrorism occurs more often in democracies than in more authoritarian regimes. Li (2005) and [START_REF] Muller | Income Inequality, Regime Repressiveness, and Political Violence[END_REF] demonstrate a non-linear relationship between political repression and violence.

We use the Democratic Accountability variable, derived from the International Country Risk Guide (ICRG), as an indicator of the type of regime, to explain internal conflicts in fragile states [START_REF] Howell | International Country Risk Guide Methodology[END_REF].

A high value indicates more democracy and vice-versa (see descriptive statistics in Table A.1 in the Appendix). We assume a positive relationship of the variable with the conflict variable for our different samples of fragile countries.

The role of Population

As well as the above variables we also study the impact of the size of a country's population on the development of conflicts in that country. Krueger and Maleckova (2003), Burgoom (2006), [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF], [START_REF] Piazza | Incubators of Terror: Do Failed and Failing States Promote Transnational Terrorism[END_REF] and [START_REF] Richardson | Relative Deprivation Theory in Terrorism: A Study of Higher Education and Unemployment as Predictors of Terrorism[END_REF] point out that more populated countries tend to have more violence. [START_REF] Gaibulloev | Terrorism and Affinity of Nations[END_REF] and [START_REF] Taydas | Why Do Civil Wars Occur? Another Look at the Theoretical Dichotomy of Opportunity Versus Grievance[END_REF] argue that it is difficult for governments to manage, serve, and respond to the demands of all in the case of large populations, particularly because of a great diversity. In this study, we assume a positive relationship between population and conflict in fragile countries. We use the logarithm of the WDI (2017) variable (see descriptive statistics in Table A.1 in the Appendix).

Estimation of the Model: Methodological Aspects

This study focuses on fragile countries which were selected from the Fund for Peace (FFP) database that publishes annually a fragility index by country: the Fragile States Index (FSI) 7 . We selected 58 countries for which the index was above 70 8 for the analysis. We analyze the development of terrorism from 2004 to 2017 for 8 different groups: (i) Total sample of fragile countries, (ii) Islamic fragile states, (iii) Fragile countries with more than one important religion 9 , (iv) States affected by major conflicts In order to be able to compare the results with the two human development proxies, we perform two sets of regressions incorporating Edum (one set, on the 58 countries of the initial sample (specification 1), another set, on the 51 countries of the PWT (specification 2)), as well as a third set of regressions including H on the 51 countries of the PWT (specification 3).

The Results of the Estimations

Table 3 presents the results for the total sample of countries, Table 4 for the Islamic States, Table 5 for the countries with more than one main religion, and Table 6 for the countries affected by major conflicts. The results for the regions are presented in the Appendix: Table A.3 for MENA, Table A.4 for Asia, Table A.5 for Africa and Table A.6 for Latin America.

For almost all of our specifications and our groups of countries, income, ineffectiveness of the justice system, and size of the population are correlated with the development of conflict in fragile states. These results corroborate the findings of [START_REF] Humphreys | Economics and Violent Conflict[END_REF], [START_REF] Collier | Greed and Grievance in Civil War[END_REF], [START_REF] Lai | Draining the Swamp": An Empirical Examination of the Production of International Terrorism, 1968-1998[END_REF], and [START_REF] Ostby | Polarization, Horizontal Inequalities and Violent Civil Conflict[END_REF], who show that low incomes are positively associated with violence. When poverty is high, disadvantaged people may develop grievances against their government. In this case, the use of violence is more likely as the opportunity cost of terror and the cost of recruiting terrorists are low. As a result, income is a policy variable that governments can use to reduce violence in fragile states.

Our results also show that another way to reduce conflict in fragile countries could be to improve institutions, especially the justice system. Our results are consistent with those of LaFree et al ( 2009) and 11 For more details on count data regression see [START_REF] Cameron | Regression Analysis of Count Data[END_REF] 12 See George (2018); [START_REF] Piazza | Incubators of Terror: Do Failed and Failing States Promote Transnational Terrorism[END_REF] in particular for Negative Binomial Regression 13 Regressions using the Negative Binomial Regression (NBR) method were also performed for our analysis. The results are consistent with those obtained with fixed effect Poisson regressions (FEPR) on the orientation of the relationship between the explanatory variables and the internal conflicts, except in the case of the trade openness variable which has less variation and has a positive influence on violence. The results are not shown here due to space constraints, but are available upon request.

14 Data for Azerbaijan, Belarus, Guinea, Guyana, Lebanon, Libya and Moldova are not available for the Human Capital Index (H) in the PWT. [START_REF] Dezhbakhsh | Does Capital Punishment Have a Deterrent Effect? New Evidence from Post Moratorium Panel Data[END_REF] who confirm the dissuasive effect of the threat of sanctions. According to [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF], the possibility of punishment by the government increases the opportunity cost and risk of violence. If the legal system punishes in a timely manner, the population will be reluctant to resort to violence and terrorists will be reluctant to continue the conflict. More generally, our results confirm that countries with fragile institutions are vulnerable to violence (Ross 1993, Basuchoudhary and[START_REF] Basuchoudhary | On Ethnic Conflict and Origins of Transnational Terrorism[END_REF].

With regard to the population size variable, our results are in line with those of [START_REF] Gaibulloev | Terrorism and Affinity of Nations[END_REF] and [START_REF] Taydas | Why Do Civil Wars Occur? Another Look at the Theoretical Dichotomy of Opportunity Versus Grievance[END_REF] who show that fragile countries with big populations are more exposed to violence.

Our results for education and democracy are less stable than those obtained for population, institutions, and income. Education and democracy correlate closely with conflict for the total sample, the Muslim states, and the countries with more than one main religion, but correlate less for the regions 15 . This may be due in part to the smaller sample size, as well as to the fact that some regions are less affected by conflict (e.g. Latin America). Education, however, appears to be a more robust dimension than democracy in explaining violence (for both human capital indicators or for the human capital index only).

Our results also show that the education and democracy variables appear to be positively related to conflicts. The impact of these two factors on violence has been discussed in the literature. Our findings confirm that education in fragile countries does not translate into an opportunity to improve living conditions or as a means of reinforcing critical thinking against terrorism, as in [START_REF] Berrebi | Evidence About the Link Between Education, Poverty and Terrorism Among Palestinians[END_REF] and [START_REF] Brockhoff | Great Expectations and Hard Times: The (Nontrivial) Impact of Education on Domestic Terrorism[END_REF]. In a state with adverse social, economic, and political conditions, education can increase frustration if the situation of educated people does not improve, especially as they are more aware of the limits of their government. This conclusion can be extrapolated to democracy, which gives more voice to discontented groups, thus increasing violence, as in [START_REF] Eubank | Terrorism and Democracy: What Recent Events Disclose?[END_REF] and [START_REF] Li | Economic Globalization and Transnational Terrorism: A Pooled Time-Series Analysis[END_REF]. This means that when fragile countries go from autarchy to democracies, they face more conflict. Our results mean that education and political rights do not have the desired effects in fragile states which must first improve the social, economic and institutional conditions of their population before they can benefit from political reforms and education. This is also the case for economic reforms, as our trade openness variable shows no impact on violence in most of our country samples (except the MENA and Africa regions), as in [START_REF] Gaibulloev | Terrorism and Affinity of Nations[END_REF].

A more detailed analysis shows interesting differences between country groups. The impact of income, while relatively stable in most of our samples, seems to be stronger in countries with more than one major religion. This is an interesting finding that shows that public policies aimed at improving the income and living conditions of people would be more effective in these particularly fragile countries. This may also be the case for our Asian region, for which the estimated coefficient of the GDP per capita variable seems particularly strong for specification 3. This instrument, however, seems less effective in the case of our Latin American countries for which this coefficient is much lower. In the case of Africa, income seems to play an opposite role, by increasing violence in our sample of countries. This may be due to the extreme poverty and fragility of many African economies, as suggested by [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] and [START_REF] Lai | Draining the Swamp": An Empirical Examination of the Production of International Terrorism, 1968-1998[END_REF], which shows that a country must exceed a certain level of development before an increased income 15 We recall that the results of the regional panels are presented in the Appendix translates into a reduction in violence. In these African countries, an overall increase in income may also be followed by an increase in inequality, or the perception of inequality, as proposed by [START_REF] Olson | Rapid Growth as a Destabilizing Force[END_REF]. This is the case, for example, if the richest people become even richer. Changes in the distribution of wealth or the perception of not getting the expected share of income can then lead to more grievances and violence in society, as in [START_REF] Blomberg | From (no) Butter to Guns? Understanding the Economic Role in Transnational Terrorism[END_REF].

The results are rather similar across our groups for the population size variable, whose impact is stronger in countries with more than one main religion, and in the Asian, African, and Latin-American regions. This may be due to the fact that several highly populated countries are located in these groups, illustrating the difficulties faced by governments in meeting the needs of a large, diverse population.

The results are more diverse for the judicial system. Improving the effectiveness of justice has more impact in Muslim states and countries with more than one main religion, as well as in the MENA and Africa regions. This is interesting because countries in these groups are more involved in conflict and exposed to violence. Improving the justice system and institutions in general would be an effective way to combat terrorism in these fragile states. Interestingly, the deterrent effect of possible sanctions does not seem to work in the case of the Asian region. In the countries of our sample, the effectiveness of justice increases violence, which underlines the back-lash effect of the sanctions on terrorism and the involvement of certain populations in conflicts, as proposed by [START_REF] Higson-Smith | A Community Psychology Perspective on Terrorism: Lessons from South Africa[END_REF].

The two education variables, the human capital index (published by the PWT), and the average number of years of schooling of the population aged 25 and older (UNDP) are almost always significant for our first four groups of country, but not in the case of the regions. As mentioned earlier, this may be due to the reduced number of observations. It may also be related to the fact that religion is mostly the driving force of conflict in these four groups. In this case, education can serve the cause of terrorists by allowing certain segments of the population to be more involved in violence. For the four country groups, the estimated coefficient differences are not very significant, except for countries with more than one main religion where the impact is smaller. The same conclusions can be drawn for democracy, with a stronger impact in Muslim countries.

Finally, as mentioned above, economic reforms do not seem to contribute to an increase or reduction of violence in our various samples of countries, with the exception of the MENA and Africa regions. In the countries of our African sample, reforms, as measured by the trade openness indicator, are perceived as a positive economic opportunity, reducing the grievances of the populations and increasing the opportunity cost of resorting to violence, as in [START_REF] Blomberg | From (no) Butter to Guns? Understanding the Economic Role in Transnational Terrorism[END_REF] and [START_REF] Kurrild-Klitgaard | The Political Economy of Freedom, Democracy and Transnational Terrorism[END_REF]. By contrast, in the MENA region, trade reforms are seen as a threat of negative change, which contributes to an increase in conflict, as in [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] and [START_REF] Wintrobe | Extremism, Suicide Terror, and Authoritarianism[END_REF]. MENA countries seem particularly reluctant to reform, as many observers have shown [START_REF] Aysan | Uncertainty, Economic Reforms and Private Investment in the Middle East and North Africa[END_REF][START_REF] Nabli | Reforms Complementarities and Economic Growth in the Middle East and North Africa[END_REF][START_REF] Véganzonès-Varoudakis | Openness, Investment Climate, and FDI in Developing Countries[END_REF]. However, this impact is less than the positive impact of the reforms on the reduction of violence in the Africa region.

Conclusion

In this article, we use Fixed Effect Poisson Regression (FEPR) with robust standard errors, to study the social, economic, and institutional determinants of conflict in 58 fragile states divided into 8 groups. We explore different reasons for conflict in fragile countries and analyze different theories and empirical determinants.

We show that poverty and weak institutions (weak justice systems in particular) are two important dimensions which contribute to violence in our sample of fragile countries. These results are consistent with those of [START_REF] Collier | Greed and Grievance in Civil War[END_REF], [START_REF] Lai | Draining the Swamp": An Empirical Examination of the Production of International Terrorism, 1968-1998[END_REF], and [START_REF] Ostby | Polarization, Horizontal Inequalities and Violent Civil Conflict[END_REF], who show that low incomes are positively associated with terrorism. When poverty is high, disadvantaged people are especially likely to resort to violence since the opportunity cost of terrorism and the cost of recruitment of terrorists are low.

Our results are also consistent with those of LaFree et al ( 2009) and [START_REF] Dezhbakhsh | Does Capital Punishment Have a Deterrent Effect? New Evidence from Post Moratorium Panel Data[END_REF], who confirm the deterrent effect of the threat of sanctions. According to [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF], effective justice increases the opportunity cost and risk of violence.

On the other hand, improving education and democracy does not seem to help reduce violence in fragile states, and both of our proxy variables show a positive relationship with conflict. These results confirm those of [START_REF] Berrebi | Evidence About the Link Between Education, Poverty and Terrorism Among Palestinians[END_REF] and [START_REF] Brockhoff | Great Expectations and Hard Times: The (Nontrivial) Impact of Education on Domestic Terrorism[END_REF] who show that education in fragile countries can increase frustration if the situation of educated people does not improve, especially as they are more aware of the limits of their government. This conclusion can be extrapolated to democracy, which gives more means of expression to the discontented and the extremists, thus increasing the violence (Eubank and[START_REF] Eubank | Terrorism and Democracy: What Recent Events Disclose?[END_REF][START_REF] Li | Economic Globalization and Transnational Terrorism: A Pooled Time-Series Analysis[END_REF][START_REF] Li | Economic Globalization and Transnational Terrorism: A Pooled Time-Series Analysis[END_REF]. Our results imply that education and political rights do not have the desired effects in fragile states, which must first improve the social, economic, and institutional conditions of their population before they can reap the benefits of political reforms and of education. This is also the case with economic reforms, as our trade openness indicator shows no impact on violence in most of our groups (except MENA and Africa).

Although this general pattern works quite well for most of our country groups, some groups experience somewhat different situations. This is the case for countries with more than one major religion, where improving incomes and efficiency of justice are more effective in reducing violence than in the other groups. This is an interesting finding which governments could take into account to fight against terrorism in these particularly fragile countries. Muslim states are also particularly sensitive to the deterrent effect of sanctions, which for government could be an effective means of combating violence. Muslim countries also experience an increase in violence during more democratic times. These findings confirm that in countries which are particularly vulnerable to terrorism, political rights cannot be reintroduced until after the restoration of order and effective institutions.

The MENA and Africa regions, which are also very affected by conflicts, have their own specificities as well. As in the case of the two previous groups, improving the effectiveness of justice has a significant impact on violence, which confirms that institutions are important in the fight against conflict in the most affected countries. The Africa region has two other particularities, which may be due to the extreme poverty and fragility of most of its countries. In this region, income seems to play an opposite role, increasing violence, contrary to what is seen in other countries. [START_REF] Olson | Rapid Growth as a Destabilizing Force[END_REF] describes this situation in which an overall increase in income is followed by an increase in inequality or perception of inequality.

A change in the distribution of wealth can then lead to grievances and violence, as [START_REF] Blomberg | From (no) Butter to Guns? Understanding the Economic Role in Transnational Terrorism[END_REF] have shown. Also in Africa, economic reforms are perceived as an economic opportunity, reducing citizens' grievances and increasing the opportunity cost of resorting to violence, as [START_REF] Blomberg | From (no) Butter to Guns? Understanding the Economic Role in Transnational Terrorism[END_REF] and [START_REF] Kurrild-Klitgaard | The Political Economy of Freedom, Democracy and Transnational Terrorism[END_REF] have shown. We can therefore note the specificity of Africa and of the policies to be put in place by governments, which differ to some extent from those in other countries. By contrast, in the MENA region, trade reforms are seen as a threat of adverse change, which contributes to worsening conflicts, as in [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] and [START_REF] Wintrobe | Extremism, Suicide Terror, and Authoritarianism[END_REF].

  use two different indexes for human development as explanatory variable for conflict: (i) The average number of years of schooling of population aged 25 or older from the United Nations Development Program (UNDP) 5 ; (ii) The Human Capital index of the Penn World Table (PWT 9.1, Feenstra et al, 2015) 6 (see descriptive statistics in Table A.1 in the Appendix).

  , and viii) Latin American fragile countries (see the lists of countries in TableA.2 in the Appendix).Since we use the annual number of conflict-based incidents from the Global Terrorism Database (GTD) as proxy for violence, this implies that our dependent variable is a non-negative integer (count data)11 . Fixed Effect Poisson Regressions (FEPR) is used with robust standard errors to address the issues related to count data. Many empirical researches have used Poisson regression or Negative Binomial Regression (NBR) for count data models 12 .[START_REF] Berrebi | Earthquakes, Hurricanes, and Terrorism: Do Natural Disasters Incite Terror?[END_REF] suggest that NBR offers potential efficiency gains, but that the consistent estimates provided by Poisson regression are more valuable than efficiency.[START_REF] Wooldridge | Distribution-Free Estimation of Some Nonlinear Panel Data Models[END_REF] confirms that Poisson regression with fixed effects is robust and consistent for count data models. Although the problem of underdispersion/overdispersion when applying Poisson regression has been highlighted in various studies, FEPR with clustered standard errors retains consistency and allows us to estimate our model with robust standard errors[START_REF] Simcoe | XTPQML: Stata Module to Estimate Fixed-Effects Poisson (Quasi-ML) Regression with Robust Standard Errors[END_REF] 13 .In the regressions, we use two proxies of human capital: (i) The average number of years of schooling of the population aged 25 or older (Edum), published by UNDP, available for all 58 countries, (ii) The Human Capital Index (H), published in the Penn World Table (PWT), available for only 51 countries 14 .

	10 , (v) Middle
	East and North African (MENA) fragile countries, vi) Asian fragile countries, vii) African fragile
	7 The Fragile States Index (FSI) is an annual ranking of 178 countries based on the different pressures they face. The FSI is calculated from
	12 key qualitative and quantitative indicators, political, social, and economic, from a variety of public sources. For more details see
	https://fragilestatesindex.org/data/

8

The Fund for Peace (FFP) defines 10 levels of fragility according to the FSI score: Very high alert (above 110); High alert (between 100 to 110); Alert (90 to 100); High warning (80 to 90); Elevated warning (70 to 80); Warning (60 to 70); More stable (40 to 60); Very stable:(30 to 40); Sustainable (20 to 30); Very sustainable (less than 20). 9 Countries where more than 10% of people belong to a different religious group 10 Countries that have 5 or more terrorist events in at least one year. countries

Table 1 : Fixed Effect Poisson Regression for Total Fragile Countries

 1 Dependent variable is annual number of terrorist-based incidents, robust standard errors are given in parenthesis, significance level: ***. **, * is less than 1%, 5% and 10% respectively.

	Variables	Specification 1	Specification 2	Specification 3
	lpop	4.318***	4.491***	2.944***
		(0.70)	(0.86)	(0.79)
	lgdpc	-1.164***	-1.063***	-0.479**
		(0.32)	(0.37)	(0.24)
	Edum	0.758***	0.681***
		(0.17)	(0.18)
	H			4.957***
				(0.98)
	Contracts	1.353*	1.360*	1.111
		(0.77)	(0.79)	(0.88)
	Open	-0.32	-0.457	0.093
		(1.00)	(1.03)	(0.99)
	Demo	0.113**	0.087*	0.262***
		(0.06)	(0.05)	(0.06)
	Observations	812	714	714
	Number of counnum	58	51	51
	Note:

Table 2 : Fixed Effect Poisson Regression for Muslim Fragile Countries

 2

	Variables	Specification 1	Specification 2	Specification 3
	lpop	4.431***	4.652***	2.734***
		(0.92)	(1.08)	(0.88)
	lgdpc	-1.251***	-1.108***	-0.556**
		(0.27)	(0.30)	(0.26)
	Edum	0.591	0.452
		(0.40)	(0.42)
	H			4.629***
				(1.63)
	Contracts	2.425***	2.518***	2.094***
		(0.81)	(0.92)	(0.67)
	Open	-0.082	-0.384	0.205
		(1.13)	(1.22)	(1.20)
	Demo	0.158**	0.135**	0.286***
		(0.06)	(0.06)	(0.06)
	Observations	350	294	294
	Number of counnum	25	21	21
	Note: Dependent variable is annual number of terrorist-based incidents, robust standard errors are given in parenthesis,
	significance level: ***. **, * is less than 1%, 5% and 10% respectively.

Table 3 : Fixed Effect Poisson Regression for Fragile Countries Affected by Major Conflicts

 3 Dependent variable is annual number of terrorist-based incidents, robust standard errors are given in parenthesis, significance level: ***. **, * is less than 1%, 5% and 10% respectively.

	Variables	Specification 1	Specification 2	Specification 3
	lpop	4.312***	4.486***	2.942***
		(0.70)	(0.86)	(0.79)
	lgdpc	-1.166***	-1.065***	-0.479**
		(0.32)	(0.37)	(0.24)
	Edum	0.761***	0.683***
		(0.17)	(0.18)
	H			4.962***
				(0.98)
	Contracts	1.339*	1.338*	1.089
		(0.78)	(0.81)	(0.89)
	Open	-0.323	-0.462	0.093
		(1.01)	(1.03)	(0.99)
	Demo	0.113**	0.086*	0.262***
		(0.06)	(0.05)	(0.06)
	Observations	588	560	560
	Number of counnum	42	40	40
	Note:

Table 4 : Fixed Effect Poisson Regression for Fragile Countries with more than One Main Religion

 4

	Variables	Specification 1	Specification 2	Specification 3
	lpop	8.312***	11.147***	9.497***
		(2.87)	(1.78)	(1.61)
	lgdpc	-1.531***	-1.571***	-1.090***
		(0.08)	(0.09)	(0.09)
	Edum	0.725***	0.499**
		(0.26)	(0.21)
	H			3.794***
				(0.94)
	Contracts	2.976	4.961**	3.977*
		(2.57)	(2.20)	(2.19)
	Open	1.867	1.834	1.907
		(1.63)	(1.72)	(1.41)
	Demo	-0.155	-0.409	-0.412
		(0.45)	(0.45)	(0.40)
	Observations	238	224	224
	Number of counnum	17	16	16

Note: Dependent variable is annual number of terrorist-based incidents, robust standard errors are given in parenthesis, significance level: ***. **, * is less than 1%, 5% and 10% respectively.

Table A .2. : Descriptive Statistics

 A

	Variables	Obs	Mean	Std. Dev.	Min	Max
	trsm	714	86,7	297	0,00	3367
	lpop	714	17,3	1,29	14,1	21,0
	lgdpc	714	7,61	1,05	2,80	9,98
	Edum	714	6,24	2,45	1,30	12,0
	H	714	2,10	0,53	1,11	3,4
	Contracts	714	1,95	0,84	0,73	4,0
	Open	714	0,55	0,29	0,12	2,21
	Demo	714	3,45	1,32	0,04	6,0

Table A .3. Fixed Effect Poisson Regression for MENA Fragile Countries

 A Dependent variable is annual number of terrorist-based incidents, robust standard errors are given in parenthesis, significance level: ***. **, * is less than 1%, 5% and 10% respectively.

	Variables	Specification 1	Specification 2	Specification 3
	lpop	3.613***	3.603***	3.107*
		(0.95)	(1.08)	(1.74)
	lgdpc	-1.246***	-1.101***	-0.650*
		(0.29)	(0.35)	(0.37)
	Edum	0.654	0.531
		(0.49)	(0.52)
	H			2.608
				(2.62)
	Contracts	3.023***	2.882***	2.967**
		(0.95)	(1.04)	(1.26)
	Open	-1.299	-1.771*	-1.277*
		(0.83)	(1.06)	(0.66)
	Demo	0.425	0.293	0.31
		(0.32)	(0.20)	(0.20)
	Observations	182	154	154
	Number of counnum	13	11	11
	Note:

Table A .4. Fixed Effect Poisson Regression for Asian Fragile Countries

 A Note: Dependent variable is annual number of terrorist-based incidents, robust standard errors are given in parenthesis, significance level: ***. **, * is less than 1%, 5% and 10% respectively.

	Variables	Specification 1	Specification 2	Specification 3
	lpop	6.625	6.647	9.469**
		(6.38)	(6.43)	(3.75)
	lgdpc	0.811	0.796	-6.162**
		(2.61)	(2.63)	(3.02)
	Edum	-0.065	-0.061
		(0.59)	(0.59)
	H			17.302**
				(7.36)
	Contracts	-3.839	-3.869	-13.662*
		(4.23)	(4.35)	(7.06)
	Open	1.124	1.126	0.511
		(1.70)	(1.70)	(1.20)
	Demo	0.059	0.058	0.237
		(0.33)	(0.33)	(0.21)
	Observations	126	112	112
	Number of counnum	9	8	8

Table A .5. Fixed Effect Poisson Regression for African Fragile Countries

 A Dependent variable is annual number of terrorist-based incidents, robust standard errors are given in parenthesis, significance level: ***. **, * is less than 1%, 5% and 10% respectively.

	Variables	Specification 1	Specification 2	Specification 3
	lpop	7.706***	7.740***	10.258***
		(2.81)	(2.82)	(3.06)
	lgdpc	4.221	4.284*	4.821*
		(2.60)	(2.59)	(2.64)
	Edum	0.356	0.346
		(0.53)	(0.53)
	H			-2.613
				(3.15)
	Contracts	7.592***	7.696***	8.226***
		(2.46)	(2.46)	(2.87)
	Open	2.652*	2.714*	2.640*
		(1.41)	(1.43)	(1.37)
	Demoa	-0.249	-0.243	-0.116
		(0.22)	(0.23)	(0.24)
	Observations	294	280	280
	Number of counnum	21	20	20
	Note:

Table A .6. Fixed Effect Poisson Regression for Latin American Fragile Countries

 A Dependent variable is annual number of terrorist-based incidents, robust standard errors are given in parenthesis, significance level: ***. **, * is less than 1%, 5% and 10% respectively.

	Variables	Specification 1	Specification 2	Specification 3
	lpop	12.429***	12.339***	14.316
		(4.23)	(4.28)	(15.42)
	lgdpc	-0.243**	-0.248**	-0.259*
		(0.11)	(0.12)	(0.14)
	Edum	-0.211	-0.198
		(0.41)	(0.41)
	H			-2.018
				(7.25)
	Contracts	1.193	1.21	1.123
		(0.94)	(0.94)	(1.18)
	Open	0.517	0.671	0.635
		(1.04)	(1.24)	(1.36)
	Demo	0.302	0.306	0.326
		(0.34)	(0.34)	(0.40)
	Observations	154	140	140
	Number of counnum	11	10	10
	Note:

Conflict and terrorism are used interchangeably in this article.Études et Documents n°

20, CERDI, 2019

http://hdr.undp.org/en/content/human-development-index-hdi

www.ggdc.net/pwt

Marie-Ange Véganzonès-Varoudakis

This work was supported by the LABEX IDGM+ (ANR-10-LABX-14-01) within the program "Investissements d'Avenir" operated by the French National Research Agency (ANR).

Études et Documents are available online at: https://cerdi.uca.fr/etudes-et-documents/

Conflicts in fragile states cause great suffering for people, as well as delays in development. If nothing is done, the World Bank (2018) predicts that nearly half of the world's poor will live in fragile countries facing conflict situations by 2030. This study highlights some tools governments could use to try to limit violence in their country. Improving the standard of living of people and restoring strong and reliable institutions are measures that seem to bear fruit in most fragile countries, with a certain specificity of Africa that we have mentioned. These results are in line with the work of [START_REF] Burgoon | On Welfare and Terror: Social Welfare Policies and Political-Economic Roots of Terrorism[END_REF] and [START_REF] Freytag | The Origins of Terrorism: Cross-Country Estimates of Socio-Economic Determinants of Terrorism[END_REF] who show that public spending and social protection policies can reduce violence, and George (2018) who suggests that in failing states, an effective counter-terrorism measure is to build reliable institutions. On the other hand, the question of the role of education, political rights, and economic reforms is more complex to deal with. If in the short term these instruments do not seem to help in the reduction of conflicts and terrorism in the countries concerned, it may be thought that the priority of fragile states is to provide their populations with a safer economic, political, and institutional environment before these populations can benefit from the fruits of more advanced reforms.