Patrice Estellé

Salma Halelfadl

Thierry Maré

Thermal conductivity of CNT water based nanofluids: Experimental trends and models overview

Keywords: CNT nanofluids, Thermal conductivity, Experiments, Models, Temperature, Nanoparticle aspect ratio, surfactant

We report in this communication thermal conductivity measurement of carbon nanotubes waterbased nanofluids. We consider in particular the influence of nanoparticle volume fraction, temperature, carbon nanotube aspect ratio and different kind of surfactant (SDBS, Lignin, Sodium Polycarboxylate) on thermal conductivity enhancement of nanofluids. In addition, various theoretical thermal conductivity models are presented in an attempt to correlate the experimental data.

Introduction

Since many years, it has been demonstrated that nanofluids (NF) are promising candidates as heat transfer fluids in heat exchangers, cooling devices, and solar collectors [START_REF] Maré | Comparison of the thermal performances of two nanofluids at low temperature in a plate heat exchanger[END_REF][START_REF] Wen | Review of nanofluids for heat transfer applications[END_REF][START_REF] Mahian | Wongwises A review of the applications of nanofluids in solar energy[END_REF] due to their enhanced thermal properties. Nanofluids are obtained by dispersing a small amount of nanoparticles with high intrinsic conductivity within currently used base fluids, such as water, ethylene glycol, oil, … Among the numerous studied systems, carbon nanotubes (CNT) appear very interesting due to their high thermal conductivity in comparison to Al2O3, CuO and TiO2. In addition, as nanofluid viscosity is related to resistance to flow and pumping power in energy systems, it is better to use low viscosity base fluid. Thermal conductivity is an important physical properties which can be used to evaluate the efficiency of nanofluid as coolants [START_REF] Halelfadl | Efficiency of carbon nanotubes water based nanofluids as coolants[END_REF][START_REF] Hemmat Esfe | Efficiency of ferromagnetic nanoparticles suspended in ethylene glycol for applications in energy devices: Effects of particle size, temperature, and concentration[END_REF], predict heat transfer within exchangers [START_REF] Wu | A review of nanofluid heat transfer and critical heat flux enhancement-Research gap to engineering application[END_REF][START_REF] Hussein | A review of forced convection heat transfer enhancement and hydrodynamic characteristics of a nanofluid[END_REF] and natural convection in cavities as well [START_REF] Abu-Nada | Effect of nanofluid variable properties on natural convection in enclosures[END_REF]. Hence, the purpose of the present communication is to report the thermal conductivity (TC) measurement of water-based nanofluids containing carbon nanotubes. CNT consist here in MWCNT stabilized by different surfactants. Actually, in addition to mechanical stirring and sonication, due to the hydrophobic behavior of CNT their dispersion and stability within water is obtained through the use of surfactant. We have considered here the influence of SDBS (sodium dodecylbenzenesulfonate), lignin, which is a by-product of paper industry and sodium polycarboxylate respectively as stabilizers. The effects of nanoparticle volume fraction within the range 0.55-0.0055%, temperature varying between 20 and 40°C, and nanoparticles aspect ratio (90; 160) on the thermal conductivity enhancement is first presented and discussed. Moreover, various theoretical approaches and empirical models are presented considering the influence of nanofluid composition and impact of several mechanisms such as volume fraction, temperature, nanoparticle shape and aspect ratio, Brownian motion, carbon nanotubes curving and wrapping, interfacial thermal resistance of CNT, … Finally, experimental results are discussed and compared to theoretical predictions.

Materials and experiments

Materials

Four types of nanofluids were here selected and investigated. They have been partially studied in our previous works [START_REF] Hemmat Esfe | Efficiency of ferromagnetic nanoparticles suspended in ethylene glycol for applications in energy devices: Effects of particle size, temperature, and concentration[END_REF][START_REF] Halelfadl | Viscosity of carbon nanotubes water-based nanofluids: Influence of concentration and temperature[END_REF][START_REF] Halelfadl | Heat transfer properties of aqueous carbon nanotubes nanofluids in coaxial heat exchanger under laminar regime[END_REF][START_REF] Halelfadl | Optimization of thermal performance and pressure drop of a rectangular microchannel heat sink using aqueous carbon nanotubes based nanofluid[END_REF][START_REF] Estellé | Lignin as dispersant for water-based carbon nanotubes nanofluids: Impact on viscosity and thermal conductivity[END_REF]. Nanofluids consists of MWCNT (purity of 90%) dispersed a mixture of deionized water and surfactant. Table 1 summarizes the composition and the properties of the different nanotubes and nanofluids. In all cases, an initial starting suspension with 1% in weigth fraction of nanotubes and 2% in weight fraction of surfactant was prepared by Nanocyl. Nanofluids with lower volume fraction were obtained from serial dilution of the starting suspension, as reported earlier [START_REF] Halelfadl | Viscosity of carbon nanotubes water-based nanofluids: Influence of concentration and temperature[END_REF][START_REF] Halelfadl | Heat transfer properties of aqueous carbon nanotubes nanofluids in coaxial heat exchanger under laminar regime[END_REF][START_REF] Halelfadl | Optimization of thermal performance and pressure drop of a rectangular microchannel heat sink using aqueous carbon nanotubes based nanofluid[END_REF][START_REF] Estellé | Lignin as dispersant for water-based carbon nanotubes nanofluids: Impact on viscosity and thermal conductivity[END_REF], conserving constant surfactant/carbon nanotubes weight ratio of 2. Finally, the whole volume fraction range investigated varies between 0.0055% and 0.55%. As evidenced by table 1, impact of average CNT aspect ratio and surfactant nature are presently studied.

Thermal conductivity measurement

A KD2 Pro thermal property analyzer (Decagon Devices Inc.), which is based on the transient hot wire method, was used to evaluate the thermal conductivity of both nanofluids and base fluids (deionized water and surfactant). The experimental set-up for thermal conductivity measurement was previously used in [START_REF] Halelfadl | Optimization of thermal performance and pressure drop of a rectangular microchannel heat sink using aqueous carbon nanotubes based nanofluid[END_REF][START_REF] Estellé | Lignin as dispersant for water-based carbon nanotubes nanofluids: Impact on viscosity and thermal conductivity[END_REF]. Its accuracy was also previously evaluated with distillated water, leading to a maximum standard deviation of 3.5%. During the measurement, both the sample and the probe were first maintained 30 min at the required temperature. Then, ten measurements were recorded with 5 mins of interval. In the following, the thermal conductivity values also consist of an average of the ten measures performed at 20, 30 and 40°C respectively for each volume fraction.

Thermal conductivity models for CNT nanofluids

Several theoretical correlations have been developed in the past to predict the thermal conductivity enhancement of CNT nanofluids. The relevance of many correlations have been presented and discussed in recent works [START_REF] Lamas | Critical analysis of the thermal conductivity models for CNT based nanofluids[END_REF][START_REF] Sohel Murshed | Superior thermal features of carbon nanotubes-based nanofluids -A review[END_REF]. Here, we intend to compare some of these correlations with our experimental data, considering different factors that can contribute to the theoretical frame of thermal conductivity enhancement. At first sight, the thermal conductivity of nanofluids can be estimated by Hamilton and Crosser model [START_REF] Hamilton | Thermal conductivity of heterogeneous two component systems[END_REF]. This model, defined by equation ( 1), can be used when the thermal conductivity of the particles is at least 100 times higher than the one of the liquid phase.

( ) ( )( ) ( ) ( ) bf bf p bf p bf p bf p nf k k k k n k k k n k n k k φ φ - - - + - - + - + = 1 1 1 (1)
In the previous equation, knf, kp and kbf are the thermal conductivity of nanofluids, nanoparticles and base fluid respectively in W/mK, φ is the volume fraction and n is a shape factor linked to nanoparticles sphericity such as n=3/ψ. Due to rod shape of nanotubes contained within the nanofluids, the sphericity ψ was here calculated from the average length and diameter of the nanotubes investigated. This leads to n values reported in Table 1 for each tested nanofluids. Table 1 shows that n values vary following CNT aspect ratio and differs from 6, as generally considered with cylindrical particles. It is noted that equation (1) does not support directly the influence of temperature. A thermal conductivity model for nanofluids containing nanotubes taking into account the effect of diameter and aspect ratio of nanotubes as well Brownian effect due to temperature has been developed by Walvekar et al. [16]. This model derives from a model initially introduced by [START_REF] Kumar | Model for heat conduction in nanofluids[END_REF] and writes as follows.

        - +                       -         + + = p p bf p p bf bf p p p p p bf nf d l l r T T C r k l r l r k k k ln ) ( ) 1 ( 3 ) ( 2 1 2 2 0 µ φ φ φ (2)
In this equation, rp is the radius of nanoparticles (m), lp is the length of the nanoparticles (m), rbf is the radius of base fluid molecule (m), µbf is the base fluid viscosity (Pa.s), and T is the temperature (K). It is worth noting that viscosity of the different base fluids was previously measured [START_REF] Halelfadl | Viscosity of carbon nanotubes water-based nanofluids: Influence of concentration and temperature[END_REF][START_REF] Estellé | Lignin as dispersant for water-based carbon nanotubes nanofluids: Impact on viscosity and thermal conductivity[END_REF] or additional measurements were performed following the procedure described in [START_REF] Halelfadl | Viscosity of carbon nanotubes water-based nanofluids: Influence of concentration and temperature[END_REF]. As reported earlier [START_REF] Estellé | Lignin as dispersant for water-based carbon nanotubes nanofluids: Impact on viscosity and thermal conductivity[END_REF][START_REF] Walvekar | Thermal conductivity of carbon nanotube nanofluid-Experimental and theoretical study[END_REF], the first part of the model is mainly related to volume fraction, shape and aspect ratio of nanoparticles and thermal conductivities of both nanoparticle and base fluid. The second term is related to Brownian movement of nanoparticles linked to temperature and base fluid viscosity. T0 is taken as 273°K which corresponds to the reference temperature below which Brownian motion becomes negligible. C depends on Boltzmann constant as C=85kB²/72π² [START_REF] Walvekar | Thermal conductivity of carbon nanotube nanofluid-Experimental and theoretical study[END_REF]. The effects of carbon nanotube curving and wrapping was investigated in [START_REF] Kumar | Model for heat conduction in nanofluids[END_REF]. Such phenomena depend on base fluids, nanotubes dimensions and presence of surfactants. In this work, several equations were developed to predict TC enhancement of CNT-based nanofluids from a distribution based modelling technology and the use of probability density functions (denoted p(x)). The authors showed that among the models developed, the uniform distribution model, denoted UDM (equation 3, obtained with p(x)=3) and the linear increase distribution model, denoted LIDM, (equation 4 with p(x)=18(1/3-x)) are able to capture the TC enhancement of CNT-based nanofluids. So, the effect of moderate curving and wrapping is captured by the following equation under the consideration of kbf/ kp <<1.

bf bf p nf k k k k         + ≈ 16 27 ln 1 φ (3)
For less curving and wrapping nanotubes, TC of nanofluid can be obtained from (kbf/ kp <<1)

bf bf p nf k k k k                 + + ≈ 19683 256 ln 3 1 1 6 1 φ (4)
Finally, Nan et al. [START_REF] Nan | Interface effect on thermal conductivity of carbon nanotube composites[END_REF] proposed a TC model for carbon-based nanofluids taking into account the effect of interfacial resistance based on multiple scattering theory and the EMT model of Maxwell, considering also the Kapitza resistance at the CNTs medium. This model was expressed as In these equations, k c 11 and k c 33 denote the equivalent TC along transverse and longitudinal axes respectively of a thin interfacial thermal layer and depend on CNT dimensions and Kapitza radius ak [START_REF] Lamas | Critical analysis of the thermal conductivity models for CNT based nanofluids[END_REF][START_REF] Nan | Interface effect on thermal conductivity of carbon nanotube composites[END_REF].

It is shown that all these equations require properly determination of both TC and dimensions of nanotubes, and the properties of base fluid. It should also be mentioned that the possible effect of particle agglomeration do not appear within the equations. As reported earlier, the TC of CNT is 3000 W/mK.

Results and discussion

As indicated in section 2.1, due to constant surfactant/carbon nanotubes weight ratio, the quantity of surfactant increase with CNT volume fraction. Moreover, three kinds of surfactant were used here. So, the effect of surfactant content and nature is first investigated reporting the TC of base fluid in function of surfactant quantity. This is shown by Figure 1 at 30°C. As reported earlier [START_REF] Estellé | Lignin as dispersant for water-based carbon nanotubes nanofluids: Impact on viscosity and thermal conductivity[END_REF], it is observed that TC of base fluid decreases when the amount of surfactant is increased, and that the TC is lower than the one of deionized water at this temperature. This means that surfactants penalize the TC of NF. It is also shown that this effect is independent of surfactant type, within the experimental uncertainty. Similar tendencies were obtained at lower and higher temperatures (20 and 40°C), TC being decreased and increased when the temperature is decreased and increased respectively. sodium polycarboxylate ; open diamond-shaped: lignin ; cross: SDBS)

Figure 2 shows the effect of temperature and volume fraction on the thermal conductivity enhancement of NF for two nanofluids N3 and N4. A similar behaviour was also noticed for N1 and N2. As often reported in literature, TC of NF increases when both the CNT nanotube volume fraction increases and temperature as well.

The TC quickly enhances for lower CNT volume fraction, in particular at 30 and 40°C. In addition, at these temperatures, TC do not follow a linear trend with volume fraction. The thermal conductivity of NF is reported in Figure 3(left) for N1, N2 and N3 at 20°C evidencing the effect of surfactant on TC. While TC of base fluid decreases with the amount of surfactant, figure 3(left) shows that TC of nanofluids increases with CNT volume fraction. When temperature is increased, similar trend is also noticed.

The figure also shows that surfactant nature do not influence TC enhancement except at higher volume fraction for SDBS. The effect of CNT aspect ratio is shown in Figure 3(right) at 30°C (at 20°C this effect is negligible; the effect is increased at 40°C). Higher the aspect ratio, higher is the TC enhancement at high volume fraction. So, this agrees well with previous published results. However, the maximum deviation, which is obtained at 0.55% and 40°C, is only around 5%. Based on these experimental findings, we focus now on the comparison between experimental data and theoretical correlations presented above considering mainly the influence of volume fraction, temperature and CNT aspect ratio. So, N3 and N4 nanofluids are only discussed in the following. As for TC, Figures 4 and5 show that relative TC (RTC) of nanofluids increases quite linearly at 20°C. When the temperature is increased, RTC of nanofluids sharply increases at low volume fraction up to 0.111%. Then, the increasing goes up more slowly. This also evidences that the penalizing effect of surfactant on TC of water reported before is not predominant in comparison with TC of nanotubes. As expected also, the better RTC is achieved for both the higher volume fraction and temperature.

It is also observed from both figures that the theoretical predictions are much lower than the experimental data except for Walvekar model. However, some of the proposed models are able to correlate the experimental data at 20°C (within the experimental uncertainty), the best correlation being obtained with the LIDM model. When the temperature is increased, the models greatly deviate in comparison with experimental data and do not report in particular the great enhancement in TC at low volume fraction in nanotubes. Finally, this experimental study evidences the potential of carbon nanotubes water-based nanofluids as heat transfer media and coolants for thermal applications due to the great enhancement of TC even at low volume fraction. In addition, none of the selected TC models properly predict TC enhancement of carbon nanotubes water-based nanofluids within the entire range of volume fraction, temperature and nanotubes aspect ratio. While several factors affecting TC have been considered, there is little difference between the studied TC models apart at the higher volume fraction in nanotubes. However, the results suggest that curving and wrapping and size effect of CNT appear at high volume fraction and low temperature of 20°C. For higher temperatures, conclusions are not so far easy and one factor cannot be only used to predict RTC enhancement from theoretical point of view.

Conclusion

A parametric experimental study of thermal conductivity of water-based carbon nanotubes was presented. In particular, we have considered the influence of surfactant used to stabilize the nanotubes, carbon nanotubes volume fraction and aspect ratio and temperature as well. It was observed that TC enhancement of CNT nanofluids increase with volume fraction and temperature. The thermal conductivity enhancement is really significant at very low volume fraction, in particular at 30 and 40°C. The effect of the used surfactants on TC enhancement of nanofluids is weak, TC is also weakly affected by the influence of CNT aspect ratio considered here.

The comparison between experiments and models show that theoretical predictions presented above cannot clearly capture the TC enhancement of CNT water based nanofluids presently investigated within the entire range of volume fraction considered and temperature. This evidences a need both to develop appropriate model for TC enhancement prediction of CNT nanofluids and measure TC of this kind of nanofluids before performing numerical studies in heat exchangers and cavities.

Figure 1 .

 1 Figure 1. Thermal conductivity of base fluids at 30°C -Impact of nature and quantity of surfactant (open circle: sodium polycarboxylate ; open diamond-shaped: lignin ; cross: SDBS)

Figure 2 .

 2 Figure 2. Thermal conductivity of N3 (left) and N4 (right) -Impact of CNT volume fraction and temperature

Figure 3 .

 3 Figure 3. Effect of surfactant (left) and CNT aspect ratio (right) on thermal conductivity of nanofluids

Figure 4 .

 4 Figure 4. Relative TC enhancement of N3 in function of nanoparticle volume fraction at 20°C (left) and 40°C (right) -Comparison with theoretical correlations

Figure 5 .

 5 Figure 5. Relative TC enhancement of N4 in function of nanoparticle volume fraction at 20°C (left) and 40°C (right) -Comparison with theoretical correlations

Table 1 .

 1 Nanotubes and nanofluids properties

		N1	N2	N3	N4
	Nanotube average	9.2	9.2	9.2	11.4
	diameter d (nm)
	Nanotube average	1.5	1.5	1.5	≈1
	length l (µm)
	Average aspect ratio	160	160	160	90
	(r=l/d)
	Density (kg/m 3 )	1800	1800	1800	2050
	Carbon purity (wt.%)	90	90	90	90
	Sphericity /	0.24 /	0.24 /	0.24 /	0.29 /
	n (H-C model)	12.5	12.5	12.5	10.23
	Surfactant	SDBS	Lignin	Sodium polycarboxylate	Sodium polycarboxylate

Acknowledgments

Nanocycl Belgium is gratefully acknowledged for preparing and providing the CNT water based nanofluids. P. Estellé wishes to thank the organization committee of ENTECH'14 for the invitation to present this work at the conference, special thanks were addressed to O. Mahian and A.S. Dalkilic.


Iovka Boneva
email: iovka.boneva@inria.fr

Angela Bonifati
email: angela.bonifati@inria.fr

Radu Ciucanu
email: radu.ciucanu@inria.fr

Graph Data Exchange with Target Constraints

Data exchange is the problem of translating data structured under a source schema according to a target schema and a set of source-to-target constraints known as schema mappings. In this paper, we investigate the problem of data exchange in a heterogeneous setting, where the source is a relational database, the target is a graph database, and the schema mappings are defined across them. We study the classical problems considered in data exchange, namely the existence of solutions and query answering. We show that both problems are intractable in the presence of target constraints, already under significant restrictions.

INTRODUCTION

Data exchange is the problem of translating data structured under a source schema according to a target schema and a set of source-to-target constraints [START_REF] Fagin | Data exchange: semantics and query answering[END_REF]. Such a problem has been studied in settings where both the source and target schemas belong to the same data model, in particular relational and nested relational [START_REF] Popa | Translating web data[END_REF][START_REF] Fagin | Data exchange: semantics and query answering[END_REF], XML [START_REF] Arenas | XML data exchange: Consistency and query answering[END_REF], or graph [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF]. Settings in which the source and the target schema are of heterogeneous data models have not been considered so far, apart from combinations of relational and nested relational schemas in schema mapping tools [START_REF] Popa | Translating web data[END_REF][START_REF] Kolaitis | Nested dependencies: structure and reasoning[END_REF].

In this paper, we focus on the problem of exchanging data between relational sources and graph-shaped target databases, which might occur in several interoperability scenarios in the Semantic Web, such as ontology-based data access [START_REF] Poggi | Linking data to ontologies[END_REF] and direct mappings [START_REF] Sequeda | On directly mapping relational databases to RDF and OWL[END_REF]. Motivations to map relational data to graphs abound, due to the far majority of data residing in relational databases and the need of integrating large amounts of linked data.

We express the relationships between the source and the target via schema mappings [START_REF] Popa | Translating web data[END_REF][START_REF] Fagin | Data exchange: semantics and query answering[END_REF][START_REF]Schema Matching and Mapping[END_REF] i.e., logical assertions between two conjunctive queries, one on the source and the other on the target. Schema mappings between graph databases have already been introduced in [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF] and we adopt their syntax for expressing the consequents of relational-toc 2015, Copyright is with the authors. Published in the Workshop Pro- ceedings of the EDBT/ICDT 2015 Joint Conference (March 27, 2015, Brussels, Belgium) on CEUR-WS.org (ISSN 1613-0073). Distribution of this paper is permitted under the terms of the Creative Commons license CCby-nc-nd 4.0 graph schema mapping assertions. We point out that the setting without target constraints directly follows from the results in [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF] on graph-to-graph data exchange. Furthermore, motivated by the fact that target constraints have been largely investigated within relational data exchange but so far disregarded for graph data exchange [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF], we add them to our setting.

In particular, we focus on two fundamental problems of interest: existence of solutions (i.e., given a source schema and an instance of it, a target schema, a set of source-to-target constraints, and a set of target constraints, decide whether there exists an instance of the target schema satisfying all given constraints) and query answering (i.e., computing the answers that hold for all solutions).

Our main contributions are the following:

' We show that in the presence of target equality-generating dependencies [START_REF] Beeri | A proof procedure for data dependencies[END_REF], both existence of solutions and query answering are intractable (NP-hard and coNP-hard, respectively). This holds even under significant restrictions.

' We relax the notion of target constraints by introducing sameAs1 target constraints, inspired by RDF 2 . We show that the existence of solutions becomes tractable while query answering is intractable (coNP-hard) for the same restrictions as for the previous case.

' We show that the notion of graph patterns [START_REF] Barceló | Querying graph patterns[END_REF], employed for graph data exchange [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF] as universal representatives of all solutions, cannot be used as such when adding target constraints.

We point out that our hardness results stand in terms of query complexity since in the proofs we have used a fixed source schema and instance, while the target schema and the mappings are part of the input. We also point out that none of our results is specific to the relational-to-graph setting, and hold in any setting where the target is a graph and the source is an arbitrary data model projecting on relational tuples. The source data can then be either XML, graph-shaped, or any other complex format as long as the left-hand sides of mappings extract relational tuples from it. Indeed, we shall pinpoint that the constraints on the target graph are solely responsible for the intractability results. Nevertheless, in the remainder of the paper, we focus on a relational data source for ease of presentation.

Organization. In Section 2, we define our problem setting.

In Section 3, we illustrate particular cases that can be solved using techniques from relational and graph data exchange. In Section 4, we characterize the complexity of the problems of interest. In Section 5, we present the challenges of defining and querying universal solutions. We discuss conclusions and future work in Section 6.

PROBLEM SETTING

Let us assume a countably infinite set of constants V that we use both as domain of relational databases and as node identifiers (or simply node ids) of graph databases.

Source schemas and queries. A source schema R is a finite collection of relational symbols. Each relational symbol has an arity that is a positive integer. An instance I of R is a function associating to each relational symbol R from R a set of tuples over V having the same arity as R. We abuse notation and use R to denote both relational symbol and its instance. A source query is a conjunction of atoms over R that uses only variables.

Target schemas and queries. A target schema Σ is a finite alphabet. An instance over Σ is a directed, edge-labeled graph G " pV, Eq, where V Ď V is a finite set of node ids and E Ď V ˆΣ ˆV is a finite set of edges. A nested regular expression (NRE ) is an expression of the following grammar:

r :" ε | a pa P Σq | a ´pa P Σq | r `r | r ¨r | r ˚| rrs,
where "`" stands for disjunction, "¨" for concatenation, "˚" for Kleene star, " ´" for traversing edges backwards, and "r s" for nesting. An NRE r defines a binary relation over graph nodes: r G is the set of pairs of nodes in G s.t. there exists a path defined by r between the two nodes. We consider the semantics of NREs as in [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF]. A target query is a conjunction of nested regular expressions (CNRE ) using variables only. We illustrate CNREs in Example 2.2.

Schema mappings.

A schema mapping is a set of sourceto-target tuple-generating dependencies [START_REF] Beeri | A proof procedure for data dependencies[END_REF] (or simply s-t tgds) i.e., a set of formulas of the form @x. pφRpxq Ñ Dy. ψΣpx, yqq, where φRpxq is query over R and ψΣpx, yq is a query over Σ. By x and y we denote vectors of variables. Moreover, all variables in x appear free in φRpxq, all variables in y appear free in ψΣpx, yq, and the variables in x that appear in ψΣpx, yq are free.

Target constraints. We consider two well-known types of target constraints: ' target equality-generating dependencies [START_REF] Beeri | A proof procedure for data dependencies[END_REF] (or simply egds) i.e., @x. pψΣpxq Ñ px1 " x2qq, ' target tuple-generating dependencies [START_REF] Beeri | A proof procedure for data dependencies[END_REF] (or simply target tgds) i.e., @x. pφΣpxq Ñ Dy. ψΣpx, yqq.

In the aforementioned definitions, φΣpxq and ψΣpxq are CN-REs over Σ, and x1 and x2 are among the variables in x. Moreover, we introduce sameAs target constraints that are a special case of target tgds i.e., @x. pψΣpxq Ñ px1, sameAs, x2qq.

In the sequel, we omit w.l.o.g. the universal quantifiers in front of a formula. Solutions. Given a setting Ω " pR, Σ, Mst, Mtq, an instance I of R and a graph database G over Σ, we say that G is a solution for I under Ω if pI, Gq satisfies Mst and G satisfies Mt. We denote the set of all solutions by Sol ΩpI q.

Usually, in relational data exchange, one aims at finding the universal solutions, from which there exist homomorphisms to all solutions [START_REF] Fagin | Data exchange: semantics and query answering[END_REF]. This notion has been redefined for graph data exchange as universal representatives captured with graph patterns [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF] that we discuss in detail in Section 3.2. Notice that Mst uses a CNRE on its right hand side. Then, a natural constraint is that a hotel is situated in exactly one city, which can be captured either by the egd Mt or by the

sameAs constraint M 1 t : Mt : px1, h, x3q ^px2, h, x3q Ñ px1 " x2q, M 1 t : px1, h, x3q ^px2, h, x3q Ñ px1, sameAs, x2q.
The two ways of expressing the aforementioned target constraint yield two different settings Ω " pR, Σ, Mst, Mtq and Ω 1 " pR, Σ, Mst, M 1 t q, respectively. We illustrate in Figure 1 solutions for I under these two settings: the graphs G1 and G2 are solutions under Ω, while G3 is a solution under Ω 1 . Problems of interest. We are interested in studying the following two problems:

1. Existence of solutions. Given a setting Ω " pR, Σ, Mst, Mtq and an instance I of R, decide whether there exists a solution for I under Ω. Additionally, we are interested in finding in our heterogeneous setting a mechanism similar to universal solutions [START_REF] Fagin | Data exchange: semantics and query answering[END_REF] or universal representatives [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF].

c1 c3 N hx hy c2 f f f h h (a) G1. c1 c3 N1 N2 hx hy c2 f f f f f h h (b) G2. c1 N1 N2 hy c3 N3 hx c2 f f f f f h h h (c) G3.
2. Query answering. Given a setting Ω " pR, Σ, Mst, Mtq, an instance I of R, and a query Q over Σ, we are interested in the certain answers of Q w.r.t. I under Ω, denoted certΩpQ, Iq, which are the answers that hold for all solutions i.e., the set Ş t Q G | G P Sol ΩpI qu (where by Q G we denote the set of tuples of nodes of G selected by the query Q). The query answering problem consists of deciding whether a given tuple of constants belongs to certΩpQ, Iq or not.

Example 2.2 (continued). Take the above instance I of the relations Flight and Hotel, and the above setting Ω. Then, take the query

Q " px1, f ¨f ˚rhs ¨f ´¨pf ´q˚, x2q.
Intuitively, this query selects the pairs of nodes px1, x2q from which the same hotel can be reached, or in other words, one can fly (possibly with connections) from the city x1 to another city that has a hotel and an ingoing flight (possibly with connections) whose origin x2 we want to select. Recall that the graphs G1 and G2 are both solutions for I under Ω. On these two graphs, the query Q selects as follows:

Q G 1 " tpc1, c1q, pc1, c3q, pc3, c1q, pc3, c3qu, Q G 2 " tpc1, c1q, pc1, c3q, pc3, c1q, pc3, c3q, pc1, N1q, pc3, N1q, pN1, c1q, pN1, c3q, pN1, N1qu.
Notice that only four pairs of nodes are common to these answer sets for the two considered graphs. Also notice that these four pairs of nodes are in fact the certain answers of Q w.r.t. I under Ω: certΩpQ, Iq " tpc1, c1q, pc1, c3q, pc3, c1q, pc3, c3qu.

On the other hand, notice that if we want to pose the same query Q under the other aforementioned example of setting (i.e., Ω 1 ), we obtain a different set of certain answers: cert Ω 1 pQ, Iq " tpc1, c1q, pc3, c3qu. Intuitively, this happens because the egds from the setting Ω ensure that in all of its possible solutions the nodes having the same hotel have been merged. In the second setting, this natural requirement has been encoded using a sameAs constraint, which is not exploited by the query Q, hence some of the certain answers of Q under Ω are no longer certain under Ω 1 .

˝3. BACKGROUND

In this section, we show that in two particular cases of our problem setting existing techniques from relational and graph data exchange can be applied (Section 3.1 and Section 3.2, respectively). This does not happen in the general case, as we show in the next section.

Relational data exchange

If we consider s-t tgds having on the right hand side conjunctions of NREs of the form a (with a P Σ), our problem setting reduces to a particular case of relational data exchange and the techniques from relational data exchange can be naturally applied. In particular, we can see the target schema as a set of binary relational symbols (one for each symbol of the target alphabet) and the chase [START_REF] Fagin | Data exchange: semantics and query answering[END_REF] returns a universal solution that can be essentially seen as a graph since it consists of a set of binary relations. We illustrate in Figure 2 the chased solution for I under pR, Σ, M 1 st , Mtq. Notice that there is no solution that has N1 and N2 on the same path from c1 to c2. Such a condition is desirable for a flight from c1 to c2 whose passengers have stopped in both hotels hy and hx, situated in the cities N1 and N2, respectively. We finally point out that we cannot capture solutions satisfying this kind of constraints for flights with an arbitrary number of stops without using the Kleene star (as in Example 2.2). c1

Graph data exchange

If we consider s-t tgds only, the existence of solutions and query answering can be solved using techniques from graphto-graph data exchange [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF]. In particular, solutions always exist and all solutions are captured by universal representatives defined as graph patterns.

Graph patterns. Let N be a countably infinite set of labeled null values. A graph pattern π over a finite alphabet Σ is a pair pN, Dq, where N Ď V Y N is a finite set of node ids or null values, and D Ď N ˆNRE pΣq ˆN , where NRE pΣq denotes the set of all NREs over Σ. The semantics of graph patterns are defined in terms of homomorphisms [START_REF] Barceló | Querying graph patterns[END_REF]. Given a graph pattern π " pN, Dq and a graph database G " pV, Eq, a homomorphism from π into G is a total function h : N Ñ V s.t.:

1. h is the identity over N X V (i.e., over the node ids from N ),

2. for all edges pu, r, vq P D (u, v P N, r P NRE pΣq), it holds that phpuq, hpvqq P r G.

We write π Ñ G if there exists a homomorphism from π to G. The set of all graphs represented by π over Σ, denoted Rep Σ pπq is the set of all graphs G over Σ such that π Ñ G.

Universal representatives. Given a setting Ω " pR, Σ, Mst, Hq and an instance I of R, a graph pattern π is a universal representative of I under Ω if Sol ΩpI q " Rep Σ pπq [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF].

In graph data exchange, universal representatives are computed using an adaptation of the standard chase procedure from relational data exchange [START_REF] Fagin | Data exchange: semantics and query answering[END_REF]. Moreover, the variant of chase that is tailored for graph data exchange [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF] can be easily adapted to construct a universal representative in our relational-to-graph heterogeneous setting. We illustrate a result of this procedure in Example Then, query answering reduces to querying the graph pattern [START_REF] Barceló | Querying graph patterns[END_REF] chased as universal representative.

Example 3.2 Take the schemas R and Σ, the instance I, and the s-t tgds Mst from Example 2.2. The graph pattern π in Figure 3 is a universal representative of all solutions for I under pR, Σ, Mst, Hq i.e., all graphs to which there exists a homomorphism from π are solutions.

c1 c3 N1 N2 hy hx c2 N3 f ¨f f ¨f ˚f ¨f f ¨f h h h f ¨f f ¨f Figure 3: Graph pattern from Example 3.2.
However, notice that the sole s-t tgds might not capture interesting mapping scenarios involving graphs. As an example, the target constraint "a hotel is situated in exactly one city" cannot be expressed in settings such as the one presented in Example 3.2.

COMPLEXITY RESULTS

In this section, we present our main contributions. More precisely, we study the complexity of the two problems of interest, namely existence of solutions and query answering, for settings that exhibit target egds (Section 4.1) or target tgds (Section 4.2), respectively.

Complexity of target egds

First, let us show the intractability of the existence of solutions when we allow egds to our setting. Theorem 4.1 Given a setting Ω " pR, Σ, Mst, Mtq where Mt consists of egds, and an instance I of R, deciding whether there exists a solution for I under Ω is NP-hard.

Proof. We prove by reduction from 3SAT, known as an NP-complete problem. The reduction works as follows. Given a formula ρ " C1 ^. . . ^Ck in 3CNF over the set of variables tx1, . . . , xnu, we construct -The setting Ωρ " pRρ, Σρ, Mρ st , Mρ t q s.t. -The instance Iρ " tR1pc1q, R2pc2qu.

'
Intuitively, the egds are defined such that a graph collapses if each variable has more than one valuation (*) or the valuation of the variables makes the formula false (**).

We illustrate the construction on the formula ρ0 " px1 _ x2 _ x3q ^p x1 _ x3 _ x4q. We have the s-t tgd R1pxq R2pyq Ñ px, a, yq^px, pt1 `f1q, xq^. . .^px, pt4 `f4q, xq, the egds of type (*) px, pti ¨fi ¨aq, yq Ñ px " yq (with 1 ď i ď 4), and the egds of type (**) px, pf1 ¨t2 ¨f3 ¨aq, yq Ñ px " yq and px, pt1 ¨f3 ¨t4 ¨aq, yq Ñ px " yq. Then, the graph in Figure 4 is a solution that encodes the valuation v s.t. vpx1q " vpx2q=true and vpx3q " vpx4q=false that makes ρ0 true.

We claim that there exists a solution for Iρ under Ωρ iff ρ P3SAT.

For the if part, we show that the existence of a valuation making ρ true implies the existence of a solution. Take a valuation v : tx1, . . . , xnu Ñ ttrue, falseu making ρ true. Then, construct the graph G " ptc1, c2u, Eq s.t. E " tpc1, a, c2qu Y tpc1, ti, c1q | 1 ď i ď n and vpxiq " trueu Y tpc1, fi, c1q | 1 ď i ď n and vpxiq " falseu. Note that G and Iρ satisfy the s-t tgd. Since there is exactly one edge labeled bi P tti, fiu from c1 to c2, the egds of type (*) are satisfied. Moreover, since the bi's correspond to a valuation making ρ true, there is at least one satisfied literal in every clause of ρ, hence the egds of type (**) are also satisfied. Thus, G is a solution.

For the only if part, take a solution G. Since G satisfies the s-t tgd, we infer that G encodes at least one valuation of every variable. Since G satisfies the egds of type (*), we infer that G encodes at most one valuation of every variable. Thus, G encodes exactly one valuation of every variable. Since G satisfies the egds of type (**), we conclude that G encodes a valuation making ρ true. c2 c1 a t1, t2, f3, f4 We point out that Theorem 4.1 holds even under significantly restricted assumptions that have been used in the proof: (i) fixed source schema consisting of two unary relations only, (ii) fixed source instance, (iii) s-t tgds using only conjunctions of NREs of the form a or a `b (with a, b P Σ) that is a slight relaxation of the restriction from Section 3.1, and (iv) egds that use only NREs of the form a1 ¨. . . ¨an, with pairwise distinct a1, . . . , an P Σ (NREs referred to as "SORE(¨)" [START_REF] Antonopoulos | Definability problems for graph query languages[END_REF]). Next, we prove that query answering is intractable under the same assumptions and for queries consisting of NREs that use disjunction and concatenation only.

Corollary 4.2 Given a setting Ω " pR, Σ, Mst, Mtq where Mt consists of egds, an instance I of R, a NRE r, and a tuple of constants pc1, c2q, deciding whether pc1, c2q P certΩpr, Iq is coNP-hard.

Proof. We take the proof of Theorem 4.1, and we additionally consider the NRE rρ " a ¨a. We claim that pc1, c2q P certΩ ρ prρ, Iρq iff ρ R3SAT. For the if part, notice that ρ R3SAT implies that there is no solution hence pc1, c2q is a certain answer. For the only if part, since pc1, c2q is a certain answer, we infer that either (i) there is no solution or (ii) there is at least a solution and pc1, c2q is an answer for all solutions. But (ii) is false since there exist solutions for which pc1, c2q is not an answer for rρ (e.g., in Figure 4). Both parts follow directly from the proof of Theorem 4.1. Finally, we point out that in our reduction the source schema and instance are fixed while the target schema and the mappings are part of the input. Hence, our hardness results stand in terms of query complexity. Similar intractability results in the presence of target constraints (particularly in combined complexity) have been shown for relational and XML data exchange [START_REF] Kolaitis | The complexity of data exchange[END_REF][START_REF] Arenas | XML data exchange: Consistency and query answering[END_REF][START_REF] Amano | XML schema mappings: Data exchange and metadata management[END_REF][START_REF] Calì | Taming the infinite chase: Query answering under expressive relational constraints[END_REF]. However, our contribution is novel since to the best of our knowledge target constraints on a graph target schema have not been previously considered in the literature, and moreover, we use a fixed source schema and instance in the proof. We also point out that our results are not specific to the relational-to-graph setting and hold in any setting where the target is a graph.

Complexity of target tgds

In this section, we use sameAs constraints instead of egds. First, let us show that the existence of solutions becomes trivial. More precisely, a solution can be computed as follows: (i) chase a graph pattern π using the s-t tgds only, (ii) take a graph G s.t. π Ñ G, and (iii) add in G the necessary sameAs edges to satisfy the sameAs constraints. Recall that the difficulty of deciding the existence of solutions in the case of egds was that we cannot merge two constants. Notice that this difficulty is overcome since we can add sameAs edges between any two nodes, even between two constants.

Next, we prove that in the presence of sameAs constraints the problem of certain answers is intractable under the same assumptions as in Section 4.1.

Proposition 4.3 Given a setting Ω " pR, Σ, Mst, Mtq where Mt consists of sameAs constraints, an instance I of R, a NRE r, and a tuple of constants pc1, c2q, deciding whether pc1, c2q P certΩpr, Iq is coNP-hard.

Proof. We take from the proof of Theorem 4.1 the same Rρ, Iρ, Σρ, Mρ st , and we replace each px " yq from Mρ t by px, sameAs, yq to obtain the set of sameAs constraints M 1 ρ t and Ω 1 ρ " pRρ, Σρ Y tsameAsu, Mρ st , M 1 ρ t q. Then, take r 1 ρ " sameAs. We claim that pc1, c2q P cert Ω 1 ρ pr 1 ρ , Iρq iff ρ R3SAT, which follows similarly to Theorem 4.1.

Moreover, we observe that sameAs constraints are a particular case of target tgds, and therefore, query answering is intractable in the presence of target tgds.

Corollary 4.4 Given a setting Ω " pR, Σ, Mst, Mtq where Mt consists of target tgds, an instance I of R, a NRE r, and a tuple of constants pc1, c2q, deciding whether pc1, c2q P certΩpr, Iq is coNP-hard.

TOWARDS UNIVERSAL SOLUTIONS

Next, we study a natural adaptation of the standard chase procedure [START_REF] Fagin | Data exchange: semantics and query answering[END_REF] to take into account egds. The result of our adapted chase is a graph pattern π. To this purpose, we consider two types of chase steps: (1) for s-t tgds we do similarly to [START_REF] Barceló | Schema mappings and data exchange for graph databases[END_REF] when computing universal representatives in graph data exchange without target constraints, and (2) for egds, for each ψΣpxq Ñ px1 " x2q, (i) if the images in π of both x1 and x2 are constants, then the chase fails, (ii) if one has as image in π a constant and the other a labeled null, then the chase replaces in π the labeled null by the constant, and (iii) if both have labeled nulls as images in π, the chase chooses one of them and replaces it in π with the other. As for relational data exchange, if the chase fails, then there is no solution. As opposed to relational data exchange, we observe that a successful chase does not guarantee the existence of a solution. Intuitively, the difficulty comes from the fact that the chase result is a graph pattern with NREs on the edges (unlike a graph with symbols on the edges). Consequently, there might not exist any graph G s.t. π Ñ G and G satisfies the target constraints because it may be the case that there is no path satisfying the NREs and the egds at the same time. The following example shows such a situation. Example 5.2 Take the source schema tR, P u, an instance Rpc1q and P pc2q, the target schema ta, b, cu, the s-t tgd Rpxq ^P pyq Ñ px, a ¨pb ˚`c ˚q ¨a, yq, and the egd px, a b `c, yq Ñ px " yq. The aforementioned adapted chase succeeds and returns the graph pattern π in Figure 6(a). Although the chase has not failed, no solution exists because there is no graph G s.t. π Ñ G and G satisfies the egds. In particular, the graph G (s.t. π Ñ G) from Figure 6(b) satisfies the s-t tgd but if we try to transform it in a solution we fail because we attempt to merge two constants. c1 We next show that, even when solutions exist, graph patterns as such cannot be used as universal representatives in the presence of egds. Proposition 5.3 Given a setting Ω " pR, Σ, Mst, Mtq where Mt consists of a non-empty set of egds, and an instance I of R, there does not exist a graph pattern π s.t. Sol ΩpI q " Rep Σ pπq.

Intuitively, let us assume that there exists a graph pattern π s.t. Sol ΩpI q " Rep Σ pπq. Then, if we take a graph G P Sol Ω and a homomorphism h : π Ñ G, we can construct the graph G 1 by adding nodes and edges to G s.t. some egd is no longer satisfied, thus G 1 is not a solution for I under Ω, but h : π Ñ G 1 is still a homomorphism. The next example clarifies when such a situation can occur.

Example 5.4 The graph in Figure 7 is not a solution for the mappings and instance from Example 2.2 although there exists a homomorphism from the chased graph pattern from Figure 5. c1 To address the problem of universal representatives in settings involving egds, a natural approach is to define the universal representative as a pair (graph pattern, set of egds). In this case, the solutions are the graphs satisfying the egds and s.t. there exists a homomorphism from the pattern. For example, the universal representatives for Example 2.2 would be the pattern in Figure 5 together with the egd in Mt from Example 2.2. We also point out that the above discussion can be easily generalized for sameAs constraints or arbitrary target tgds.

CONCLUSIONS AND FUTURE WORK

We have presented our work on relational-to-graph data exchange. Our main results are the proofs of intractability of the existence of solutions and query answering that hold even under considerable restrictions of the problem setting. As future work, we would like to investigate the complexity upper bounds of these problems and look for tractable fragments to have a complete picture of the difficulty of our setting. A natural question that remains open is how to query universal representatives consisting of a pair (graph pattern, set of target constraints). We would also like to investigate practical scenarios of relational-to-RDF data exchange and other classes of heterogeneous schema mappings. Additionally, it would be interesting to combine existing learning techniques for relational [START_REF] Bonifati | Interactive inference of join queries[END_REF] and graph [START_REF] Bonifati | Learning path queries on graph databases[END_REF] queries in order to propose algorithms that automatically infer relational-tograph mappings from examples provided by the user.

Example 2 . 2

 22 Take a source schema R consisting of two relations: Flight storing information about flights that may have intermediate stops between the source and destination cities, and Hotel storing information about the hotels in which the passengers of such flights have stopped. Moreover, take the following instance I: schema consisting of the alphabet Σ " tf, hu. The edges labeled by f indicate a direct flight between two cities while the edges labeled by h indicate that a city has a hotel. Moreover, consider the following s-t tgd that basically requires that for each hotel where the passengers of a flight have stopped, there exists a city where the respective hotel is situated, and there exist flights from src to such city and from such city to dest:Mst : Flightpx1, x2, x3q ^Hotelpx1, x4q Ñ Dy. px2, pf ¨f ˚q, yq ^py, h, x4q ^py, pf ¨f ˚q, x3q.

Figure 1 :

 1 Figure 1: Solutions from Example 2.2. The dotted edges are labeled by sameAs.

Example 3 . 1

 31 Take the schemas R and Σ, the instance I, and the egds Mt from Example 2.2. Since we consider only NREs of the form a (with a P Σ), we cannot express the same Mst as in Example 2.2. However, we can express the following: M 1 st : Flightpx1, x2, x3q ^Hotelpx1, x4q Ñ Dy. px2, f , yq ^py, h, x4q ^py, f , x3q.

Figure 2 :

 2 Figure 2: Solution from Example 3.1.

Figure 4 :

 4 Figure 4: Solution for ρ0.

Example 5 . 1 Figure 5 :

 515 Figure

Figure 6 :

 6 Figure 6: Result of a successful chase.

Figure 7 :

 7 Figure 7: Graph from Example 5.4.

  Definition 2.1 A (relational-to-graph) data exchange setting Ω " pR, Σ, Mst, Mtq consists of a relational source schema R, a graph target schema Σ, a set Mst of s-t tgds, and a set Mt of target constraints.

  Rρ " tR1, R2u, both unary relations,

' Σρ " ta, t1, f1, . . . , tn, fnu. ' Mρ st contains a unique s-t tgd R1pxq^R2pyq Ñ px, a, yqp x, t1 `f1, xq ^. . . ^px, tn `fn, xq. ' Mρ t contains two types of egds: (*) px, ptj ¨fj ¨aq, yq Ñ px " yq, for 1 ď j ď n, (**) px, pbi 1 ¨bi 2 ¨bi 3 ¨aq, yq Ñ px " yq, for 1 ď i ď k, for 1 ď i1, i2, i3 ď n, xi 1 , xi 2 , xi 3 are the variables used in clause Ci, and for 1 ď l ď 3, bi l is ti l if xi l appears in a negative literal in Ci, and fi l , otherwise.

http://www.w3.org/wiki/WebSchemas/sameAs

http://www.w3.org/RDF/


Loïc Caroux
email: loic.caroux@inria.fr

Ludovic Le Bigot
email: ludovic.le.bigot@univ-poitiers.fr

Nicolas Vibert
email: nicolas.vibert@univ-poitiers.fr

How visual background motion and task difficulty modulate players' performance in a shooting task

Keywords: Video game, Challenge, Eye movements, Low-level visual features, Visual perception Highlights -Lateral

Caroux, L., Le Bigot

Introduction

Because challenge is a main factor in players' engagement in a game [e.g., 1], optimal player-video game interaction is obtained when the game presents a challenge for players. In contrast with typical human-computer interactions (i.e., linked to productivity), video game displays do not need to be simplified as much as possible to optimize the interaction but must rather be adapted to players' abilities and expectations to maintain their high level of motivation [START_REF] Malone | Making learning fun: A taxonomy of intrinsic motivations for learning[END_REF][START_REF] Pagulayan | User-Centered Design in Games[END_REF].

Many studies have shown that challenge is generally set by the difficulty of execution of the main task, which may depend on the number of enemies to hit or avoid, the speed of the enemies' motion, or their level of artificial intelligence [e.g., 4,5-10]. However, only few studies [e.g., [START_REF] Jie | Video game design using an eye-movement-dependent model of visual attention[END_REF][START_REF] Knez | Lighting in digital game worlds: Effects on affect and play performance[END_REF][START_REF] Wolfson | The effects of sound and colour on responses to a computer game[END_REF] have assessed how the characteristics of the game interface, including the visual background, can also be used to modulate game difficulty.

For example, in many video games, the overall scene background moves either periodically or continuously. As detailed below, many studies have shown that the features of the visual background, including background motion [START_REF] Caroux | Impairment of shooting performance by background complexity and motion[END_REF][START_REF] Caroux | Impact of the motion and visual complexity of the background on players' performance in video game-like displays[END_REF][START_REF] Harrison | Multisensory integration with a headmounted display: Background visual motion and sound motion[END_REF][START_REF] Kaminiarz | Localization of visual targets during optokinetic eye movements[END_REF][START_REF] Tozzi | The effect of optokinetic nystagmus on the perceived position of briefly flashed targets[END_REF], could impair people's performance in various tasks and situations. Generally, the negative impact of background motion can be explained by people's visual behavior, which reflects attentional processes [e.g., 19]. However, few studies have investigated the combined effect of background motion and the difficulty of the game on players' performance. The objective of the present study was to focus on how lateral background motion interacts with the level of difficulty of a simple game to influence players' performance.

Influence of the design of visual interfaces on players' performance

Several studies have investigated how the characteristics of visual interfaces, such as the position of heads-up displays on the screen [e.g., [START_REF] Caroux | Maximizing players' anticipation by applying the proximitycompatibility principle to the design of video games[END_REF][START_REF] Sabri | High-resolution gaming: Interfaces, notifications, and the user experience[END_REF], 3D stereoscopy [e.g., 22], screen size [e.g., 23], or the point of view [e.g., [START_REF] Bae | The effects of egocentric and allocentric representations on presence and perceived realism: Tested in stereoscopic 3D games[END_REF][START_REF] Yannakakis | Towards affective camera control in games, User Model[END_REF], influence players' performance, players' experience, or both. The results are potentially interesting for designers who may better control the challenge presented by games by adjusting the parameters of the visual displays.

Only few studies have addressed the influence of background characteristics on players' performance [START_REF] Jie | Video game design using an eye-movement-dependent model of visual attention[END_REF][START_REF] Knez | Lighting in digital game worlds: Effects on affect and play performance[END_REF][START_REF] Wolfson | The effects of sound and colour on responses to a computer game[END_REF]. Knez and Niedenthal [START_REF] Knez | Lighting in digital game worlds: Effects on affect and play performance[END_REF] studied the impact of background lighting in video games. They showed that better performance was obtained with a warm, reddish lighting than with a cool, bluish lighting. The warm background lighting increased performance because the players found it more pleasant than the cool lighting. Wolfson and Case [START_REF] Wolfson | The effects of sound and colour on responses to a computer game[END_REF] assessed the impact of background color on players' performance across many successive games. When the background was blue, performance increased regularly until the end of the session. When the background was red, the performance increased faster but decreased in the second half of the session. This impact of background color was associated with the players' level of arousal. Red provoked a faster arousal, but habituation effects provoked a decrease in performance after a large number of games were played. Jie and Clark [START_REF] Jie | Video game design using an eye-movement-dependent model of visual attention[END_REF] tested the impact of background complexity on players' performance.

Participants had to hit targets that were displayed in areas of the screen with either a high or low density of background visual information. The time needed to hit targets was shorter when the target appeared at locations of lower background density. High background complexity disturbed the participants' visual information processing and slowed the target detection processes.

All visual information displayed on the screen, including background information, may have a significant impact on players' performance. According to our knowledge, however, no study has yet investigated the combined impact of visual background motion and the difficulty of the main game task on players' performance.

Impact of background motion on users' performance

Video game displays are dynamic as all their elements can be modified and they can appear or disappear at any time. The scene background often moves to simulate motion of the player or of the player's avatar within the virtual environment of the game. Several types of apparent motion occur in video games. One of the most frequent motions is lateral motion toward the left or right, which is simulated by a lateral movement of the entire background toward the opposite direction 2 .

Both in natural scenes and virtual environments, large-scale motion of the visual background triggers the optokinetic nystagmus (OKN) [START_REF] Kim | Eccentric gaze dynamics enhance vection in depth[END_REF][START_REF] Riecke | Cognitive factors can influence self-motion perception (vection) in virtual reality[END_REF]. The OKN is a reflexive, conjugate movement of both eyes in which two phases alternate. During the slow phase, the eyes move in the direction of background motion, ideally at the same velocity, whereas the fast phase regularly returns the eyes to the opposite direction [START_REF] Ilg | Slow eye movements[END_REF][START_REF] Waespe | Slow eye movements induced by apparent target motion in monkey[END_REF]. The slow phase of the OKN is a compensatory eye movement that allows the observer to maintain visual input on the retina.

The existence of the OKN has strong implications for activities performed on moving visual backgrounds. Indeed, triggering the OKN negatively affects observers' performance in simple perceptual tasks. Kaminiarz et al. [START_REF] Kaminiarz | Localization of visual targets during optokinetic eye movements[END_REF] and Tozzi et al. [START_REF] Tozzi | The effect of optokinetic nystagmus on the perceived position of briefly flashed targets[END_REF] studied the impact of OKN on a target localization task. Participants had to localize a briefly flashed target that was displayed on a laterally moving, patterned background. Because the moving background triggered the OKN, large errors of localization were observed compared with the fixed version of the same background. Caroux et al. [START_REF] Caroux | Impairment of shooting performance by background complexity and motion[END_REF][START_REF] Caroux | Impact of the motion and visual complexity of the background on players' performance in video game-like displays[END_REF] studied the effect of background motion on the perception of superimposed items during a shooting task. Participants had to detect targets that appeared randomly on patterned backgrounds and shoot them as rapidly as possible. They showed that performance (time to shoot targets) was worse when the background was laterally moving than when it was stationary. Similarly, Harrison et al. [START_REF] Harrison | Multisensory integration with a headmounted display: Background visual motion and sound motion[END_REF] demonstrated that background motion decreased performance in a simple task involving the integration of brief auditory and visual signals. Therefore, moving backgrounds decrease 2 Examples of recent, best-selling video games that use lateral background motion include platform games (e.g., New Super Mario Bros U, Nintendo, 2012) or shoot'em ups (e.g., Sine Mora, Microsoft Studios, 2012). performance in tasks that are rather simple, namely tasks that involve transient presentations of stationary items and do not mobilize many attentional resources. However, moving visual backgrounds do not always have a negative impact on performance, most likely because human observers are able to voluntarily suppress the OKN by fixating any visual item that is superimposed on the moving background [e.g., [START_REF] Ilg | Slow eye movements[END_REF][START_REF] Pola | Suppression of optokinesis by a stabilized target: Effects of instruction and stimulus frequency[END_REF][START_REF] Rubinstein | Optokinetic nystagmus suppression as an index of the allocation of visual attention[END_REF][START_REF] Wyatt | A mechanism for suppression of optokinesis[END_REF]. Menozzi and Koga [START_REF] Menozzi | Visual information processing in augmented reality: Some aspects of background motion[END_REF] compared how people read a text displayed on a laterally moving, patterned background to a fixed version of the same background. Background motion had no effect on reading times or on the eye movements while reading. The main difference with the previous studies was that reading demands many more attentional resources than localizing a briefly flashed target and involves sustained attention to many fixed words and letters that are continuously superimposed on the background. The fact that readers must constantly fixate on text words was apparently sufficient to cancel the OKN and suppress its negative impact on the task. Finally, from a broader point of view, more attention-demanding visual tasks can override automated biological behaviors in general. For example, the effect of background motion on individuals' postural sway (when they are standing) is minimized when the tasks require more foveal fixation [START_REF] Stoffregen | Modulating postural control to facilitate visual performance[END_REF].

The present study

Two experiments were designed to simultaneously assess the impact of lateral motion of the scene background and of the difficulty level of the task on participants' performance and eye movements in a video game-like environment. The shooting task was designed with two different difficulty levels.

The goal was to find, aim at and hit as fast as possible successive targets, which were always displayed among four distractors. The task difficulty was set by the number of visual features that had to be considered to differentiate the target from distractors. Indeed, visual search experiments have consistently shown [see [START_REF] Reali | Inefficient conjunction search made efficient by concurrent spoken delivery of target identity[END_REF][START_REF] Thornton | Parallel and serial processes in visual search[END_REF][START_REF] Treisman | A feature-integration theory of attention[END_REF][START_REF] Wolfe | Guided Search 2.0: A revised model of visual search[END_REF] for reviews] that search is more difficult when the target differs from distractors by a conjunction of visual features (i.e., finding a red, vertical bar among green, vertical bars and red, horizontal bars) than if the target differs from all distractors by a single feature (i.e., finding a red bar among green bars or a vertical bar among horizontal bars).

According to visual search experiments [START_REF] Reali | Inefficient conjunction search made efficient by concurrent spoken delivery of target identity[END_REF][START_REF] Thornton | Parallel and serial processes in visual search[END_REF], the first hypothesis was that the performance would be lower when the task is difficult (i.e., when the target differs from distractors by a conjunction of visual features) than when the task is easy (i.e., when the target differs from distractors by a single visual feature). Eye movement recordings have consistently shown that both the number and average duration of eye fixations increased with task difficulty, both during reading and visual search [for review , 38]. Therefore, the second hypothesis was that the number and average duration of fixations are greater when the task is more difficult. Generally, the number of participants' fixations was expected to increase in parallel with shooting times. Although the OKN decreases performance in simple target detection tasks [e.g., [START_REF] Kaminiarz | Localization of visual targets during optokinetic eye movements[END_REF][START_REF] Tozzi | The effect of optokinetic nystagmus on the perceived position of briefly flashed targets[END_REF], its negative impact can be suppressed when the visual task involves more sustained attention on stationary items [START_REF] Menozzi | Visual information processing in augmented reality: Some aspects of background motion[END_REF]. Therefore, the third hypothesis was an interaction hypothesis, which stated that the performance would be lower when the background is moving than when it is stationary but only for the lower level of task difficulty.

An additional goal of the present study was to investigate whether these factors had an effect regardless of whether the background was in black and white or in a "neutral" color. Green was chosen because the literature states that this color has a lower impact on individuals' arousal levels and emotions than red or blue [START_REF] Wolfson | The effects of sound and colour on responses to a computer game[END_REF][START_REF] Bonnardel | The impact of colour on Website appeal and users' cognitive processes[END_REF][START_REF] Valdez | Effects of color on emotions[END_REF]. Therefore, the findings were expected to be the same regardless of the background color. Consequently, because making a hypothesis that predicts an absence of difference would be incorrect, two separated experiments were conducted. The three hypotheses explained above were tested in the same way in both experiments.

Experiment 1: Green-colored background 2.1. Methods

Participants

Twenty-two volunteers (15 women) aged M = 20.1 years (SD = 3.0) participated in the experiment.

All participants were native French speakers. They had normal or corrected-to-normal vision and did not suffer from colorblindness.

Apparatus

A head-free Tobii T120 eye-tracker with a 17-inch screen (approximately 27 deg of visual angle; 1280 x 1024 pixels; 75-Hz refresh rate) was used to mimic, as accurately as possible, natural interaction with a computer game interface. A single computer controlled the eye tracker and collected all the data. Gaze positions were obtained at 120 Hz with an average precision of 0.5 degree of visual angle (approximately 5 mm on the screen). Eye movements were analyzed using Tobii Studio 2.0.6 software. Eye fixations were defined as any period in which the gaze remained focused for 58 ms or more within an area of 30 pixels in diameter (approximately 9 mm or 0.9 deg of visual angle).

According to the literature, the minimal useful duration of eye fixation for processing information is approximately 50-60 ms [START_REF] Rayner | Eye movements in reading and information processing: 20 years of research[END_REF]. The sampling rate of the eye-tracker that was used in the present experiments was 120 Hz (i.e., one measurement was made every 8.33 ms). Therefore, the nearest value to 50-60 ms that is a multiple of 8.33 was 58 ms. A speaker located in front of the participant was used to display an auditory description of the target (see below). The participants performed the experimental task with a keyboard.

Material

The material was created with "Adobe Director 11" software. A visual background was designed with elements extracted from the video game "Child of Eden" (Ubisoft, 2011) (Figure 1). The background displayed a mainly green dotted pattern on which abstract objects were regularly scattered (main HSV color scale of the screen: Hue = 120, Saturation = 100, Value = 0 to 100). The objects covered 50% of the surface of the dotted pattern. A stationary and a laterally moving version of this background were used. The laterally moving background moved leftwards at a speed of 121 mm/s (approximately 12 degrees of visual angle per second). The size of the entire visual display was 1280 x 1024 pixels. It was displayed on the 17-inch screen of a Tobii T120 eye-tracker, which was used to collect the eye movement data.

The target and distractors of the shooting task were taken from among four versions of a creature, which could be either blue (HSV: 228, 74, 25-84) or red (HSV: 7, 74, 25-84) and either small (85 x 66 pixels, approximately 22 x 17 mm on the screen) or large (85 x 99 pixels, approximately 22 x 26 mm).

The cursor appeared as a weapon crosshair 114 pixels in diameter (approximately 30 mm). The four elements of target description were 0.5 second-long recordings of words uttered by a male voice, namely "blue", "red", "large" and "small" ("bleu", "rouge", "grand" and "petit" in French).

[Figure 1 near here]

Design and procedure

The experimental design was a 2 X 2 design with the presence/absence of background motion and the level of difficulty of the task (easy or difficult) as factors. These factors were manipulated within participants.

At the beginning of each trial, one of the backgrounds was displayed and an empty black square of 74 mm per side (approximately 7.4 degree of visual angle) was shown at the center of the screen for 1 second to orient the participant's gaze toward the center of the display without cancelling the potential effects of background motion such as the OKN. The participants were instructed to focus their gaze as much as possible within the square. The two words that described the color and size of the target were uttered one after the other at the moment the black square was displayed. The order of the color and size words was counterbalanced. Then, the target, the four distractors and the cursor all appeared at the same random horizontal position on the screen. The cursor was located on the central vertical axis of the screen, whereas the target was displayed at a random distance to the right or left. Two of the distractors were located in the right half of the screen, and the two other distractors were located in the left half, again at random distances. When the task was easy, the target differed in size and color from all the distractors. When the task was difficult, two randomly determined distractors were the same size as the target but a different color. The two other distractors were the same color but a different size (see examples in Figure 1).

After the target and distractors were displayed on the screen, the participants could move the cursor to aim at the target. The participants had to aim at the target of the color and size given by the two words. To do so, they could move the cursor to the left or to the right of the screen by pressing the left and right arrow keys of the keyboard, respectively. The participants could shoot when they wanted by pressing the "space" key of the keyboard. They could move the cursor and shoot as often as they wished until the target was hit (i.e., as long as the cursor and target were not superimposed when the shot was fired). When the target was hit, the target, distractors and cursor disappeared from the screen, and another trial began.

The shooting task was presented as a simple video game. The participants were asked to shoot the enemy (the target) as fast as possible. A set of 64 trials was presented to the participants as one game. Each participant performed four games, with a pause between each game. A global score was given after the four games had been performed. All trials in a game were performed on the same background, which stayed visible between each trial. If a moving background was used, the motion was continuous for the entire game. The order of presentation of the 4 games (2 games on the moving background and 2 games on the stationary background) was randomized. Within each game, task difficulty was also randomized so that half of the trials were easy, and the other half were difficult.

Dependent measures

The participants' performance was assessed using the average time needed to hit the target (shooting time) as the dependent measure. Additionally, the average number of shots per trial was also measured to assess task accuracy. The participants' eye movements were analyzed using the average number of fixations per trial and their mean duration as dependent measures. For each trial, only the eye fixations that were made while searching for the target were analyzed. Specifically, neither the fixation that was interrupted by the appearance of the target and distractors nor the fixation that was ongoing when the target was hit were included in the analysis. All variables were analyzed using repeated measures ANOVAs with the background motion (presence or absence) and the task difficulty (easy or difficult) as within-participant factors. As is often observed in reaction time experiments, the shooting times followed a non-normal, positively skewed distribution. Therefore, the shooting time data were logarithmically transformed before ANOVAs were performed.

Results

All premature (shooting times shorter than 100 ms) and late responses (shooting times greater than 3000 ms) were considered errors and were excluded from analyses. Data from one participant for whom the proportion of excluded trials exceeded 15% were not analyzed. For the 21 other participants, the proportion of excluded trials ranged from 0.0% to 9.8% (M = 2.5%) and did not vary significantly across conditions.

Shooting time

As shown in Figure 2, task difficulty had an impact on shooting times, F(1,20) = 188.00, p < .001, η² p = .90. Shooting times were longer when the task was difficult (M = 1592 ms, SD = 225) than when it was easy (M = 1392 ms, SD = 239). Background motion also had an influence on shooting times, F(1,20) = 35.50, p < .001, η² p = .64, which were longer with the moving (M = 1546 ms, SD = 247) than with the stationary background (M = 1439 ms, SD = 247). The interaction between the two factors did not reach significance, F(1, 20) < 1.

[Figure 2 near here]

Number of shots

Background motion influenced the number of shots made by the participants, F(1,20) = 14.02, p < .01, η² p = .41, which was higher with the moving (M = 1.20, SD = .12) than with the stationary background (M = 1.13, SD = .11). In contrast, there was no impact of task difficulty on the number of shots, F(1,20) < 1. The interaction between the two factors did not reach significance, F(1, 20) < 1.

Number and duration of eye fixations

Qualitative observation of the eye movement data displayed by a sample of participants showed that when the background was moving, an OKN consisting of slow phases oriented leftwards interrupted by quick phases oriented rightwards was present between trials. The maximum velocity of slow phases reached 5 to 10 deg/s depending on the participants. When the target and distractor appeared, the OKN disappeared, and only fixations and saccades were visible, most likely because the target and/or distractors were used as stationary "anchoring points" to cancel the nystagmus [START_REF] Ilg | Slow eye movements[END_REF].

As shown in Table 1, task difficulty impacted the number of fixations per trial, F(1,20) = 36.43, p < .001, η² p = .65, which was greater when the task was difficult (M = 3.22, SD = 1.32) than when it was easy (M = 2.67, SD = 1.16). There was a marginal effect of background motion, F(1, 20) = 3.19, p = 0.09, so that the number of fixations per trial tended to be higher with the moving (M = 3.10, SD = 1.24) than with the stationary background (M = 2.79, SD = 1.28). The interaction between the two factors did not reach significance, F(1, 20) < 1.

Task difficulty had no significant impact on the mean duration of fixations, F(1,20) = 1.26, p = .26, which was M = 201 ms, SD = 55 when the task was difficult and M = 197 ms, SD = 64 when it was easy. There was no significant effect of background motion, F(1, 20) < 1, or any significant interaction between the two factors, F(1, 20) < 1.

[Table 1 near here]

Experiment 2: Black-and-white background

Methods

The apparatus, design, procedure and participants of Experiment 2 were the same as those of Experiment 1. The material was the same as in Experiment 1, but a black-and-white version (HSV: 0, 0, 0-100) of the background of Experiment 1 was used.

Results

As in Experiment 1, all premature (shooting times shorter than 100 ms) and late responses (shooting times greater than 3000 ms) were considered errors and were excluded from analyses. Data from one participant for whom the proportion of excluded trials exceeded 15% were not analyzed. For the 21 other participants, the proportion of excluded trials ranged from 0.0% to 9.8% (M = 2.8%) and did not vary significantly across conditions.

Shooting time

As shown in Figure 3, task difficulty impacted shooting times, F(1,20) = 199.13, p< .001, η² p = .91. Shooting times were longer when the task was difficult (M = 1,586 ms, SD = 240) than when it was easy (M = 1,381 ms, SD = 239). Background motion also influenced shooting times, F(1,20) = 8.16, p< .001, η² p = .29, and the interaction between the two factors was significant, F(1, 20) = 6.90, p< .05, η² p = .26. Planned comparisons demonstrated that background motion had an impact only when the task was easy. In this case, shooting times were longer with the moving background than with the stationary background, F(1, 20) = 14.80, p< .05. When the task was difficult, shooting times were not significantly different between the moving and stationary backgrounds, F(1, 20) = 1.71, p = .21.

[Figure 3 near here]

Number of shots

Background motion influenced the number of shots made by participants, F(1,20) = 7.37, p < .05, η² p = .27, which was higher with the moving (M = 1.18, SD = .12) than with the stationary background (M = 1.14, SD = .11). In contrast, there was no impact of task difficulty on the number of shots, F(1,20) < 1. The interaction between the two factors did not reach significance, F(1, 20) < 1.

Number and duration of eye fixations

As in Experiment 1, qualitative observation of the eye movement data displayed by a sample of the participants suggested that when the background was moving, an OKN was triggered between trials.

As shown in Table 2, task difficulty impacted the average number of fixations per trial, F(1,20) = 57.21, p < .001, η² p = .74, which was greater when the task was difficult (M = 3.05, SD = 1.13) than when it was easy (M = 2.53, SD = 1.06). There was no significant effect of background motion, F(1, 20) < 1, but there was a marginal interaction between the two factors, F(1, 20) = 3.13, p = 0.09, so that the impact of background motion on the number of fixations per trial tended to be higher when the task was easy (M = 2.69, SD = 1.32 with the moving background versus M = 2.38, SD = .71 with the stationary background) than when the task was difficult (M = 3.10, SD = 1.44 with the moving background versus M = 3.00, SD = .73 with the stationary background).

Task difficulty had an impact on the mean duration of fixations, F(1,20) = 5.55, p < .05, η² p = .22.

Fixations were longer when the task was difficult (M = 195 ms, SD = 56) than when it was easy (M = 187 ms, SD = 47). There was no significant effect of background motion, F(1, 20) < 1, or any significant interaction between the two factors, F(1, 20) < 1.

[Table 2 near here]

Discussion

Combined impact of lateral background motion and task difficulty on participants' performance and eye movements

The first hypothesis was supported. The participants' performance was lower when the task was more difficult, in accordance with results of previous visual search studies [START_REF] Reali | Inefficient conjunction search made efficient by concurrent spoken delivery of target identity[END_REF][START_REF] Thornton | Parallel and serial processes in visual search[END_REF][START_REF] Treisman | A feature-integration theory of attention[END_REF][START_REF] Wolfe | Guided Search 2.0: A revised model of visual search[END_REF]. The present data confirm that the enemies' visual features may be used to set task difficulty in the present situation. The second hypothesis was also supported. The present data confirm that the number and duration of fixations increases or tends to increase with task difficulty during visual search as well as in most visual tasks, in accordance with the literature [START_REF] Rayner | Eye movements and attention in reading, scene perception, and visual search[END_REF].

The third hypothesis was that the performance would be lower when the background is moving than when it is stationary but only in the lower level of task difficulty. This hypothesis was confirmed only with the black-and-white background (Experiment 2), in which shooting times were longer with the moving background only when the shooting task was easy. In contrast, the hypothesis was not supported with the colored background (Experiment 1), in which the simple effect of background motion on shooting times was observed whatever the difficulty of the target detection task.

The simple, negative effect of background motion on performance, which was observed with both the black-and-white and colored backgrounds, confirmed previous studies that demonstrated the negative impact of background motion on simple visual tasks that involve only transient presentations of stationary items [START_REF] Harrison | Multisensory integration with a headmounted display: Background visual motion and sound motion[END_REF][START_REF] Kaminiarz | Localization of visual targets during optokinetic eye movements[END_REF][START_REF] Tozzi | The effect of optokinetic nystagmus on the perceived position of briefly flashed targets[END_REF]. The shooting times and number of shots were higher when the background was moving. In the present situation, background motion should trigger the participants' OKN [START_REF] Caroux | Impairment of shooting performance by background complexity and motion[END_REF], which would decrease the shooting performance. Altogether, the present data show that in addition to other low-level features of the background, such as its complexity and color [START_REF] Jie | Video game design using an eye-movement-dependent model of visual attention[END_REF][START_REF] Knez | Lighting in digital game worlds: Effects on affect and play performance[END_REF][START_REF] Wolfson | The effects of sound and colour on responses to a computer game[END_REF], lateral background motion can be used to modulate the difficulty of a simple shooting game.

The data obtained on the black-and-white background supports previous studies. Indeed, Ilg [START_REF] Ilg | Slow eye movements[END_REF] and Menozzi and Koga [START_REF] Menozzi | Visual information processing in augmented reality: Some aspects of background motion[END_REF] demonstrated that when the main visual task involves sustained attention on fixed items superimposed on a moving background, participants can suppress the OKN and eliminate its negative impact on performance. The reason why the same interaction pattern was not observed with the colored background is not clear. Compared to the reading task used by Menozzi and Koga [START_REF] Menozzi | Visual information processing in augmented reality: Some aspects of background motion[END_REF], the level of sustained attention on stationary items involved in the difficult version of the shooting task may be insufficient to observe the expected interaction whatever the visual characteristics of the background. According to the literature, green has a lower impact on participants' arousal levels and emotions than red or blue [START_REF] Wolfson | The effects of sound and colour on responses to a computer game[END_REF][START_REF] Bonnardel | The impact of colour on Website appeal and users' cognitive processes[END_REF][START_REF] Valdez | Effects of color on emotions[END_REF], which should not have a significantly different impact from that of black-and-white. Another explanation may be that the two backgrounds used in the present experiment were actually different in terms of color "hue" and "saturation". Because hue and saturation were higher in the colored background, the contrast between the background and the creatures was therefore lower for the colored than for the blackand-white background. Therefore, all creatures were most likely more difficult to discriminate from the colored than from the black-and-white background. Indeed, the number of participants' fixations per trial and their average duration tended to be higher with the colored than the black-and-white background.

An additional statistical analysis (i.e., a repeated measure ANOVA) of shooting time data with a three-factor 2 X 2 X 2 design (background color X background motion X task difficulty) was made a posteriori to better clarify the influence of background color in the present study. The analysis did not show any significant simple effect or interaction involving background color on the participants' performance. Further experiments are needed to clarify the impact of background color on shooting tasks.

The eye movement data revealed that the shooting time and the number of fixations per trial tended to behave in a similar way whatever the color of the background. This finding is in accordance with the idea that increased response times often reflect an increase in the number of fixations that are needed to complete the task, as stated in the introduction. In contrast, the average duration of the participants' fixations was not significantly impacted by background motion.

Application to video game design

The present data can be used to generate recommendations for video game designers creating simple shooting tasks performed on laterally moving backgrounds. In addition to the other features that game designers can use to control challenge in games, background motion and task difficulty may be manipulated together. For example, when the main task is easy, the presence or absence of background motion should modify task difficulty. In contrast, when the main game task is more attention-demanding (i.e., more difficult), using a moving background will not increase task difficulty, at least on a black-and-white background, or will increase it less than when the task is easier.

However, further research is needed to generalize these recommendations to other video game contexts.

Conclusion and future studies

The present study demonstrated that performance in a shooting task may be impaired by lateral background motion, in accordance with previous studies performed using other visual tasks in various environments [e.g., [START_REF] Caroux | Impact of the motion and visual complexity of the background on players' performance in video game-like displays[END_REF][START_REF] Harrison | Multisensory integration with a headmounted display: Background visual motion and sound motion[END_REF][START_REF] Kaminiarz | Localization of visual targets during optokinetic eye movements[END_REF][START_REF] Tozzi | The effect of optokinetic nystagmus on the perceived position of briefly flashed targets[END_REF]. On the black-and-white background, background motion impaired performance only when the main target detection and shooting task was easy. Background motion did not have an additive impact on participants' performance when the main task was already difficult.

Further experiments should be made to extend these findings to the other types of background motion that exist in commercial video games. For example, some games display forward or backward motion, simulated by a radial expansion or contraction of the entire background. Additionally, as stated above, the impact of background color must be explored in more detail. If the task was easy, the target differed in size and color from all the distractors (here: a large, blue target with four small red distractors). If the task was difficult, two of the distractors were the same size as the target but a different color, whereas the two other distractors were the same color but a different size (here: a large, blue target with two large, red and two small, blue distractors). For more than ten years, he used in vitro and in vivo electrophysiology to study the control of posture and eye movements in rodents. His main interests have been in cognitive psychology since 2007. He is mainly working on visual search for both verbal and non-verbal information within documents and/or interactive environments.

Level of task difficulty

Figure 1 .

 1 Figures

Figure 2 .Figure 3 .

 23 Figure 2. Mean time (in ms) needed to hit each target in each condition of task difficulty and background motion in Experiment 1 (colored background). The error bars represent ±1 standard error of the mean.

Table 1 .

 1 Means (M) and standard deviations (SD) of number and duration of eye fixations according to task difficulty and background motion in Experiment 1 (colored background).

	Easy task		Difficult task
	M	SD	M	SD

Table 2 .

 2 Means (M) and standard deviations (SD) of number and duration of eye fixations according to task difficulty and background motion in Experiment 2 (black-and-white background).Nicolas Vibert is a senior CNRS researcher at the "Centre de Recherches sur la Cognition et l'Apprentissage" in Poitiers. He graduated in biology at the Ecole Normale Supérieure in Paris, France, and received his Ph.D. in neuroscience in 1994 from the University Pierre and Marie Curie (Paris 6).

	Easy task		Difficult task
	M	SD	M	SD

Acknowledgements

Loïc Caroux was supported by a Ph.D. fellowship from the Direction Générale de l'Armement (DGA, French Ministry of Defense) and followed in the frame of this fellowship by Didier Bazalgette.

Vitae