Jinshan Liu
email: jinshan.liu@inria.fr

Val Érie Issarny
email: valerie.issarny@inria.fr

An Incentive Compatible Reputation Mechanism for Ubiquitous Computing Environments

Keywords: D.2.0 [SOFTWARE ENGINEERING]: General-Protection mechanisms; C.2.4 [COMPUTER COMMUNI-CATION NETWORKS]: Distributed Systems-Distributed applications Reputation mechanism, ubiquitous computing, incentive com- patibility, mobile ad hoc networks

The vision of ubiquitous computing is becoming a reality thanks to the advent of portable devices and the advances in wireless networking technologies. It aims to facilitate user tasks through seamless utilization of services available in the surrounding environments. In such distributed environments featuring openness, interactions, especially service provision and consumption, between entities that are unknown or barely known to each other, are commonplace. Trust management through reputation mechanism to facilitate such interactions is recognized as an important element of ubiquitous computing. It is, however, faced by the problems of how to stimulate reputation information sharing and honest recommendation elicitation. We present in this paper an incentive compatible reputation mechanism to facilitate the trustworthiness evaluation in ubiquitous computing environments. It is based on probability theory and supports reputation evolution and propagation. Our reputation mechanism not only shows robustness against lies, but also stimulates honest and active recommendations. The latter is realized by ensuring that active and honest recommenders, compared to inactive or dishonest ones, can elicit the most honest (helpful) recommendations and thus suffer the least number of wrong trust decisions, as validated by simulation based evaluation.

INTRODUCTION

With the advent of portable devices (e.g., smartphones) and the advances in wireless networking technologies (e.g., WLAN, GPRS, UMTS), the vision of ubiquitous computing [START_REF] Weiser | The computer for the 21st century[END_REF] is becoming a reality. It refers to the creation of environments saturated with a spectrum of heterogeneous computing and communication capabilities, which seamlessly integrate with the physical world [START_REF] Satyanarayanan | Pervasive computing: vision and challenges[END_REF]. It aims to facilitate daily tasks and enhance user productivity through the utilization of those capabilities in an unobtrusive fashion, such that they completely blend in the physical environment and become "invisible".

The heterogeneous capabilities available in the ubiquitous computing environment can be generalized as services, leading to Service oriented Computing (SoC), which is a computing paradigm that utilizes services as fundamental elements for developing applications [START_REF] Papazoglou | Service-oriented computing[END_REF]. A device carried by a user can be a service client, which is an entity in need of services; or a service provider, which is an entity that offers services. SoC fits ubiquitous computing thanks to its minimalist philosophy [START_REF] Sen | Service-Oriented Software System Engineering: Challenges and Practices, chapter Service Oriented Computing Imperatives in Ad Hoc Wireless Settings[END_REF], i.e., an entity only needs to carry a small amount of codes locally and discover and exploit other services to realize its tasks. A service, a set of functionalities provided by one entity for the use of others [START_REF]Service oriented architecture reference model[END_REF], is characterized by its functional and non-functional attributes.

The networking between devices can be through network infrastructure (e.g., a home wireless LAN), which is assumed to be always accessible for nomadic mobile devices. However, it requires deployment and maintenance and cannot assume to be always available. Therefore, in order to achieve "all the time everywhere" access to services in ubiquitous computing environments, it necessitates a more flexible alternative for networking. Mobile Ad hoc NETworks (MANET) pose as a good choice: mobile devices dynamically establish connections with others when needed [START_REF]IETF working group: Mobile ad hoc networks (manet)[END_REF]. The devices (nodes) are free to move around and the network can be reorganized arbitrarily. In contrast with infrastructured networks, MANETs are deployment-free and realize spontaneous networking of devices. Thus they support impromptu interaction between entities, which is a desirable feature for ubiquitous computing [START_REF] Kindberg | System software for ubiquitous computing[END_REF]. Hence, with MANETs, a user equipped with her device, even when she is moving, can dynamically find and exploit the services available in the surrounding environments, which are not necessarily pre-deployed. In summary, MANET poses as a flexible and suitable underlying networking paradigm for ubiquitous computing environments. Therefore, in this paper, entities are assumed to be connected via ad hoc networks. The terms of device, node and entity are used interchangeably in the rest of this paper.

Overall, the service provision in ubiquitous computing environments has the following characteristics:

• There does not exist any party that is centralized or pre-trusted, due to the independence of any infrastructure to allow for more flexible interactions.

• The devices exhibit great mobility. It makes nodes' joining and leaving of a network much more frequent than in traditional wired networks, thus increasing the network's openness. Subsequently, it is very likely for an entity to encounter others, which it has no or very little knowledge of.

• Devices can be selfish because providing services consumes limited resources. Therefore, services bear prices, which are charged by service providers on clients, in order to enforce cooperation between devices. Different services have different prices depending on factors such as the offered QoS.

Before interacting with a service provider, a client needs to evaluate its trustworthiness, because a dishonest service provider can cheat (e.g., exaggerate its offered QoS) for more revenues. Traditional security mechanisms such as authentication and access control (e.g., X.509 [START_REF] Adams | RFC2510 -Internet X.509[END_REF]) fall short for the above purpose because of their reliance on security infrastructure such as Certificate Authority. More importantly, as it is commonplace to interact with strangers in ubiquitous computing environments, even with authentication and authorization services at disposal, authenticating an unknown entity does not provide any access control information. Trust and reputation, on the other hand, can provide protection against such threats. Trust deals with the estimation of a node's future behavior. For example, a client trusts a service provider in that the latter will actually offer the QoS as claimed. Trust is generally difficult to establish between strangers [START_REF] Resnick | Reputation systems[END_REF], because they do not have any previous experiences and are not subject to a network of informed entities about their behaviors. Reputation, which is "perception that a node creates through past actions about its intentions and norms" [START_REF] Mui | A computational model of trust and reputation[END_REF], is important for fostering trust [START_REF] Resnick | Reputation systems[END_REF], because it dissuades entities to misbehave resulting from no fear for future revenge. It has been proved to be a useful model and widely deployed in various scenarios such as electronic market places (e.g., eBay1 ). The reputation assessment of a trusted node, named trustee, by a trusting node, named trustor are dependent on [START_REF] Yu | Detecting deception in reputation management[END_REF]: (i) the trustor's own direct experiences with the trustee; (ii) the trustor's indirect experiences, i.e., recommendations (also named ratings) from other entities. The entities that give recommendations are called recommenders. To prevent loops, recommendations are only based on recommenders' own direct experiences.

Given the openness of the environments, it is very likely that before interacting with an entity, the accumulated direct experiences are too few or too old to derive a trust decision. Recommendations are thus indispensable for alleviating the above problem. However, recommendations can be difficult to elicit, i.e., entities are reluctant to recommend. This is because [START_REF] Miller | Eliciting honest feedback in electronic markets[END_REF]: entities may be reluctant to give positive recommendations because they lift the reputation of the trustees, which are potential competitors; entities may be afraid of retaliation for negative feedbacks; last but not least, the (truthful) recommendations only benefit others. Meanwhile, recommendations are also subject to manipulation and can be false, e.g., colluders give high recommendations for each other. A false recommendation is called a lie. Since truthful recommendations are critical for a reputation mechanism to operate effectively [START_REF] Resnick | Reputation systems[END_REF], the two above issues pose obstacles for designing a reputation mechanism that is capable of recognizing the real trustworthiness of an entity.

Existing reputation mechanisms (e.g., [START_REF] Jurca | An incentive compatible reputation mechanism[END_REF][START_REF] Whitby | Filtering out unfair ratings in bayesian reputation systems[END_REF][START_REF] Patel | A probabilistic trust model for handling inaccurate reputation sources[END_REF]) do not solve the two aforementioned problems altogether. Therefore, we propose a distributed reputation mechanism that motivates entities to recommend truthfully and actively. Our mechanism empowers an entity to distinguish (1) between trustworthy and untrustworthy service providers and (2) between honest and dishonest recommenders. It not only shows robustness against lies, but also stimulates active and truthful recommendations. The latter is achieved by enforcing that honest and active recommenders can benefit more from others, while liars are identified and isolated.

In the rest of the paper, Section 2 surveys related work on distributed reputation systems. Section 3 shows the representation of reputation based on Beta distribution. Then we explain how the reputation is formed based on direct and indirect experiences (i.e., recommendations) in Section 4. It is followed by reputation evolution in Section 5. Then we proceed to present the propagation of reputation and the incentives for active and honest recommendation provision in Section 6. In Section 7, the proposed reputation mechanism is evaluated with respect to its different treatment for recommenders of different honesty and activeness. This paper finishes with concluding remarks.

RELATED WORK

Reputation mechanism has been widely used and deployed in online service provision (e.g., ebay), peer-to-peer systems (e.g., [START_REF] Kamvar | The EigenTrust algorithm for reputation management in P2P networks[END_REF]) and mobile ad hoc networking (e.g., [START_REF] Michiardi | CORE: a collaborative reputation mechanism to enforce node cooperation in mobile ad hoc networks[END_REF]). During online service provision, especially e-commerce, it is commonplace for parties that are unknown to each other to interact [START_REF] Resnick | Reputation systems[END_REF]. This opens up an issue of lack of trust between two parties before an interaction takes place. P2P networks (e.g., Gnutella2 ) are subject to attacks from anonymous malicious peers, such as virus spreading and fake file attack [START_REF] Kamvar | The EigenTrust algorithm for reputation management in P2P networks[END_REF]. In mobile ad hoc networks, since nodes rely on the service of "packet forwarding" provided by their neighbors in order to communicate with others that are out of their communication range, reputation is necessary for evaluating a node's degree of being cooperative (i.e., in forwarding packets). In the following, we survey existing reputation mechanisms, especially focusing on their handling of recommendations. Some reputation mechanisms do not distinguish between reputation of providing a service and providing a recommendation (e.g., [START_REF] Kamvar | The EigenTrust algorithm for reputation management in P2P networks[END_REF]). They assume that trust on an entity's capability to provide services can be transferred to its opinions. For example, in [START_REF] Kamvar | The EigenTrust algorithm for reputation management in P2P networks[END_REF], a peer that provides authentic files is trusted to give honest opinions. But such assumption makes the reputation system vulnerable to reputation manipulation. For example, a good service provider can exploit it to demote the reputation of its competitors, as its opinions are considered as truthful as its services. Therefore, it is necessary to distinguish the reputation for providing services and recommendations, namely service reputation (SRep) and recommendation reputation (RRep) respectively. A trustor can evaluate the trustee's overall reputation (ORep) based on its SRep and others' recommendations. The latter is taken into consideration depending on the recommenders' RReps.

Due to the existence of lies, recommendations need to be carefully incorporated towards the trust decision of whether to interact with a service provider. In another word, a reputation mechanism needs to be able to identify lies such that it is robust against them. Yu and Singh [START_REF] Yu | Detecting deception in reputation management[END_REF] present a reputation model that aims to detect lies in multiple agent systems. Recommendations are compared against the new direct experience to evaluate the recommenders' RReps, which determine the credibility of their recommendations. Only recommendations from helpful nodes (i.e., with high RReps) are accepted and weighed corresponding to their RReps. Similar approach is also taken in [START_REF] Huynh | On handling inaccurate witness reports[END_REF]. Although they are capable of identifying lies, there is no penalty for either liars or free-riders, which can always benefit from the recommendations of others.

In [START_REF] Whitby | Filtering out unfair ratings in bayesian reputation systems[END_REF], all recommendations are aggregated to derive the public opinion. Each individual recommendation is then compared against the public opinion; too much deviation leads the recommendation to be considered false and thus excluded. The public opinion is then recalculated and compared against each remaining recommendation until no more recommendation is filtered out. This kind of approaches to identify lies are endogenous since the truthfulness of recommendations is judged depending on the recommendations themselves. In contrast, exogenous approaches use external factors, such as RRep, for doing so. The implicit assumption underlying endogenous approaches is that the majority of recommendations are honest such that they dominate the lies. Therefore, a recommendation that deviates from the majority is considered a lie. This assumption is not solid in open environments where recommendations can be very few in number, most of which can be untruthful. A variant of endogenous approach is used in [START_REF] Patel | A probabilistic trust model for handling inaccurate reputation sources[END_REF], where each entity records all the ratings and subsequent interaction experiences. Assume node a receives a recommendation from recommender r, a first picks out all the entities whom r has recommended with a similar value (e.g., within the range [a..b]). The accumulated experiences with those entities are calculated and compared against the rating range to obtain r 's RRep. Their approach is exogenous, because it is the accumulated direct experiences that are used to determine the trustworthiness of a recommendation. Meanwhile, it is also endogenous because such comparison is done only within the range of recommendation values that are considered relevant.

Jurca and Faltings [START_REF] Jurca | An incentive compatible reputation mechanism[END_REF] propose an incentive-compatible reputation mechanism to deal with inactivity and lies. A client buys a recommendation about a service provider from a special broker named R-nodes. After interacting with the provider, the client can sell its feedback to the same R-node, but gets paid only if its report coincides with the next client's report about the same service provider. One issue is that if the recommendation from an R-node is negative such that a client decides to avoid the service provider, the client will not have any feedback to sell. Or in the existence of opportunistic service providers that, for example, behave and misbehave alternatively, an honest feedback does not ensure payback. This opens up the possibility of an honest entity to have negative revenue and thus is unable to buy any recommendation. Besides, the effectiveness of their work depends largely on the integrity of R-nodes, which is assumed to be trusted a priori.

In summary, although current reputation mechanisms are capable of identifying lies, they lack measures to enforce voluntary and honest recommending. Therefore, they are not incentive compatible, i.e., there does not exist any incentive for entities to actively provide honest recommendations. As there is no deterrent for liars, lies can be rampant and honest recommendations can become difficult to acquire due to lack of motivation. Therefore, a distributed reputation mechanism for ubiquitous computing environments not only needs to be robust against lies, but also needs to enforce both active and honest recommendation. In the following, we present such a reputation mechanism, starting with reputation representation.

REPUTATION REPRESENTATION

Since reputation essentially aggregates past experiences and dynamically evolves, it bears great similarity with Bayesian analysis, which is a statistical procedure that estimates parameters of an underlying distribution based on observations. An extensively used distribution in Bayesian analysis is Beta distribution.

Beta Distribution

According to the probability theory, the posterior probability for binary events can be estimated by beta distribution. For example, given a process with two possible outcomes (T , ¬T ), let r, s be the observed number of T and ¬T respectively, the Probability Density Function (PDF) of the probability p of having the outcome T for the next time can be given by beta distribution (with α = r +1 and β = s+1):

f (p|α, β) = 1 B(α, β) p α-1 (1 -p) β-1 , where 0 ≤ p ≤ 1, α, β ≥ 0 B(α, β) = Z 1 0 t α-1 (1 -t) β-1 dt
where α and β are two parameters used to index the continuous family of Beta distribution and B(α, β) is the beta function. f (p|α, β) represents a probability distribution of p in terms of integrals. Formally, the probability of

p falling into [a, b] is R b a f (p|α, β)dp.
The prior distribution (the initial state) is f (p|1, 1), leading to uniform distribution (Figure 1). It reflects the fact that without any knowledge, the probability of having T for the next time can be any value between 0 and 1 with equal possibility. New observations are used to update the PDF of p. For example, having observed 8 times T and 2 times ¬T , the PDF can be expressed as f (p|9, 3), as plotted in Figure 1.

The expected (mean) value of the beta distribution f (p|α, β) assumes a simple form:

E(p) = α α + β
It gives the mean value of p, based on (α+β-2) observations accumulated so far. For example, in Figure 1, the expected values of both f (p|9, 3) and f (p|21, 7) equal to 0.75. It can be interpreted as that the probability of observing outcome T in the future is uncertain, but the expected value is 0.75. In addition, f (p|21, 7) has more confidence saying so (i.e., f (0.75|21, 7) > f (0.75|9, 3)), thanks to more accumulated observations.

Beta Reputation

As reputation is essentially an a posteriori estimation based on historic experiences (either direct or indirect), beta distribution has been recognized as a useful model to model reputation [START_REF] Mui | A computational model of trust and reputation[END_REF][START_REF] Josang | The beta reputation system[END_REF][START_REF] Buchegger | A robust reputation system for P2P and mobile ad-hoc networks[END_REF]. Therefore, we represent reputation based on beta distribution (abbreviated as beta reputation). A reputation value assumes a tuple of (α, β) (α, β ≥ 1), with α and β representing positive and negative experiences respectively.

As beta distribution only considers binary events, it is not enough to describe the experience of service consumption, which can fall into the range between being completely satisfactory and completely unsatisfactory. Therefore, an experience is evaluated with Quality of Experience (QoE), saying, between 0 (completely unsatisfactory) and 1 (completely satisfactory). This experience is split into two parts: QoE contributing to the positive experience and (1 -QoE) to the negative experience. Therefore, beta reputation f (p|α, β) gives the PDF of the probability of having a complete satisfactory experience, i.e., the expected QoE.

Thanks to sound statistical properties of beta distribution, beta reputation has the following advantages:

1. It is easy to assess the trustworthiness of an entity with reputation of (α, β), i.e., by calculating α α+β .

2. It is easy to evaluate how many experiences (i.e., α + β -2) have contributed to the current reputation. The larger this value is, the more probably the reputation assumes the expected value. Only newcomers' reputation is based on 0 experience.

3. It facilitates the combination of experiences from multiple sources, including the trustor itself and different recommenders. This is because the add operation of beta reputation is straightforward:

f (p|α1, β1) + f (p|α2, β2) = f (p|α1 + α2, β1 + β2).
4. It reflects the nature of reputation, which is the aggregation of observations. An entity dynamically adjusts the reputation with more experiences being accumulated, which is similar to deriving posterior distribution after observations are made.

5. It captures the uncertainty of reputation. Beta distribution only gives the PDF of the probability of having an outcome, which matches the fact that reputation can only give probabilistic estimation of an entity's future behavior.

Alternatively, reputation can be also represented with a single value from discrete (e.g., [START_REF] Abdul-Rahman | Supporting trust in virtual communities[END_REF]) or continuous value space (e.g., [START_REF] Marsh | Formalising Trust as a Computational Concept[END_REF]). Compared to beta reputation, single-value based reputation representation does not reflect the amount of experiences that contribute to the reputation. In addition, with single value based reputation, ignorance, which refers to the reputation without any knowledge, generally bears the value of 0. It can not be distinguished from the 0 reputation values that result from a mixture of positive and negative experiences (e.g, [START_REF] Marsh | Formalising Trust as a Computational Concept[END_REF][START_REF] Mui | A computational model of trust and reputation[END_REF]). While with beta reputation, only newcomers have a reputation of (1, 1). Beta distribution's feature of easy experience aggregation facilitates the derivation of an entity's reputation, which is formed based on the trustor's direct experiences and others' recommendations, as explained as follows.

REPUTATION FORMATION

Before we proceed to show how reputation is formed, we first explain the notations to be used in the reputation mechanism. As reputation is always about an entity o (i.e., trustee) held by some entity a (i.e., trustor), we denote o's reputation from the point of view of a as Repa(o). Table 1 lists the notations we use, including service reputation (SRep), recommendation (Rec), recommendation reputation (RRep) and overall reputation (ORep). They are expressed using beta reputation, with two parameters representing positive and negative experiences respectively. ORep can rely solely on the trustor's direct experiences (i.e., SRep) if they are significant enough to derive a trust decision. This can be judged by checking whether the total accumulated (sp + sn -2) experiences reach a certain threshold. Otherwise, it asks for recommendations from others. The recommendations and the node's own direct The weights of different recommendations are further normalized by dividing with the sum of all weights. Therefore, ORep can be evaluated using SRep and the recommendations from helpful recommenders:

ORep = δ × SRep + (1 -δ) × P r∈R (Recr(o) × wr) P r∈R (wr) (1)
where δ is the weight given to its direct experience (SRep) and is generally greater than 0.5. The favor of direct experiences over recommendations is due to the fact that entities tend to rely on their own experiences more than on others' recommendations [START_REF] Kollock | The emergence of exchange structures: an experimented study of uncertainty, commitment, and trust[END_REF]. Therefore, an entity can make a trust decision based on the overall reputation (ORep) of the trustee. ORep is not kept as a field of the acquaintance record, instead it is dynamically evaluated when needed, since it evolves with time and new experiences.

REPUTATION EVOLUTION

An entity can change its behavior over time, making old experiences become irrelevant for the actual reputation evaluation [START_REF] Josang | The beta reputation system[END_REF][START_REF] Liu | Enhanced reputation mechanism for mobile ad hoc networks[END_REF]. This calls for discount of past, which gives more weight to recent experiences than old ones. Such discounting also prevents an entity from capitalizing on its previous good behavior forever. Hence, reputation fades with time, as shown as follows.

Time Fading

Since both recent behaviors and past histories contribute to the reputation, their assigned weights decide how fast the reputation builds up. For example, if recent behavior is assigned a very high weight, a node's reputation tears down very fast after a few misbehaviors. We assign more weight to recent behavior, as suggested by the studies in [START_REF] Dellarocas | The digitization of word-of-mouth: promise and challenges of online feedback mechanisms[END_REF].

Given the time interval of ∆t, the reputation (α, β) evolves after every ∆t:

α = 1 + (α -1) × ρ ∆T β = 1 + (β -1) × ρ ∆T
where ρ is time fading factor, whose value falls into the range of [0..1]. The lower value ρ has, the more quickly histories are forgotten. When ρ equals 0, histories are immediately forgotten; while when ρ equals 1, the history is forever kept and considered equivalent regardless of age.

As shown in the above equations, when ∆T → +∞, ρ ∆T → 0. It expresses the fact that inactivity between two parties for a long time leads to complete discount of experience, making its reputation the same as that of newcomer. This is because the experiences can be too old to be indicative of the trustee's trustworthiness. Both SRep and RRep fade according to the above equations. For simplicity, the reputation value in the rest of this paper does not bear a timestamp and it always refers to the current reputation unless indicated otherwise.

Reputation also evolves with new experiences, as reputation aggregates the overall experiences with an entity. This is reflected in both SRep and RRep, which aggregate the experiences of consuming services and utilizing recommendations respectively.

Evolution of Service Reputation (SRep)

Since SRep(sp, sn) combines all direct experiences, it is updated whenever a new experience occurs. An experience is described with the metric of Quality of Experience (QoE ). As the goal of the reputation mechanism is to identify dishonest service providers that do not comply with their advertised QoS, QoE is accordingly measured based on the QoS conformance of the service provider. More specifically, given n QoS dimensions of di (i = 1..n) (e.g., availability, latency) which client a cares about, service provider o states in its service advertisement (p1, p2, .., pn) in which pi is the promised value for dimension di. After the service completes, the QoS that a receives is represented by (a1, a2, .., an), in which ai is the actual value for dimension di. The QoEa(o) can be assessed by:

QoE = X 1≤i≤n comp(ai, pi)/n (2)
where comp(ai, pi) is a function to calculate one-dimension degree of conformance between the actual and promised QoS. Depending on the QoS dimension, it assumes the following forms:

1. comp(ai, pi) = M IN (1, ai/pi) when dimension i is quantitative and stronger with larger values, for example, availability.

2. comp(ai, pi) = M IN (1, pi/ai), when dimension i is quantitative and stronger with smaller values, for example, latency.

3. comp(ai, pi) = 1 -(ai ⊗ pi) when dimension i is qualitative and bears Boolean values, for example, confidentiality. ⊗ represents XOR function, i.e., x ⊗ y = 0 if x equals y, and 1 otherwise.

4. For dimensions whose value space is literals (e.g., service adaptation policy), comp(ai, pi) equals 1 when the required policy is satisfied, 0 otherwise.

For example, given a service provider's advertisement of (latency = 0.8 ms, availability = 99%), a service client's actual experienced QoS is (latency = 1.0 ms, availability = 100%), then QoE = (M IN (1, 0.8/1.0)+M IN (1, 100%/99%))/2 = 0.9.

With a new QoE, the SRep(sp, sn) is updated as described in Section 3.2: (i) s p = sp + QoE; (ii) s n = sn + (1 -QoE).

Evolution of Recommendation Reputation (RRep)

Similarly, RRep dynamically evolves with recommendations being elicited and services being consumed. A recommendation bears the form of (cp, cn), which is equal to SRep for an honest recommender. Given a new QoE of e ∈ [0..1], the honesty of a recommender is adjusted according to the helpfulness of its recommendation. Assume that before a client c has a new experience (e) of 0.8 with service provider o, it has received recommendations of [START_REF] Adams | RFC2510 -Internet X.509[END_REF][START_REF] Clausen | Optimized link state routing protocol[END_REF] and (4, 2) from two recommenders a and b respectively. As ∆min = 0.6 (using Equation 3), the helpfulness of a's recommendation is e = 0.24 and b's recommendation leads to e = 0.81. It thus enables distinguishing between honest and dishonest recommenders, as well as different degree of honesty/dishonesty.

Based on the features of beta reputation, the value of (rp + rn -2) is high if an entity is active in providing recommendations; the expected value of f (p|rp, rn) is high if an entity is honest in doing so. With two values δ h and δa defined as threshold trustworthiness and activeness in providing recommendations, a recommender with RRep(rp, rn) is considered active if rp + rn -2 ≥ δa, and inactive otherwise; it is considered honest if rp rp+rn ≥ δ h , and dishonest otherwise. It leads to 5 possible states of a recommender: active truth-teller (AT), inactive truth-teller (IT), active liar (AL), inactive liar (IL) and newcomer (Figure 3). A recommender can convert from one state to another, depending on its behavior. An active truth-teller enforces its state by continuing recommending honestly and weakens its state by lying. If it continues lying, with the fading of previous good behavior, the accumulated experiences will eventually work against it and degrade it to an active liar. If a recommender has not provided any recommendation for so long a time that its RRep decays, it is considered as an inactive recommender and even a newcomer.

Note that an active and honest recommender can be considered inactive due to the fact that it does not have any direct experience with the trustee being evaluated by the recommendation requester. Therefore, although inactivity can result from an entity's withholding recommendations on purpose, it does not necessarily infer free riding. But in order to motivate a node to become an active truth-teller, active and honest recommenders should be able to have better success in identifying dishonest entities using the reputation mechanism. This is realized during reputation propagation, where different recommenders are treated differently in terms of their accessibility to helpful recommendations.

REPUTATION PROPAGATION

Lack of enough direct experiences triggers a trustor's elicitation of recommendations (e.g., by broadcasting the request) from nearby entities. Of all the collected recommendations, only those from truth-tellers (i.e., honest recommenders) are taken into account. If there is no recommendation from any truth-teller, the trustor takes into consideration those from inactive and first-time encountered recommenders by calculating their average. With the recommendations from others, the trustor evaluates the trustee's ORep using Equation 1. Otherwise, the trustor has to rely on its direct experiences which are too few to make a sound decision. The trust decision will then have to be made depending on other factors, e.g., the trustor's attitude towards strangers. If the trust decision leads to a service consump-tion and thus a new QoE, the latter is compared against all recommendations to update the recommenders' RReps.

A trustor elicits recommendations indiscriminately but accepts only those from honest recommenders. This is for the purpose of ensuring robustness against lies, while empowering the trustor with the capability of recognizing new recommenders and continuously updating a dishonest recommender's RRep. More specifically, even though the recommendations from liars are not taken into account, they are used to update the RReps of the recommenders, which can be improving if they become honest or deteriorating if they continue lying.

Whenever an honest recommender a receives a request for recommendation regarding an entity o, it first checks whether its direct experiences with o are significant enough for recommending. If that is not the case, a does nothing as it cannot be of any help. Otherwise, i.e., a has enough direct experiences for recommending, it handles the request depending on the state of the recommendation requester:

• If the requester is considered as an active truth-teller, a sends back its SRepo(a) immediately.

• If the requester is considered as an active liar, a simply ignores the request.

• If the requester is considered inactive, a gives back its recommendation with a probability depending on diff = δa -(rp + rn -2). Inactive recommenders are better treated than liars due to the fact that inactive recommenders do not necessarily withhold their recommendations. To distinguish inactive truth-tellers (IT), newcomers and inactive liars (IL), the IT and IL's probabilities are increased and decreased with an small value of respectively. Therefore, the less active an entity is, the less possible that it receives helpful recommendations from others. Note that newcomers also suffer from low probability of eliciting honest recommendations.

The reason of honest recommenders' going through the above process of treating different type of recommendation requesters differently is that if honest recommenders are over-generous by treating everybody alike, other entities are not motivated to return the favor because doing that does not give them any advantage. Eventually, rational entities choose to withhold their recommendations while liars remain unpunished. Honest recommenders will suffer by having less and less useful recommendations from others and will eventually draw no favor back. Therefore, honest recommenders have to assume the defensive strategy of holding 'grudges' against liars by keeping others' RRep in order to guard their own interests. In contrast, dishonest recommenders, i.e., liars, treat all types of recommendation requesters alike since their utmost goal is to spread lies as widely as possible to take advantages such as promoting their colluders' reputation.

The deterrent for nodes to lie thus lies in the consequence of lacking helpful recommendations from honest recommenders, who hold grudges. At the same time, refusing to provide recommendations leads to less accessibility to helpful recommendations. Lack of recommendations forces a trustor's trust decision to be solely dependent on its direct experiences, which often can be too few or old to be helpful in open environments. This causes wrong trust decisions, making the client either interact with dishonest service providers or avoid honest ones. It is more clearly demonstrated in the next section, which evaluates the performance of our reputation mechanism.

REPUTATION MECHANISM EVALUA-TION

In this section, we evaluate the performance of our reputation mechanism in helping nodes distinguish honest and dishonest service providers, and to identify honest and active recommenders, based on simulations.

Experiment Setting

The simulation is carried out with Network Simulator (ns-2) with CMU wireless extensions [START_REF]Network simulator ns-2[END_REF]. Our simulated network consists of 40 mobile nodes in an area of 400m × 400m, with each node having a transmission range of 100m. We use the Random Waypoint mobility model with each node moving at walking speed, i.e., between 0.5 m/s and 1.5 m/s, with pause time of 0, i.e., nodes are always in motion. The Distributed Coordination Function (DCF) of the IEEE 802.11 protocol is used as the MAC layer protocol. The underlying routing protocol is Optimized Link State Routing Protocol (OLSR) [START_REF] Clausen | Optimized link state routing protocol[END_REF]. The simulation parameters are summarized in Table 3. The population of 40 nodes includes 8 types of entities with different behavior in service providing (honest or not), recommendation providing (honesty and activeness), as shown in Table 4. Each type of entity has the same population, i.e., 5 each (different settings with different population sizes will also be studied later). For simplicity without losing generality, we assume that every node can be the service provider for the other. Start-ing from time 50 3 , for every 1 second, a node makes a trust decision whether to interact with a random node in its routing table, in a round robin way. A trust decision is made as follows: (1) the service client first checks whether the SRep of the service provider is based on enough experiences (threshold δa = 1.0); (2) if yes, it calculates whether the expected value of SRep reaches a threshold value (δ h = 0.6);

(3) if not, it elicits recommendations from its neighbors (we set the request broadcast range to 2 hops). If the aggregation of SRep and others' recommendations are still not enough for making a trust decision, the node decides whether to interact with a service provider with a certain probability. In our experiments, the probability is set to 1.0, assuming an optimistic attitude facing uncertainty.

A total of 60 rounds have been executed. An honest service provider offers a QoE of 0.9, while a dishonest one offers a QoE of 0.1. Honest recommenders recommend with their SRep(sp, sn) regarding the trustee, while dishonest recommenders send back lies which are complementary to their SReps, i.e., a recommendation assumes the value of (rp = sn, rn = sp). Active recommenders offer recommendations with 90% probability, while inactive ones offer with 10% probability.

We investigate and compare the performance of the 4 different types of recommenders: active truth-teller (type 1 + type 5 in Table 4), inactive truth-teller (type 2 + type 6), active liar (type 4 + type 8) and inactive liar (type 3 + type 7). The advantage of being an active truth-teller is reflected in the fact that they can elicit more honest recommendations, which help them make right trust decisions regarding whether to interact with an entity or not. Therefore, we show (1) the number of honest recommendations obtained by the four types of recommenders respectively. When a client fails to acquire any helpful recommendation, it has to base its trust decision solely on its direct experiences, which are not significant enough for a sound decision. Namely, the client is subject to mistakes, i.e., wrong trust decisions, which refer to either false positives (when an honest service provider is identified as an untrustworthy one) or false negatives (when a dishonest service provider is not identified as being so). Thus, (2) the number of mistakes made by different recommenders are also displayed. These metrics are recorded every 200 seconds to show the evolution of reputation. They are detailed below.

Evaluation Results

Elicited Honest Recommendations

Figure 4 shows the number of elicited honest recommendations for different type of recommenders. It can be observed that at the beginning (before time 500s), very few recommendations are propagated and the four types of recommenders do not have much difference in the number of obtained honest recommendations. With the accumulation of experiences, the honest entities have enough experiences to recommend. Recommendation reputation is gradually recognized and the order of benefit (AT > IT > IL > AL) starts to be established, from time 1500s in Figure 4.

Mistakes

3 This aims to give OLSR enough time to build routing table, as OLSR is a proactive protocol. Lack of honest recommendations can lead to mistakes. Figure 5 presents the number of mistakes made by the four types of recommenders. It can be seen that, at the beginning, every type of nodes make mistakes as many as half of the total transaction number. It is because most decisions are blind and honest service providers occupy half of the population.

With more accumulated experiences, every type of recommenders make less and less mistakes. Especially, with the help of honest recommendations, AT nodes make the least number of mistakes and AL nodes make the most (the order of AT > IT > IL > AL is enforced). Note that dishonest or inactive recommenders can also tell the honesty and activeness of a recommender using reputation system. However, they have access to less number of truthful recommendations for making the right trust decision.

In order to demonstrate more clearly the advantages brought by useful recommendation, the percentages of mistakes out of all transactions for different recommenders are shown in Figure 6. It can be seen that, starting from time 1500s, ATs make less than 5% of mistakes while ALs suffer more than 20% of mistakes.

Other Results

In the above simulations, we have set the population size to be relatively small (40) to lessen the time for bootstrapping (about 1500 seconds for 40 nodes), because nodes need to acquire experiences to be able to give useful recommendations. Basically, a larger population takes longer time to bootstrap, but the reputation mechanism shows similar ef-fects. We did similar simulations with larger population (80) and the percentage of mistakes is shown in Figure 7. It can be observed that the order of benefit is established eventually, although it takes more time than in a community of 40 nodes (about 3500 seconds into simulation). The reputation mechanism also exhibits similar performance with different population percentage of different recommenders. We have carried out the simulations by decreasing the population of active truth-teller (AT ) to 10% and increasing active liar (AL) to 40%. The percentages of mistakes for different recommenders are presented in Figure 8. It shows that the order of the treatment (i.e., AT > IT > IL > AL) is also established.

CONCLUDING REMARKS

In this paper, we have presented a distributed reputation mechanism for recognizing the trustworthiness of a service provider in ubiquitous computing environments, including reputation representation, formation, evolution and propagation. Our contribution includes: (1) proposing a simple yet effective reputation mechanism that not only is lie-proof, but also motivates active and truthful recommendation sharing; (2) modeling a reputation that continuous evolves, with time and with new experiences; (3) evaluating the effectiveness and performance of the proposed reputation mechanism via simulation tests.

As an entity has to handle the reputation independently and autonomously, in our reputation mechanism, it stores the reputation values of all of its acquaintances. This might raise an issue if the population of the acquaintances is so large such that it brings considerable overhead for reputation storage and manipulation. A possible solution is to manage nodes by groups, each of which share a group reputation [START_REF] Sabater | Regret: A reputation model for gregarious societies[END_REF][START_REF] Mui | A computational model of trust and reputation[END_REF]. The reputation of an entity depends on the group it belongs to; the behavior of a member affects the reputation of its group. This requires strong group support [START_REF] Liu | Group management for mobile ad hoc networks: Design, implementation and experiment[END_REF], as the group members need to trust each other and have common interests such that they are motivated to protect the group's reputation.

An important issue in reputation mechanism is identity changing. Most online reputation systems protect privacy and each agent's identity is normally a pseudonym. It causes problems because pseudonym can be changed easily [START_REF] Mui | A computational model of trust and reputation[END_REF]. When a user ends up having a reputation lower than that of a new comer, she can discard her initial identity and start from the beginning. This calls for the necessity of special treatments of newcomers. We partly address this issue by putting newcomers in a unfavorable position, such that they have difficulties obtaining helpful recommendations, until they accumulate enough good behavior. But to completely solve this issue, it would have to rely on other mechanisms, such as introducing an "entry fee" for each pseudonym or use of once in a lifetime pseudonym that is bound to a real-world entity [START_REF] Friendman | The social cost of cheap pseudonyms[END_REF]. A very related issue is called Sybil attack [START_REF] Douceur | The sybil attack[END_REF]: if there is no control over creation of new entities, a real-world entity can create as many identities as it wishes to challenge the use of majority in reputation systems. The only challenge this attack can bring to our reputation system is when there is no recommendation from an active truth-teller, the trustor relies on the average of all recommendations from unknown (or barely known) recommenders. The addressing of these challenges will be part of future work.

Figure 1 :

 1 Figure 1: Beta Distribution values

  experiences are then combined to evaluate the overall reputation (ORep) of the trustee. Assuming a recommender r gives a recommendation regarding o (i.e., Recr(o)) to client c and RRepr(c) = (rp, rn), the recommendation is considered trustworthy and accepted if (1) r is honest enough, by checking whether rp rp+rn is high enough and (2) the RRep is evaluated based on enough evidences by checking whether (rp +rn -2) is large enough. If the recommendation is taken into account, it is given a weight wr = E(Beta(rp, rn)) = rp rp+rn .

Figure 2 :

 2 Figure 2: Calculation of ∆e

Figure 3 :

 3 Figure 3: The states of a recommender

Figure 4 :Figure 5 :

 45 Figure 4: Number of elicited honest recommendations

Figure 6 :Figure 7 :

 67 Figure 6: Percentage of wrong trust decisions

Figure 8 :

 8 Figure 8: Percentage of wrong trust decisions with different population composition

Table 1 :

 1 Notations in the reputation mechanismEach node keeps both SRep and RRep of its acquaintances, the entities with which it has interacted before (either as a service client or a recommendation requester), as shown in Table2. This table of acquaintance records is named acquaintance table. In the table, aID denotes

	Label	Value Range Meaning
	SRepa(o)	(sp, sn)	a's direct experiences with
			o
	Reca(o)	(cp, cn)	Recommendation	made
			by node a regarding node
			o. Helpful recommenders
			give	recommendations
			based on their own di-
			rect experiences,	i.e.,
			Reca(o) = SRepa(o)
	RRepa(o)	(rp, rn)	Recommendation reputa-
			tion of node o held by
			node a
	ORepa(o)	(op, on)	Overall reputation of node
			o held by node a

Table 2 :

 2 An entry of the acquaintance table aID SRep RRep sp sn ts rp rn tr acquaintance ID and ts and tr represent respectively the timestamps when the SRep(sp, sn) and RRep(rp, rn) were updated last time.

Table 3 :

 3 NS-2 simulation parameters

	Parameter	Value
	Mobility Model	Random Way Point
	Moving Speed	0.5 -1.5 m/s
	Pause Time	0
	Transmission Range	100 m
	Area	400m x 400m
	Number of Nodes	40
	Routing Protocol	OLSR

Table 4 :

 4 The types of nodes with different behavior

	Type Service Providing Honesty	Recommendation Honest Active
	1	+	+	+
	2	+	+	-
	3	+	-	+
	4	+	-	-
	5	-	+	+
	6	-	+	-
	7	-	-	+
	8	-	-	-

http://www.ebay.com

http://www.gnutella.com

ACKNOWLEDGEMENTS

This research is partially supported by the European IST PLASTIC project 4 (EU-IST-026955).


Bernard G Barthès

Didier Brunet

Henri Ferrer

Jean-Luc Chotte

Christian Feller

Determination of total carbon and nitrogen contents in a range of tropical soils using NIRS: influence of replication and sample grinding and drying

Keywords: soil, carbon, nitrogen, near infrared reflectance spectroscopy (NIRS), sample preparation, replication

Near infrared reflectance spectroscopy (NIRS) has been receiving increasing attention for the rapid and inexpensive determination of soil properties, total carbon (Ct) and nitrogen contents (Nt) especially. However, methodological aspects such as sample grinding and drying or replication have not been addressed extensively. The objectives of the paper were thus to assess how NIRS predictions of Ct and Nt were affected by sample grinding (2 mm sieving vs. 0.2 mm grinding), drying (air-drying vs. oven-drying at 40°C during 24 h), and replication (use of one to six subsamples to determine average spectra). This was performed on a range of tropical soils that differed widely in mineralogy (low and high activity clay soils, allophanic soils) and texture (sandy to clayey).

The accuracy of NIRS predictions of Ct and Nt was higher with oven-dried compared to airdried samples, and more markedly, with 0.2 mm ground compared to 2 mm sieved samples.

Replication had a positive effect on NIRS predictions when 2 mm sieved samples were used, especially for air-dried samples, but this effect was not clear with 0.2 mm ground samples.

Thus the most accurate predictions of Ct and Nt were obtained with oven-dried finely ground samples, with limited response to sample replication. Accurate predictions were, however, also obtained with four replicates on oven-dried 2 mm sieved samples. Acceptable and less tedious results could thus be achieved when replacing fine grinding by replication. Even with this procedure, the r² between predicted (NIRS) and measured (reference) values was 0.9 and the ratio of standard error of prediction to mean (CV%) was 20%, considered satisfactory for the heterogeneous sample set under study.

Introduction

Studies on carbon and nitrogen cycles often require numerous determinations of soil carbon and nitrogen contents, which are rather time-consuming and expensive when standard analytical procedures are used. Therefore, much attention is given to possible alternatives such as near infrared reflectance spectroscopy (NIRS), which is a physical non-destructive, rapid and low-cost method. The NIRS analysis aims at developing calibration models to predict properties of materials (e.g. carbon content) according to their reflectance in the wavelength range between 800 and 2500 nm. Reflectance depends on vibrations in bonds between H and C, N, O, P, and S atoms. The models are developed from partial least square (PLS) calibration of spectral data carried out on samples that have also been characterized by reference methods. Calibration models are then used to characterize other samples from only their NIRS spectra.

NIRS was first used for the assessment of moisture content of seeds and other plant products, 1 and then for the evaluation of seed and forage quality. 2 Its first application to soils was reported during the sixties. 3 Accurate NIRS predictions of total soil carbon (Ct) and nitrogen contents (Nt) were reported during the seventies 4 , and to a larger extent, during the nineties. [5][6][7] Some methodological aspects have, however, not been addressed extensively. Some studies regarding NIRS determination of Ct and Nt reported that spectroscopic measurements of soil samples were performed in duplicate [8][9] or in triplicate 10 using different subsamples. However, the usefulness of replication has rarely been discussed. Moreover, several papers have discussed the usefulness of grinding samples for NIRS determination of Ct 8,[11][12] whereas others have reported accurate predictions using un-ground samples. [13][14][15] Some authors even suggested that grinding the samples did not improve the prediction accuracy. 16 Additionally, the conventional determination of Ct and Nt by dry combustion (Elemental Analyzer) is generally carried out on an oven-dry basis (40°C). The question arises whether NIRS analyses should also be carried out on oven-dried samples. As far as soil samples are concerned, this point has not been addressed in the literature.

The objective of this paper was to assess the effects of sample preparation (2 mm sieving vs. 0.2 mm grinding, and air-vs. oven-drying) and replication (use of one to six subsamples to calculate average spectra) on the accuracy of NIRS determination of Ct and Nt. This was performed on a wide range of tropical soils, including low activity clay soils (e.g. Alfisols, Oxisols, Ultisols), high activity clay soils (Vertisols), and allophanic soils (Andosols).

Materials and methods

Soil samples

The set studied included 123 soil samples originating from tropical Africa and America, which represented a wide range of soil types, textures, and Ct and Nt (Table 1). The distribution of Ct was rather even over the sample set: 23, 28, 23, 21, 19 and 9 samples had Ct between 0 and 10, 10 and 20, 20 and 30, 30 and 40, 40 and 50, and greater than 50 g kg -1 , respectively. The distribution of Nt was slightly less even : 22, 32, 19, 18, 22 and 10 samples had Nt between 0 and 0.8, 0.8 and 1.6, 1.6 and 2.4, 2.4 and 3.2, 3.2 and 4.0, and greater than 4.0 g kg -1 , respectively. The composition of sets that have even distributions of studied properties is a current practice in NIRS applications. [START_REF] Bertrand | La Spectroscopie Infrarouge et ses Applications Analytiques[END_REF] In the present study, it was obtained by selecting 32 additional samples to complete the initial set of 91 samples. Considering the complete set, Ct ranged from 1.7 to 67.3 g kg -1 , and Nt from 0.18 to 6.32 g kg -1 . The samples were air-dried then gently crushed using a mortar and pestle, and sieved to pass a 2 mm mesh.

Aliquots were finely ground to pass a 0.2 mm mesh, also using a mortar and pestle.

Reference analyses for carbon and nitrogen

The reference determinations of Ct and Nt were carried out on finely ground (< 0.2 mm) and oven-dried (40°C) samples by dry combustion using an Elemental Analyzer (CHN Fisons / Carlo Erba NA 2000, Milan, Italy). Replication was not achieved for these conventional determinations. In the absence of carbonates, all carbon was assumed to be organic.

NIRS analyses

Reflectance was measured between 1100 and 2500 nm at 2 nm interval with a Foss NIRSystems 5000 spectrophotometer (Silver Spring, MD, USA), using a static ring cup (5 cm diam.) containing ~ 5 g of soil. Each spectrum, automatically averaged from 15 scans, was recorded as the logarithm of the inverse of the reflectance (log [1/R], i.e. absorbance).

Principal component analysis (PCA) and a modified partial least-square (MPLS) analysis were conducted using the WinISI III-v.1.50e software (Infrasoft International, LLC, State College, PA, USA). Absorbance bands being much wider than 2 nm in general and recorded spectra thus including redundant information, [START_REF] Bertrand | La Spectroscopie Infrarouge et ses Applications Analytiques[END_REF] spectral data sets were reduced to condense information. Following Sørensen and Dalsgaard, 9 this was achieved by keeping the first out of four adjacent spectral points, yielding 173 data points per spectra. Based on previous unpublished results, spectra were mean centered and variance scaled (standard normal variate with 4 point gap and 4 point smoothing), then a first derivate was applied using the finitedifference method. [START_REF] Collatz | The Numerical Treatment of Differential Equations[END_REF] A PCA was carried out on spectral data for the calculation of the Mahalanobis distance H. [START_REF] Mark | [END_REF] Samples with H > 3 were considered outliers and were eliminated from further investigations 21 (H > 3, probably due to particular sample properties, was observed for one Ultisol sample from Martinique with all four sample preparations [see below], and for two air-dried sieved Oxisol samples from Brazil). After eliminating spectral outliers, MPLS regressions were used to derive calibration models from spectra and reference values of Ct and Nt. 22 Each set was divided into a calibration subset, which included 90 samples, and a remaining validation subset, which included 32 or 30 samples. The calibration subset was selected by the software to include the most representative samples of the set. 21 Based on H distance between all pairs of spectra, an algorithm identified the spectrum that had the most neighbouring spectra closer than a minimal distance, retained that spectrum and discarded its neighbours. The process was continued until no samples remained with neighbours closer than the minimal distance, which was calculated by the software so that the calibration subset included 90 samples. Random selection of the calibration subset did not seem appropriate as different selections sometimes led to very different results, as reported by Brown et al. 23 Cross validation was performed on the calibration subset to determine the optimal number of terms to be included in the prediction model. For this purpose, the calibration subset was divided into six groups, five being used for developing the model and one for testing the calibration. The procedure was performed six times to use all samples for both model development and prediction. The residuals of the six predictions were pooled to calculate the standard error of cross validation between predicted and measured values (SECV). Samples with residual greater than 2.5 times SECV (calibration outliers) were removed and another cross calibration was performed, the procedure being carried out twice. Then all remaining calibration samples were used to calculate the final model. The number of factors giving the lowest final SECV determined the optimal number of terms to be used for the calibration. The performance of the calibration model was assessed using the coefficient of determination (R²) and the ratio of standard deviation to SECV (denoted RPD). The prediction accuracy of the model was evaluated on the validation subset, using validation r² and standard error of prediction (SEP) between predicted and measured values. According to Morra et al., 5 the performance of the MPLS calibration model was also evaluated using the coefficient of variation (CV, in %), calculated as the ratio of SEP to the mean reference value. Additionally, a paired t-test was carried out on the validation subset to assess whether measured and predicted values differed significantly.

Treatments: sample preparation and replication

NIRS analyses were carried out on 2 mm sieved and 0.2 mm ground air-dried samples, then on the same samples after oven-drying at 40°C during 24 h. Four sample preparations were thus considered: air-dried and sieved, air-dried and ground, oven-dried and sieved, and ovendried and ground. For clayey samples and Andosols, oven-drying resulted in a decrease in weight that could reach 10% (data not shown). Moreover, spectroscopic measurements were carried out on six subsamples per sample, using independent refilling of the ring cup, and six final spectra were considered for each sample preparation: the spectrum obtained with the first subsample only, the average spectrum resulting from the two first subsamples, that resulting from the three first subsamples, etc., and the average spectrum resulting from all six subsamples. Thus 24 spectrum sets were studied, involving four sample preparations with one to six replicates. Three-way ANOVAs were carried out to assess whether SEP and validation r² were affected by grinding, oven-drying, and replication level (three replication levels were considered: low, medium and high, corresponding to one or two, three or four, and five or six replicates, respectively).

Results

Overall NIRS results

Considering all treatments, RPD ranged from 2.88 to 3.93 for Ct and from 2.75 to 3.62 for Nt (Table 2). SEP ranged from 4.07 to 6.73 g kg -1 for Ct, representing 16% to 26% of mean Ct, and from 0.30 to 0.52 g kg -1 for Nt, representing 14% to 25% of mean Nt. Validation r² ranged from 0.811 to 0.938 for Ct and from 0.866 to 0.944 for Nt. Whatever the sample preparation and the number of replicates, paired t-tests carried out on validation subsets indicated that predicted and measured values did not differ significantly at p < 0.05.

Influence of sample preparation

On the whole, whatever the number of subsamples used to determine sample spectra, calibration accuracy for both Ct and Nt tended to increase (i.e. SECV tended to decrease and calibration R² to increase) as follows: air-dried sieved < oven-dried sieved < oven-dried ground < air-dried ground (Table 2, Figures 1 and2). However, sample preparations were not always ranked in this order when sample spectra were determined using one subsample only.

Validation accuracy for both Ct and Nt tended to increase (i.e. SEP tended to decrease and validation r² to increase) as follows: air-dried sieved < oven-dried sieved < air-dried ground < oven-dried ground. Thus the accuracy of NIRS predictions of Ct and Nt was generally higher with ground than with sieved samples, and with oven-than with air-dried samples.

Factorial ANOVAs indicated that the effects of grinding and oven-drying on SEP and validation r² were significant for Ct and Nt (p < 0.05), but that the interaction of grinding and oven-drying was not significant.

Influence of replication

Regarding Ct or Nt, calibration accuracy was not clearly affected by the number of subsamples used to determine sample spectra (Table 2, Figures 1 and2).

Replication had a positive effect of validation accuracy when 2 mm sieved samples were used: SEP tended to decrease and validation r² to increase when the number of replicates increased, particularly for Ct prediction using air-dried sieved samples. By contrast, the effect of replication on validation accuracy was not clear when 0.2 mm ground samples were used (except for Ct prediction with oven-dried ground samples). Factorial ANOVAs indicated that SEP and validation r² for Ct and Nt were not significantly affected by replication level, however they were significantly affected by the interactions grinding  replication level, oven-drying  replication level, and grinding  oven-drying  replication level (p < 0.05). This confirmed that replication affected prediction accuracy with some sample preparations only (e.g. sieving).

Discussion

Overall NIRS results

For the soil samples under study, RPD was generally higher than 3 and always higher than 2.7, indicating that the ability of the models to predict Ct and Nt was satisfactory. [START_REF] Williams | Near Infrared Technology in the Agricultural and Food Industries[END_REF] For sieved and ground samples, the ranges of validation r² were 0.81-0.91 and 0.86-0.94, and the ranges of validation CV, 19-26% and 14-23%, respectively. These predictions of Ct and Nt were more accurate than most predictions carried out on sample sets that included wide ranges of soil types and texture: for heterogeneous sample sets, ranges of validation r² and CV reported in the literature were 0.70-0.87 and 25-35%, 9,13,14,[START_REF] Mccarty | [END_REF] respectively. The relatively even distribution of samples across Ct and Nt classes might have contributed to this rather good prediction accuracy. The use of sets having even distributions of studied properties was reported by Bertrand [START_REF] Bertrand | La Spectroscopie Infrarouge et ses Applications Analytiques[END_REF] as a current practice for NIRS applications in general, and was mentioned for soil studies by Sørensen and Dalsgaard. 9

Influence of sample preparation

The accuracy of NIRS predictions of Ct and Nt was generally higher with oven-than with airdried samples, and with 0.2 mm ground than with 2 mm sieved samples. As a consequence, the most accurate predictions were achieved using 0.2 mm ground oven-dried samples, and the less accurate with 2 mm sieved air-ground samples. Moreover, the accuracy of Ct and Nt predictions was more affected by grinding than by drying. Regarding Ct prediction, average decreases in SEP upon grinding and oven-drying were 1.17 and 0.89 g kg -1 , and average increases in validation r² were 0.051 and 0.039, respectively. Regarding Nt, average decreases in SEP upon grinding and oven-drying were 0.08 and 0.07 g kg -1 , and average increases in validation r², 0.042 and 0.017, respectively.

The positive effect of fine grinding on the accuracy of NIRS predictions of Ct and Nt has been reported in the literature, especially for sets including clayey soils and for heterogeneous sets including several soil types. 8,11,12 Nevertheless, lower prediction accuracy with 0.5 mm ground than with 4 mm sieved samples was reported for coarse-textured soils. 16 These contradictory results might be explained by the size and arrangement of soil particles, which affect light transmission 13 and differ between clayey and coarse-textured soils. In clayey soils, aggregation is well developed and results in a wide range of particle sizes that affects reflectance adversely, 11 thus aggregate destruction upon grinding, which reduces the heterogeneity of particle-size distribution, might explain increasing prediction accuracy. By contrast, coarse-textured soils include few aggregates and their particle-size distribution is dominated by coarse quartz particles often coated with fine particles (except in very sandy soils). In that case, grinding requires much energy to break quartz particles up, which might alter sample composition, moreover it probably causes the peeling of coatings, which might result in a more heterogeneous particle-size distribution. The sample set under study was dominated by clayey soils (79 out of the 123 samples), thus higher prediction accuracy with ground than with sieved samples was consistent with the above-mentioned explanation and with literature data.

Comparisons between NIRS predictions using air-dried and oven-dried soil samples have not been reported in the literature yet. Nevertheless some studies compared NIRS predictions obtained with dried vs. field-moist or thawed samples. Regarding Ct, higher prediction accuracy has been reported with ground dried than with un-ground field-moist samples, 26 and with thawed than with air-dried un-ground sandy samples, 16 however some studies reported similar accuracy with dried and field-moist un-ground samples. 12,27 Regarding Nt, higher prediction accuracy was generally observed with field-moist or thawed samples than with airdried ones, 16,26,27 but no explanation was proposed. Chang et al. 27 mentioned that soil water might adversely affect the ability of NIRS to predict soil properties, because the strong H 2 O absorption bands often masked peaks associated with organic functional. Though oven-drying (40°C) has not been addressed in previous studies, its positive effect on prediction accuracy might thus be attributed to a reduction of this adverse influence of moisture on reflectance.

Influence of replication

Replication (i.e. using several subsamples to determine sample spectra) had little influence on calibration results. Similarly, its effect on validation results was not clear in general when using 0.2 mm ground samples (except for Ct with oven-dried samples). By contrast, prediction accuracy tended to increase with the number of replicates for 2 mm sieved samples, air-dried ones especially, which yielded poor predictions. From a general viewpoint, replication helps characterizing heterogeneous samples, but is less useful for homogeneous samples. In clayey soils, grinding decreases the heterogeneity of sample-size distribution, due to the destruction of aggregates. As clayey soils dominated the studied set, samples were less heterogeneous in general in the ground than in the sieved set, which probably contributed to the smaller effect of replication on prediction accuracy for ground than for sieved samples.

As far as soils are concerned, determination of average spectra from several subsamples has been reported for 2 mm sieved samples, [8][9][10]23 and to a lesser extent, for finely ground samples. 8 However, though replication has been mentioned in the Materials and methods section of several papers, its interest has rarely been discussed. The question was addressed by Sørensen and Dalsgaard 9 , who noticed that the accuracy of NIRS predictions could not be improved significantly by performing double measurements instead of single ones. For 2 mm sieved soil samples, they found that the variability of independent single predictions of clay content was less than 0.8%. Similarly, in a study regarding the NIRS prediction of the composition of a ground pharmaceutical preparation, Blanco et al. 28 found that the variability of 12 independent results was lower than 0.9%. NIRS studies on plant materials (forages, litters, etc.), which have developed earlier than on soils, often involve the determination of average spectra using several subsamples, probably because plant samples are rather hard to grind and are not finely ground in general (e.g. 1 mm preparation [29][30][31] ). Nevertheless, single NIRS measurement was reported with rather finely ground plant samples (0.5 mm preparation 32 ). It might thus be suggested than replication has sometimes been adopted in soil studies because it was widely used with plant materials, though it seems less necessary for soils than for plant materials. Indeed, fine grinding is easier for soil samples than for plant materials and yielded more accurate predictions than coarse grinding.

In the present study, the highest prediction accuracy was generally obtained with six replicates on oven-dried ground samples (validation r² and CV for Ct and Nt were 0.94 and 16-17%, respectively). However, using one single replicate on oven-dried ground samples did not decrease prediction accuracy markedly (0.91-0.94 and 14-17%, respectively). Moreover, replacing one single replicate on oven-dried ground samples by four replicates on oven-dried sieved samples also caused a limited decline in prediction accuracy (0.90-0.91 and 19-20%, respectively). Paired t-tests confirmed that the three procedures yielded Ct and Nt predictions that did not differ significantly at p < 0.05. As it is less tedious than fine grinding, replication on oven-dried sieved samples could thus be considered an acceptable procedure (Figure 3).

Conclusion

The present study was carried out on a range of tropical soils that widely differed in mineralogy (low and high activity clay soils, allophanic soils), texture (sandy to clayey), and carbon content (1.7 to 67.3 g kg -1 ). It confirmed the interest of NIRS for the determination of soil carbon and nitrogen contents. Prediction accuracy was higher with oven-dried (40°C during 24 h) than with air-dried samples, and to a larger extent, with 0.2 mm ground than with 2 mm sieved samples. Moreover, replication (i.e. the use of several subsamples to calculate average NIRS spectra) increased prediction accuracy when 2 mm sieved samples were used, air-dried ones especially, but the effect of replication was less clear with ground samples.

The most accurate predictions of total soil carbon and nitrogen contents were generally obtained with oven-dried 0.2 mm ground samples and six replicates, but the decrease in prediction accuracy was limited when one single replicate only was used. Moreover, the decrease in prediction accuracy was also limited when the procedure involving one single replicate on oven-dried 0.2 mm ground samples was replaced by four replicates on oven-dried 2 mm sieved samples. As far as samples were oven-dried, acceptable results could thus be achieved when replacing tedious fine grinding by replication.

Figure 1 .Figure 2 .Figure 3 .

 123 Figure1. Effect of replication (use of several subsamples to calculate average sample spectra), 2 mm sieving vs. 0.2 mm grinding, and air-vs. oven-drying of soil samples on calibration and validation results for Ct (air-dried sieved ; air-dried ground ; oven-dried sieved ; ovendried ground ).

Table 1 .

 1 Presentation of the soil samples.

	Location	Texture and soil type 33	Number of samples	Sample depth (cm)	Ct a (g kg -1 )	Nt a (g kg -1 )
	Benin	Sandy loam Ultisol	11	0-5 to 25-30	5.7 ± 4.0	0.48 ± 0.36
	Brazil	Clayey Oxisol	13	0-5 and 5-10	19.2 ± 6.4 1.34 ± 0.49
	Burkina Faso Sandy Alfisol	11	0-10 to 20-40	6.1 ± 4.0	0.48 ± 0.26
	Congo b	Clayey Oxisol	6	0-10 and 10-20 21.8 ± 7.2 1.30 ± 0.34
	Madagascar Clayey Inceptisol	15	0-5 and 5-10	45.2 ± 4.8 3.42 ± 0.38
	Martinique c Clayey Inceptisol	15	0-10	25.3 ± 13.8 2.24 ± 1.07
	Martinique c Clayey Ultisol	10	0-10 to 20-30	24.1 ± 6.6 2.00 ± 0.49
	Martinique c Clayey Vertisol	20	0-10 to 20-30	28.6 ± 15.5 2.50 ± 1.37
	Martinique c Andosol	21	0-10 to 60-70	36.8 ± 13.6 3.26 ± 1.32
	Senegal	Sandy Alfisol	1	0-10	5.5	0.39
	Total set	-	123	0-5 to 60-70	25.7 ± 15.9 2.11 ± 1.36

a mean ± standard deviation. b Congo-Brazzaville. c French West Indies.

Acknowledgments

We thank Anastase Azontonde, Edgar De Luca, Edmond Hien, Aurélie Metay, Tantely Razafimbelo, and Corinne Venkatapen for sample collection. We also thank anonymous referees for their helpful recommendations.

SECV and SEP are standard error of cross validation and of prediction, respectively. RPD is the ratio of performance to deviation, i.e. the ratio of standard deviation to SECV.