Ahmed Abdelghany
email: ahmed.abdelghany@univ-rennes1.fr

Member, IEEE Bernard Uguen
email: bernard.uguen@univ-rennes1.fr

Senior Member, IEEE Christophe Moy
email: christophe.moy@univ-rennes1.fr

Dominique Lemur
email: dominique.lemur@univ-rennes1.fr

Decentralized Adaptive Spectrum Learning in Wireless IoT Networks based on Channel Quality Information

Keywords: IoT, LPWAN, LoRa, Packet Loss Rate, RSSI, Effective Signal Power, Measurement, Smart City, Spectrum Allocation, Machine Learning, Reinforcement Learning, UCB

In the Internet of Things (IoT) context such as Low Power Wide Area Network (LPWAN), it is essential to reduce the packet losses, e.g., to save energy. Decentralized artificial intelligence techniques have been proposed to combat radio collisions, but the approach here is extended to deal additionally with the channel propagation effects. In this article, a Quality of Channel Allocation (QoC-A) learning technique based on bandit algorithms is proposed in order to choose the transmission channel. This aims to reduce the effect of the propagation impairments between the radio channels while using the Effective Signal Power (ESP) as a quality metric. In addition, a Discounted QoC-A (DQoC-A) algorithm is proposed to adapt rapidly to any abrupt change in the channels' conditions. An experimental campaign on a real IoT device is carried out to demonstrate the low complexity and efficiency of these proposed decentralized algorithms. In the given results, QoC-A outperforms the classical UCB policy with a more accelerated learning process. On the other hand, the feasibility of using the DQoC-A in non-stationary scenarios is illustrated by its rapid convergence when abrupt changes in the channels' conditions occur. At the end of the process, these proposed learning techniques give 4.1 and 2.4 times fewer packet losses than the traditional ones with a random channel assignment scheme, in the stationary and non-stationary scenarios, respectively.

I. INTRODUCTION

A. Background I NTERNET of Things (IoT) has been utilized in a wide range of domains, such as smart city, health monitoring, livestock, surveillance, etc [START_REF] Abdelghany | A Pre-processing Algorithm Utilizing a Paired CRLB for TDoA Based IoT Positioning[END_REF], [START_REF] Al-Jarrah | Decision Fusion for IoT-Based Wireless Sensor Networks[END_REF], [START_REF] Ciuonzo | Distributed Detection in Wireless Sensor Networks Under Multiplicative Fading via Generalized Score Tests[END_REF]. For some IoT applications, the characteristics of large coverage, low power consumption and a low-cost deployment network are required, which could be fulfilled using Low Power Wide Area Network (LPWAN). For providing these capabilities, LoRaWAN (Long Range Wide Area Network) is considered as the leading technology that is based on a Chirp Spread-Spectrum (CSS) solution and operating in unlicensed bands, i.e. 868 MHz in Europe and 915 MHz in the USA. Hence, it can interconnect low-cost and mostly battery-powered devices over long ranges to the gateway [START_REF] Oliveira | Long Range Communications in Urban and Rural Environments[END_REF].

As LoRaWAN protocol has no exclusive rights in these unlicensed bands [5], also called Industrial, Scientific and Medical (ISM) application bands, channel impairments may occur on the link between the end node and the gateway, reducing the reliability of communications in these networks [START_REF] Augustin | A Study of LoRa: Long Range & Low Power Networks for the Internet of Things[END_REF]. Consequently, packet loss will be the weak point of these networks as it degrades the performance of the entire network in the long term. These packet losses may occur either due to collisions as depicted in [START_REF] Rahmadhani | When LoRaWAN Frames Collide[END_REF], or propagation effects as manifested in [START_REF] Abdelghany | On Superior Reliability of Effective Signal Power versus RSSI in LoRaWAN[END_REF], [START_REF] Abdelghany | Modelling of the Packet Delivery Rate in an Actual LoRaWAN Network[END_REF] and [START_REF] Liu | Characterizing Packet Loss in City-Scale LoRaWAN Deployment: Analysis and Implications[END_REF]. Serious outcomes are caused by this transmission failure that may affect various IoT applications, in particular those using the acknowledged messaging mode for the important sensor data. If the end node does not receive the Acknowledgment (ACK) packet, the end node will retransmit the data packet. However, extra energy consumption is required by this retransmission that impacts the battery life of the end node devices plus occupying an additional spectrum and raising the interfering level.

B. Related Works and Motivation

Recently, many works are proposing different solutions for reducing the packet loss rate. For example, in [START_REF] Li | DyLoRa: Towards Energy Efficient Dynamic LoRa Transmission Control[END_REF] the authors propose DyLoRa, a dynamic LoRa transmission control system to improve energy efficiency, as an alternative to the state-of-the-art LoRaWAN Adaptive Data Rate (ADR). Thus, the idea of DyLoRa is to adjust the transmission parameters, i.e. transmission power and Spreading Factor (SF), among different environments. Moreover, a Collision Avoidance Resource Allocation (CARA) algorithm is proposed in [START_REF] Chinchilla-Romero | Collision Avoidance Resource Allocation for LoRaWAN[END_REF] with the objective of increasing the system capacity by mitigating packet losses from the collisions. However, these previous works are either centralized approaches (on the network side), hence, they do not consider the different interference conditions in the proximity of each end node which is located in a specific area. Or, they are imposing changes on the IoT protocol with extra packet transmissions and time synchronization between the end nodes, as depicted in Table I.

While in [START_REF] Moy | IoTligent: First World-Wide Implementation of Decentralized Spectrum Learning for IoT Wireless Networks[END_REF] and [START_REF] Moy | Decentralized Spectrum Learning for Radio Collision Mitigation in Ultra-dense IoT Networks: LoRaWAN case study and experiments[END_REF], the first implementation of a decentralized spectrum learning for IoT wireless networks is proposed in order to mitigate radio collisions without changing anything to LoRaWAN protocol. Moreover, they can be used in addition to conventional ADR techniques. They propose to use a learning algorithm on LoRa devices that can cope ACCEPTED MANUSCRIPT / CLEAN COPY with spectrum scarcity which could occur in unlicensed bands. Nevertheless, this learning algorithm does not exploit the channel quality at each frequency band on the end node side to accelerate the learning process. This decentralized approach could be extended, which was just to avoid collisions to the management of channel quality too. Hence, the channel quality is estimated from the channel parameters, i.e. SNR (Signalto-Noise Ratio), Received Signal Strength Indicator (RSSI) and Effective Signal Power (ESP), which are considered as one of the main factors affecting the packet loss rate [START_REF] Abdelghany | On Superior Reliability of Effective Signal Power versus RSSI in LoRaWAN[END_REF], [START_REF] Abdelghany | Modelling of the Packet Delivery Rate in an Actual LoRaWAN Network[END_REF]. Moreover, these channel parameters could be obtained on the end node side for implementing a decentralized approach, thanks to the reciprocity between the uplink and downlink Channel State Information (CSI).

C. Contributions

The main contributions of this article are threefold as follows:

• A Quality of Channel Allocation (QoC-A) algorithm is proposed by extending the classical Upper Confidence Bounds (UCB) technique to deal with the channel propagation effects besides collisions. This proposed decentralized machine learning algorithm takes into account the quality of the channel in addition to the traditional binary reward. Subsequently, it reduces the packet losses by learning a proper frequency allocation scheme that averts using a channel with poor propagation conditions and then accelerates the learning process.

• ESP is utilized instead of RSSI as the channel quality indicator, to overcome the RSSI limitation as discussed in [START_REF] Abdelghany | On Superior Reliability of Effective Signal Power versus RSSI in LoRaWAN[END_REF].

• A Discounted QoC-A (DQoC-A) algorithm is proposed in order to tackle situations where the channels' conditions are non-stationary on a long-term basis.

Here, this adaptive algorithm fulfills the necessity of introducing a specific mechanism for forgetting the outdated channels' states. Based on that, the CSI shape evolution which happens when an end node moves from one place to another is typically the kind of nonstationary behavior that is addressed by this algorithm. Another non-stationary scenario could occur when the end node exhibits a changing environment model, for example, if it is placed in a road where there are moving cars and objects. These moving obstacles may introduce a temporal evolution of the CSI shape between the morning and night period [START_REF] Rauh | Multipath Characteristics of Indoor-to-Outdoor Radio Channels in the 868-MHz Band[END_REF].

On the other hand, the proposed reinforcement learning algorithms could be embedded at the IoT end node side with low hardware extra cost in terms of processing power, memory footprint, etc. Hence, in a real network deployment within the university campus in Rennes, these algorithms are implemented inside an end node device and executed in different scenarios, i.e. stationary and non-stationary. Consequently, the whole results from the experiment are extensively evaluated among the proposed reinforcement learning algorithms against the UCB policy as well as the traditional scheme with random frequency allocation. Moreover, important remarks are given for adjusting the algorithms' configurations based on the properties of each of the potential IoT applications.

D. Organization

The remainder of this article is organized as follows. Section II presents the main factors of the packet losses. Section III provides sufficient detail about the system model of the proposed algorithm. The proposed algorithms are then illustrated in Section IV. While Section V shows the experimental architecture and network configuration used for the measurement campaign. In Section VI, the experimental results of the proposed algorithms are tested through the different scenarios. Additional remarks are given for adjusting the algorithms' configurations in Section VII. Finally, the work is concluded in Section VIII. A list of key acronyms used throughout this article is presented in Table II.

II. KEY FACTORS OF PACKET LOSS

Packet losses are the main drawback for IoT [START_REF] Guo | Experimental Evaluation of the Packet Reception Performance of LoRa[END_REF]. Hence, packet losses cause many retransmissions at the cost of a lower battery lifetime of the end nodes and may lead to an increase of the RF (Radio Frequency) contention level. Even worse, a total failure of the IoT service could happen, either because end nodes can not succeed in sending any data to the gateway or because all their energy is consumed much faster than expected due to the multiple repetitions of the transmission. Without loss of generality, LoRaWAN is used as an example in this article but any other IoT protocol could be utilized. Thus, the major sources of the packet loss are described in the following subsections, as shown in Figure 1.

A. Packet collision

Channel contention occurs when multiple devices attempt to send data over the same channel simultaneously [START_REF] Rahmadhani | When LoRaWAN Frames Collide[END_REF], [START_REF] Moy | Decentralized Spectrum Learning for Radio Collision Mitigation in Ultra-dense IoT Networks: LoRaWAN case study and experiments[END_REF]. Whereas the end nodes are uncoordinated, the packet transmission is initiated by the end node, not the network. Hence, the traditional LoRa device does not check if the channel is preempted by other devices before transmitting a packet, so ACCEPTED MANUSCRIPT / CLEAN COPY it may cause packet collision. Additionally, the IoT networks are superposed with no coordination between them. So, these collisions could also occur no matter whether the interfered signal is from other end nodes of the same network or the surrounding IoT networks, using the same IoT standard or not. Moreover, interference could occur from other radio signals present in the ISM bands which are not IoT signals, so they can be considered "jammers" by definition. Last but not least, electromagnetic radiations could disturb the end nodes due to the proximity of other electronic devices suffering from leakage radiations, for instance, this could happen in an industrial environment.

B. Channel factors

The end node can be located far away from the gateway, especially in LPWAN networks, which causes shadowing and signal attenuation across the transmission range [START_REF] Chall | LoRaWAN Network: Radio Propagation Models and Performance Evaluation in Various Environments in Lebanon[END_REF]. Packet transmission success is closely related to the channel state, indeed, a channel facing bad propagation conditions has the same effect as caused by collisions. These propagation conditions are directly determined by the channel parameters which are SNR, RSSI and ESP. SNR is the ratio of signal power to the measured noise power. Consequently, the higher SNR is, the smaller the noise mixed in the signal, and the easier it is to separate the effective signal. RSSI is a relative value of signal power measured by the end node or the gateway at its receiving end. However, ESP is a more reliable parameter as it overcomes the RSSI limitation, especially at low SNR (< 0 dB) as depicted in [START_REF] Abdelghany | On Superior Reliability of Effective Signal Power versus RSSI in LoRaWAN[END_REF] and [START_REF] Abdelghany | Modelling of the Packet Delivery Rate in an Actual LoRaWAN Network[END_REF].

Without loss of generality, ESP is computed as:

ESP dBm = RSSI dBm + SN R dB -10 log 10 (1 + 10 SN R dB 10
).

(1) In general, ESP value decays with the shadowing effect and increase of distance, in particular for the long transmission range, as in most IoT applications. Due to the low transmission power, i.e. maximum transmit power of the LoRa signal is 14 dBm, and the large propagation attenuation, this value is usually negative in dBm. Furthermore, these channel parameter values depend on the specific environmental conditions around each end node, hence, each CSI is different from one location to another.

III. SYSTEM MODEL

The proposed learning approach can help IoT devices to reduce packet losses due to both weak channel propagation conditions and also collisions. That for, the proposed approach is inspired from [START_REF] Moy | IoTligent: First World-Wide Implementation of Decentralized Spectrum Learning for IoT Wireless Networks[END_REF] and [START_REF] Moy | Decentralized Spectrum Learning for Radio Collision Mitigation in Ultra-dense IoT Networks: LoRaWAN case study and experiments[END_REF] where a solution to radio collisions is proposed, while imposing no change on the IoT protocols, as, for instance, LoRaWAN. Employing the acknowledged messaging mode is the only required condition to utilize the proposed solution. Based on the investigation in [START_REF] Abdelghany | On Superior Reliability of Effective Signal Power versus RSSI in LoRaWAN[END_REF], the underlying hypothesis is that the channels' Packet Delivery Rate (PDR) is not equally balanced across the K different frequency bands an IoT device can use. In other words, some channels are less attenuated than others. These channel conditions are possibly be predicted online in time and space in a decentralized manner (on the end node side). As the end nodes may be quite far away from the gateways and suffer from different jamming and channel conditions, it is much more efficient to implement a spectrum allocation approach on the end node side than on a centralized unit. While taking into consideration that no extra processing can be afforded at the end node where every Watt is counted at transmission to save energy.

To be compatible with the constraint of low complexity of the end node hardware, a kind of Artificial Intelligence (AI) algorithm is considered [START_REF] Min | Learning-Based Privacy-Aware Offloading for Healthcare IoT With Energy Harvesting[END_REF]. This proposed approach is based on reinforcement learning algorithms which have been introduced by the machine learning community [START_REF] Lai | Asymptotically Efficient Adaptive Allocation Rules[END_REF] and first proposed for cognitive radio communications more than 10 years ago [START_REF] Jouini | Upper Confidence Bound Based Decision Making Strategies and Dynamic Spectrum Access[END_REF]. It is also experimentally validated on real radio signals for cognitive radio and especially for Opportunistic Spectrum Access (OSA) in [START_REF] Moy | Reinforcement Learning Real Experiments for Opportunistic Spectrum Access[END_REF]. As asserted for OSA, Multi-Armed Bandit (MAB) problem can be utilized to model the IoT spectrum access issue [START_REF] Moy | IoTligent: First World-Wide Implementation of Decentralized Spectrum Learning for IoT Wireless Networks[END_REF]. Thus, ACCEPTED MANUSCRIPT / CLEAN COPY reinforcement learning is based on a feedback loop that gives a success/failure measure of the action. In the IoT context, a binary reward, i.e. 1|0 for the presence|absence of the ACK packet which is sent by the gateway to the end node, is considered, as shown in Figure 2. If a message has been successfully transmitted from the end node to the gateway on the uplink channel, as well as the ACK message has been successfully transmitted from the gateway and received by the end node on the same channel in the downlink, a reward of "1" is given plus the channel parameters, i.e. SNR, RSSI and ESP, are estimated to optimize and accelerate the learning process as illustrated in the following sections. While a reward of "0" means that packet loss has happened either on uplink or downlink so that ACK has not been received by the end node. Maximizing the PDR is the main target, or equivalently, maximizing its cumulated reward. This proposed approach can adapt to any other IoT protocol, moreover, it has the following main advantages:

• Coordination between the end nodes is not necessary.

Therefore, no extra retransmission, no data to be added into the uplink or downlink packet. While the content of the ACK packet isn't changed.

• The very low processing and memory overhead of both the implementation and execution of the proposed approach [START_REF] Moy | IoTligent: First World-Wide Implementation of Decentralized Spectrum Learning for IoT Wireless Networks[END_REF]. Consequently, it is possible to execute the proposed algorithm in the end node devices whose complexity is negligible in terms of processing, hardware, memory as well as energy consumption overhead.

• The strong mathematical proof of convergence of the Bandit algorithms [START_REF] Bonnefoi | Multi-Armed Bandit Learning in IoT Networks: Learning helps even in nonstationary settings[END_REF], [START_REF] Auer | Finite-time Analysis of the Multiarmed Bandit Problem[END_REF]. Thanks to the good matching between models and reality, these proofs are verified in real radio conditions [START_REF] Moy | Reinforcement Learning Real Experiments for Opportunistic Spectrum Access[END_REF].

• Rapid convergence of the proposed learning techniques in real experiments [START_REF] Besson | GNU Radio Implementation of MALIN: "Multi-Armed bandits Learning for Internet-of-things Networks[END_REF].

• Thanks to the reinforcement learning concept, any prior training isn't needed. This proposed algorithm can efficiently start learning from scratch.

• These proposed learning algorithms' results will always outperform the given state-of-the-art ones with random frequency allocation [START_REF] Besson | GNU Radio Implementation of MALIN: "Multi-Armed bandits Learning for Internet-of-things Networks[END_REF].

IV. PROPOSED REINFORCEMENT LEARNING TECHNIQUES

Bandit algorithms are used at the end node side to handle IoT wireless spectrum issues. While LoRaWAN is the considered example, a simple ALOHA-based protocol is the utilized communications between the end nodes and the gateway. Whenever the end nodes decide, they can transmit their packets in one of the K ≥ 2 channels which are predefined in frequency f i . As stated in the previous section, the channel conditions in unlicensed ISM bands suffer in particular from propagation conditions and interference which are different from one place to another. Even in one place, these channel conditions are very often unevenly distributed over the K different channels.

From the point of view of a single end node in the network, it has to choose one channel (or arm), denoted as i ∈ {1, ..., K}, every step index n when it sends a packet to the gateway, then, it starts to wait for a fixed delay (one second in LoRaWAN) in the same channel i for receiving an ACK packet from the gateway, as shown in Figure 2. But due to propagation issues, the message sent by the end node to the gateway, or the ACK sent by the gateway to the end node, could be lost. Hence, selecting the channel i at packet index n yields a random feedback, i.e. the binary reward r i (n) and the channel quality g i (n). Maximizing the transmission success rate of the end node or, equivalently, maximizing the cumulative reward is the main target. Sequence of rewards drawn from a given arm i is assumed to be i.i.d., consequently, this problem is considered as a "stochastic" MAB [START_REF] Auer | Finite-time Analysis of the Multiarmed Bandit Problem[END_REF]. A player (here, an end node) has to try all arms (here, channels), a sufficient number of times to get a robust estimate of their qualities, while not selecting the worst arms too much. This requires tackling the so-called exploration-exploitation dilemma to be able to progressively focus on the best arm i.e., the arm with the largest average reward, using the proposed algorithms in the following subsections.

A. UCB Algorithm

Exploiting the channel with the highest estimated mean by selecting it at each time could be a first naive solution, however, this "greedy" approach is known to fail dramatically [START_REF] Lai | Asymptotically Efficient Adaptive Allocation Rules[END_REF]. Thus, the selection of arms is highly dependent on the first draws with this greedy policy. For example, if the first transmission in one channel succeeds and the first one on the other channel fails, the end node will never use the other channel again, even it is the best one and has the best channel conditions on average. While Upper Confidence Bounds (UCB) algorithm instead is adding an extra exploration term to the empirical mean, which can be viewed as a confidence ACCEPTED MANUSCRIPT / CLEAN COPY bound [START_REF] Auer | Finite-time Analysis of the Multiarmed Bandit Problem[END_REF]. At each end node, the number of times the channel i is selected up-to packet index n ≥ 1 is calculated as:

T i (n) = n m=1 1 A(m)=i ∀i, (2)
where A(m) ∈ {1, ..., K} is a discrete action which corresponds to the chosen channel index at packet index m. Hence, the empirical mean estimation of the successful transmissions obtained in channel i by selecting it up to packet index n, is denoted by the mean reward as:

R i (n) = 1 T i (n) n m=1 r i (m)1 A(m)=i ∀i. (3)
Subsequently, the upper confidence bound B i (n) of the channel i is denoted by the sum of the empirical mean and a confidence term as:

B i (n) = R i (n) + α ln n T i (n) , (4)
where the exploration factor α is recommended by the theory to be ≥ 0.25 [START_REF] Bubeck | Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems[END_REF]. At this point, the maximum upper confidence bound B i (n) is chosen by the end node to decide the next channel for sending the packet, thus, the next action A(n + 1) is obtained by choosing the best channel as:

A(n + 1) = arg max i (B i (n)). (5)
For each end node, the packet index n corresponds to the total number of transmitted packets from the beginning. As time is not slotted, this packet index n isn't shared across different end nodes. Every end node implements its own UCB algorithm independently, which can be described as follows in Algorithm 1.

Data: K, [α]

Result: A(n + 1) for n = 1 to ∞ do if n < K then Initialize policy by trying each channel for at least one time.

A(n + 1) = n + 1 else T i (n) = n m=1 1 A(m)=i ∀i R i (n) = 1 Ti(n) n m=1 r i (m)1 A(m)=i ∀i B i (n) = R i (n) + α ln n Ti(n) A(n + 1) = arg max i (B i (n)) end end
Algorithm 1: UCB policy as depicted in [START_REF] Auer | Finite-time Analysis of the Multiarmed Bandit Problem[END_REF].

B. QoC-A Algorithm

As mentioned in the previous sections, there is a strong dependency between the PDR and the channel quality. Hence, a Quality of Channel Allocation (QoC-A) policy is proposed to find the channel which is optimal in terms of both quality and probability of receiving the ACK packet [START_REF] Modi | QoS Driven Channel Selection Algorithm for Cognitive Radio Network: Multi-User Multi-Armed Bandit Approach[END_REF]. As first stated in Algorithm 2, all the channels are explored at least once to acquire the initial binary reward and their channel qualities. At the final step, Algorithm 2 returns the channel index A(n + 1) which has to be used in the next packet index. Again, T i (n) defines the number of times channel i has been utilized up to packet index n. After n ≥ K steps, the term B i (n), i.e. corresponding to the score of the ith channel at packet n, are updated as [START_REF] Modi | QoS Driven Channel Selection Algorithm for Cognitive Radio Network: Multi-User Multi-Armed Bandit Approach[END_REF]:

B i (n) = R i (n) + Q i (n) + α ln n T i (n) , (6)
where R i (n) denotes the exploitation term, or equivalently the empirical mean of the states (ACK packet received or not) of the ith channel at packet index n. While the bias term α ln n Ti(n) forces to explore the other channels, if the scheme leads to a channel whose average rewards degrades. Furthermore, the quality term Q i (n) defines the quality information of the channel i which can be calculated as:

Q i (n) = β( G i (n) G max (n) -1) ln n T i (n) (7)
with

G i (n) = 1 T i (n) Ti(n) k=1 g i (k) (8)
and

G max (n) = max i G i (n), (9)
where G i (n) is the empirical mean of quality observations g i (n) collected from channel i and G max (n) is the maximum expected quality value within the set of channels. Moreover, the new parameter β forces the algorithm to give some weight to the quality term Q i (n) in the score computation, whereas the parameter α forces the exploration of other channels to check their probability of receiving the ACK packet. Such a formulation tends to select a channel with the highest quality and probability to be acknowledged. For instance, if G i (n) = G max (n), the term Q i (n) will be equal to zero. While if the average quality of channel i is less than the average quality of the best channel (G i (n) < G max (n)), the value of Q i (n) will be negative and then the score term B i (n) will decrease. Accordingly, channel i will be less likely to be selected.

An important contribution of this article compared to the previous works in the cognitive radio field [START_REF] Modi | QoS Driven Channel Selection Algorithm for Cognitive Radio Network: Multi-User Multi-Armed Bandit Approach[END_REF], is that the quality observation g i (n) is the channel quality, i.e. ESP in linear scale, of the ACK packet. On the contrary, the channel parameters are obtained from a sensing phase before sending the packet in the OSA context, as the "listen-beforetalk" model in [START_REF] Modi | QoS Driven Channel Selection Algorithm for Opportunistic Spectrum Access[END_REF], which consumes power. It also worth mentioning that ESP is the used parameter that is obtained as a function of SNR, thus, it has an enlarged range when the SNR is very low, unlike the RSSI which has a limitation as detailed in Section II. Accordingly, this proposed algorithm is ACCEPTED MANUSCRIPT / CLEAN COPY simple to implement and to use in practice, even on embedded microprocessors with limited computation and memory capabilities as detailed in the following sections.

Data: K, [α, β]

Result: A(n + 1) for n = 1 to ∞ do if n < K then Initialize policy by trying each channel for at least one time.

A(n + 1) = n + 1 else T i (n) = n m=1 1 A(m)=i ∀i R i (n) = 1 Ti(n) n m=1 r i (m)1 A(m)=i ∀i G i (n) = 1 Ti(n) Ti(n) k=1 g i (k) G max (n) = max i G i (n) Q i (n) = β( Gi(n) Gmax(n) -1) ln n Ti(n) B i (n) = R i (n) + Q i (n) + α ln n Ti(n) A(n + 1) = arg max i (B i (n)) end end
Algorithm 2: QoC-A policy.

C. DQoC-A Algorithm

In many IoT applications, the end node could be in a non-stationary scenario, for instance, when it moves across different locations whose CSI shapes are different. Based on that, the probability of receiving the ACK packet and the quality of each channel are likely to experience changes in time, which exhibits the limitation of the aforementioned MAB algorithms. Although the convergence of these algorithms is very fast, however, the stationarity of the environment is required. Resetting the learning algorithm from time to time can be a simple solution, however, it may fail to determine when the propagation conditions change as the acquired reward distribution evolves with time occasionally.

In this article, a Discounted QoC-A (DQoC-A) algorithm is proposed to learn on the same channel conditions, i.e. quality and the probability of receiving the ACK packet, as the previous QoC-A but in non-stationary scenarios [START_REF] Modi | Machine Learning and Statistical Decision Making for Green Radio[END_REF]. Since the confidence interval of the standard QoC-A policy becomes tighter when time goes up, it is not appropriated for the non-stationary environment as stated before. While the motivation for the DQoC-A policy is to find an optimal channel in the case of changing environments, with less exploration. Therefore, discount factors (λ and λ g ) are considered for the DQoC-A to guaranty the adaptiveness of DQoC-A policy in a non-stationary environment, as stated in Algorithm 3. The idea behind the inclusion of these discount factors (λ and λ g ) is to give more weight to recent observations compared to the ones acquired in the past. A remarkable contribution of this article compared to the previous work in [START_REF] Modi | Machine Learning and Statistical Decision Making for Green Radio[END_REF], is that two different discount factors (λ and λ g ) are considered rather than using one. Thus, λ and λ g should have different values as they are used to average two different distributions, which are the binomial distribution of the binary reward r i (n) and the log-normal distribution of the channel quality g i (n), respectively.

Based on that, this proposed DQoC-A policy learns a channel that is optimal in terms of the probability of receiving the ACK packet and quality in a gradual manner. As with QoC-A policy, an end node employing DQoC-A policy first starts to explore all channels at least once initially. After n ≥ K steps, it updates the scoring term B i (n), however, each term in the equation is adapted to take into account the non-stationary hypothesis as:

B i (n) = R i (n) + Q i (n) + α ln W (n) N i (n) , ( 10
)
where N i (n) is the discounted number of times channel i has been used up to packet index n, and W (n) is the total discounted time. Contrary to QoC-A policy, the empirical mean of rewards R i (n) and channel quality G i (n) are estimated by taking into account the discount factors (0 < λ < 1 and 0 < λ g < 1), as shown in Algorithm 3. While the coefficients α and β, are the same as in the QoC-A policy, to weight exploration for the probability of receiving the ACK packet and channel quality, respectively. Furthermore, a relative comparison between the three policies is depicted in Table III.

Data: K, [α, β, λ, λ g ] Result: A(n + 1)
for n = 1 to ∞ do if n < K then Initialize policy by trying each channel for at least one time.

A(n + 1) = n + 1 else N i (n) = n m=1 λ n-m 1 A(m)=i ∀i W (n) = K i=1 N i (n) R i (n) = 1 Ni(n) n m=1 λ n-m r i (m)1 A(m)=i ∀i N g i (n) = n m=1 λ n-m g 1 A(m)=i ∀i G i (n) = 1 N gi(n) n m=1 λ n-m g g i (m)1 A(m)=i ∀i G max (n) = max i G i (n) Q i (n) = β( Gi(n) Gmax(n) -1) ln W (n) Ni(n) B i (n) = R i (n) + Q i (n) + α ln W (n) Ni(n) A(n + 1) = arg max i (B i (n)) end end
Algorithm 3: DQoC-A policy.

V. EXPERIMENT SETUP

Comparing the proposed algorithms against the state-ofthe-art method with random frequency allocation in real conditions of operation, is the main target of the experiment. This is done by setting the LoRaWAN configuration as ACCEPTED MANUSCRIPT / CLEAN COPY presented in Table IV, but it could be done with any other IoT standard, as soon as it uses acknowledged messaging. A Tektelic KONA Macro Gateway is used whose antenna is fixed on the roof of the university building [START_REF]Tektelic KONA Macro IoT Gateway[END_REF], as shown in Figure 3a and 3b. While the end node is implemented using a Pycom card, i.e. programmed in the MicroPython language, composed of an Expansion Board and a LoPy 4 module which can support LoRa wireless connectivity [30], as shown in Figure 3c. First, the network is joined with an Over-The-Air-Activation (OTAA). Then, the proposed algorithms are executed sequentially at each step index n inside the Pycom node. An uplink packet is transmitted at the channel i which is chosen by the algorithm, then the node waits about 10 seconds before sending the next packet to respect the duty cycle. By default, the gateway attempts to send one acknowledgment at the same channel i and center frequency f i as the message transmitted. Subsequently, the node writes the information of the last received downlink packet (packet number, ESP, etc.) to the payload of the next uplink packet. In this experiment, there is no retransmission attempt if the node does not receive the acknowledgment packet. For analyzing purposes only in this experiment, a desktop computer that runs a Python program is used as an Application Server (AS) which is connected with the LoRa Network Server (LNS) through the internet. This computer receives data from the LNS, as well as LoRa metadata with all parameters of the LoRaWAN transmission (f i , SF, W , RSSI, SNR, etc.). Those data are analyzed as detailed in the following sections. Moreover, they are provided to the research community on this online repository [START_REF]Measurement Data[END_REF].

VI. MEASUREMENT RESULTS

The scope of this section is to compare the aforementioned learning policies against the state-of-the-art ones with random frequency allocation that is considered as the reference. For emulating the state-of-the-art frequency allocation, a uniform Round-Robin algorithm is executed that simply transmits the packets sequentially at each frequency band f i across the packet index n. Furthermore, the experiments are performed in two different environments as detailed in the following subsections.

A. Scenario 1: Stationary IoT node

The first experiment is carried out by placing the end node in a fixed position without moving it to have stationary channel conditions. Hence, the CSI shapes are almost identical across the whole experiment duration of ≈ 8.8 hours and 800 steps (each algorithm transmits 800 packets), as shown by the received power level in Figure 4. Each CSI shape is acquired by averaging the ESP values at each frequency band f i independently every 200 steps. Moreover, the frequency selectivity of this CSI is clear, particularly at 867.3 MHz with a deep fade of more than 10 dB depth. These unequal channel qualities across the frequency bands f i could be exploited using the proposed algorithm QoC-A.

As depicted in Figure 5, the performance of UCB (α = 0.6), and QoC-A (α = 0.6 and β = 0.2), i.e. with ESP in the linear scale as the quality observation g i (n) that is shown in Algorithm 2, are compared against the uniform frequency allocation. As promised in the previous sections, all the learning algorithms outperform the uniform frequency allocation. On the other hand, the final average reward obtained using the QoC-A policy outperforms the UCB policy, as manifested in Figure 5a. Accordingly as shown in Figure 5b, the cumulative regret obtained for all the methods preserve the same performance rank over the whole packet index n with final total lost packets of 32, 39 and 132, while using the proposed algorithm QoC-A, the classical UCB, and ACCEPTED MANUSCRIPT / CLEAN COPY the uniform frequency allocation, respectively.

As shown in Table V, QoC-A policy outperforms all the other algorithms by a total number of successfully transmitted packets of 768 over 800, which is actually 4.1 times fewer packet losses than the uniform frequency allocation. This indicates that the proposed policy QoC-A is exploiting properly the channel quality to converge faster. Hence, it does not need to lose some time to acquire this knowledge before learning actually ends. For analyzing the behavior of MAB learning policies in a non-stationary scenario with an abrupt changing environment, the end node is moved during the experiment across three different positions to have unconstant channel conditions. As shown in Figure 6, the CSI shapes are different across the whole experiment duration of ≈ 6.6 hours and 600 steps (each algorithm transmits 600 packets). Again, each CSI shape is estimated by averaging the ESP values every 200 steps at each frequency band f i independently. Although all the locations are indoor, nevertheless, a progressive reduction is observed in the received power across locations 1 to 3. This reduction is reasonable as the end node goes deeper inside the building from location 1, i.e. behind the window as shown in Figure 3c, to location 3. Moreover, the CSI shape which is represented in location 1 shows fades of ≈5 dB, especially at 867.1 MHz and 868.5 MHz, while the best channel quality is obtained at 867.9 MHz. The opposite behavior is obvious in the CSI shapes of locations 2 and 3 whose best channel conditions are almost around 868.1 MHz, 868.3 MHz and 868.5 MHz. While they have degradation in the channel quality at 867.9 MHz, contrary to the CSI of location 1. These abrupt changes in the channel qualities from one location to another could be learned using the proposed algorithm

In this non-stationary environment, identifying the abrupt change in the reward distribution with reduced delay should be the ability of an optimal policy. As shown in Figure 7, the performance of UCB (α = 0.6), QoC-A (α = 0.6 and β = 0.2) and DQoC-A (α = 0.6 , β = 0.2, λ = 0.98 and λ g = 0.90) are compared against the naive frequency allocation. For both the QoC-A and DQoC-A algorithms, the linear scale of the ESP value is utilized as the quality observation g i (n). Moreover, the discount factor λ is equal to 0.98 in the DQoC-A policy, while λ g is set to 0.90 to acquire more rapidly the most recent ESP values, which follows a log-normal distribution from the channel shadowing when the end node moves and subsequently to converge faster. Motions of the end node are represented by the two breakpoints at step index n = 200 and n = 400 in which an abrupt change in the reward distribution is indicated. Before the first breakpoint (at n = 200), the evolution of the cumulative regret is almost flat using any algorithm. This is a reasonable behavior as most of the frequency bands f i at location 1 have relatively high ESP values and low packet losses. While after the first breakpoint (at n = 200), DQoC-A achieves significantly lower regret ACCEPTED MANUSCRIPT / CLEAN COPY and higher average reward than QoC-A and UCB policy in this non-stationary environment.

As shown in Table VI, DQoC-A policy outperforms all the other algorithms by a total number of successfully transmitted packets of 520 over 600, which is 2.4 times fewer packet losses than the uniform frequency allocation. This is plausible due to the inclusion of the discount factors (λ and λ g ) in the DQoC-A calculation, so it wastes significantly less time than QoC-A to identify an abrupt change (at n = 200 or n = 400) in the channel conditions. While the UCB and QoC-A are prevented to adapt quickly to changes as the old rewards have a higher influence on them. In other words, all the learning algorithms converge to the optimal mean reward in the long run, but DQoC-A policy benefits from less dependency on past observations.

VII. ADDITIONAL REMARKS ON THE ALGORITHMS' CONFIGURATIONS

The aforementioned results confirm the feasibility of utilizing the proposed policies to achieve lower packet losses in different scenarios. However, the parameters of all the proposed learning algorithms should be adjusted based on the environment's conditions. Thus, the exploration factor α is chosen depending on the channel conditions in terms of channel qualities or presence of interference signals [START_REF] Melián-Gutierrez | Hybrid UCB-HMM: A Machine Learning Strategy for Cognitive Radio in HF Band[END_REF]. Furthermore, the influence of the optimal choice of α is higher as the number K of channels increases, and less as it decreases. In the case of a small number of arms, choosing the value of the exploration factor α does not influence the policy performance much. In the opposite case, if the number of arms to explore is large, the choice of this factor will have a greater influence. If, for example, the chosen alpha parameter is from the optimal value for a large number of arms to be explored, significant degradation in performances may be observed. Hence, the algorithm will then have either a tendency either to over-explore or to over-exploit.

On the other hand, the discount factors (λ and λ g ) values should be adjusted based on the requirements of the potential application. Thus, they will regulate properly the amount of dependency on the old observations to track an abrupt change in the reward distribution. For example, if an IoT node sends one packet every a fixed short time, therefore, the discount factors in the DQoC-A algorithm should be close to one to benefit also from the older observations as the environment is stationary over such a short horizon of time, and vice versa.

VIII. CONCLUSION

This article introduces a decentralized learning technique to mitigate the channel impairments in the IoT signal propagation. Thus, the proposed QoC-A policy could learn a proper frequency allocation based on the channel quality, i.e. ESP, as an extra observation to avert using the channels whose quality is poor. Besides, another DQoC-A policy is proposed to adapt rapidly to any change in the channels' conditions, as a result of the IoT node motion for example. To ACCEPTED MANUSCRIPT / CLEAN COPY demonstrate the low complexity of these proposed algorithms and the feasibility of implementing them on the IoT device side, at a very low cost of implementation and no protocol overhead, a real experiment campaign is carried out in the city of Rennes. Consequently, the results show that QoC-A has a more optimized and accelerated learning process than the classical UCB policy, and then it has lower packet losses at the end of the process. On the other hand, DQoC-A policy converges faster than QoC-A policy in the non-stationary scenario, thanks to the discount factor in DQoC-A algorithm which decreases the dependency on the old observations gradually.

For future work, these proposed reinforcement algorithms could be implemented to decrease the packet losses in the potential IoT applications. Thus, the configurations of the implemented policy should be adjusted based on the given conditions. It would also be interesting to conduct long-term evaluations of the behavior of the proposed algorithms with new practical measurements. Using a greater number of nodes in more conducted experiments, the feasibility of using these learning algorithms in highly interfering scenarios could be investigated. Over and above, we are currently conducting measurements to calculate the amount of energy consumed by an IoT device with and without executing the proposed algorithms.

Fig. 1 :

 1 Fig. 1: An envisioned IoT network with the potential factors of the packet losses.

Fig. 2 :

 2 Fig.2: An end node sends a packet with the acknowledged messaging mode, whereas the reward value depends on the presence|absence of the ACK packet.

  (a) Position of the gateway monopole antenna fixed on the roof of the IETR lab. (b) The gateway connected to the antenna cable.(c) The packaged Pycom device is fixed on a rod and connected to a battery inside a building.

Fig. 3 :

 3 Fig. 3: Views from the end node and gateway sites.

867. 1 Fig. 4 :

 14 Fig. 4: Stability of the CSI shape throughout the 800 steps (one CSI every 200 steps) in the stationary scenario.

  Cumulative regret over 800 steps.

Fig. 5 :

 5 Fig. 5: Result of the algorithms against the uniform frequency allocation (non-learning) in the stationary scenario.

Fig. 6 :

 6 Fig. 6: Evolution of the CSI shape throughout the 600 steps (one CSI every 200 steps) in the non-stationary scenario.

  Packet (a) Average reward over 600 steps. Packet (b) Cumulative regret over 600 steps.

Fig. 7 :

 7 Fig. 7: Result of the algorithms against the uniform frequency allocation (non-learning) in the non-stationary scenario.

TABLE I :

 I Main distinctive characteristics of different solutions for LoRa

	Algorithm	Decentralized	No synchronization among the end nodes	Utilizing the channel quality information
	DyLoRa [11]
	CARA [12]
	UCB [13]
	QoC-A & DQoC-A

TABLE II

 II

		: ACRONYMS
	ACK	Acknowledgment
	ADR	Adaptive Data Rate
	AI	Artificial Intelligence
	AS	Application Server
	CARA	Collision Avoidance Resource Allocation
	CSI	Channel State Information
	CSS	Chirp Spread Spectrum
	DQoC-A	Discounted Quality of Channel Allocation
	DyLoRa	Dynamic LoRa
	ESP	Effective Signal Power
	IoT	Internet of Things
	ISM	Industrial, Scientific and Medical
	LPWAN	Low Power Wide Area Networks
	LoRaWAN	Long Range Wide Area Network
	LNS	LoRa Network Server
	MAB	Multi-Armed Bandit
	OSA	Opportunistic Spectrum Access
	OTAA	Over-The-Air-Activation
	PDR	Packet Delivery Rate
	QoC-A	Quality of Channel Allocation
	RF	Radio Frequency
	RSSI	Received Signal Strength Indicator
	SNR	Signal-to-Noise Ratio
	SF	Spreading Factor
	UCB	Upper Confidence Bounds

TABLE III :

 III Comparison of the implemented policies

	Algorithm	Node mobility condition	Complexity	Preconfigured parameter	Online parameter
	UCB	Stationary	O(K)	K, [α]	Binary reward
	QoC-A	Stationary	O(K)	K, [α, β]	Binary reward + ESP
	DQoC-A	Stationary | Non-stationary	O(K)

K, [α, β, λ, λg] Binary reward + ESP

TABLE IV :

 IV LoRaWAN configuration

	LoRaWAN Parameter	Value
	Modulation technique	LoRa (based on CSS)
	SF	7
	Coding rate	4/5
	Bandwidth W	125 kHz
	Transmission power	14 dBm
	Number of channels K	8
	Center frequency f

i {867.1, 867.3, 867.5, 867.7, 867.9, 868.1, 868.3, 868.5} MHz

TABLE V :

 V Number of successfully transmitted and lost packets in the stationary scenario

	Algorithm	Succeed	Lost	Success rate
	Uniform	668	132	83.5%
	UCB	761	39	95.1%
	QoC-A	768	32	96.0%
	B. Scenario 2: Non-Stationary IoT node

TABLE VI :

 VI Number of successfully transmitted and lost packets in the non-stationary scenario

	Algorithm	Succeed	Lost	Success rate
	Uniform	405	195	67.5%
	UCB	487	113	81.2%
	QoC-A	497	103	82.8%
	DQoC-A	520	80	86.7%

ACKNOWLEDGMENT

The authors would like to thank Jean Franc ¸ois Legendre from Gwagenn company for borrowing from him the gateway [33].


Célia Moustiès

Claire Bourlieu-Lacanal

Bruno Barea

Adrien Servent

Pascaline Alter

Marc Lebrun

Youna Morgane Hémery

Arnaud Laillou

Sylvie Avallone
email: sylvie.avallone@supagro.fr

Célia Moustiés

Claire Bourlieu

Youna Hemery

Lipid Composition and State of Oxidation of Fortified Infant Flours in Low-Income Countries Are Not Optimal and Strongly Affected by the Time of Storage

Keywords: lipid oxidation, vitamins, mycotoxins, packaging, volatile compounds. Graphical gas chromatography, DAD: diode array detector, FLUO: fluorometric detector, HPLC: high performance liquid chromatography, PCA: principal component analysis, PV: peroxide value, UHPLC-MS: ultra-high performance liquid chromatographymass spectrometer alpha-linolenic acid, Alu / PE: aluminium / polyethylene, aw mineral and vitamin complex, DAD: diode array detector, DHA: docosahexaenoic acid, EU: European Union, GC: gas chromatography, HPLC: high performance liquid chromatography, FA: fatty acid, medium chain fatty acid, MSMS: tandem mass spectrometry, PCA, Principal Component Analysis, OTR: oxygen transmission rate, RE: retinol equivalent, ROS: reactive oxygen species, UV: ultra violet, WVTR: water vapor transmission rate

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

ABSTRACT

Food fortification is widely used to address the public health problem of nutrient deficiencies.

Our purpose was to assess the lipid profile and nutritional quality of 13 fortified infant flours (FI) collected "in the field" in Africa and Asia after different periods of storage. The lipid content, fatty acid profiles, lipophilic vitamin content, lipid oxidation state (peroxide values, secondary oxidation products) were determined. To complete this panorama, mycotoxins in FI and packaging materials were characterized. The lipid content averaged 9.1 ± 3.5 g/100 g. Fatty acid profiles were dominated by linoleic (43.3 ± 8.8%), oleic (29.5 ± 7.4%) and palmitic acid (17.8 ± 6.7%) and resulted in average ω6/ω3 ratio of 12.2 ± 5.9 but with high values for some FI (maximal at 31.7). Very high overages in vitamins A, D and E were observed in FI stored for short periods (1 -6 months) whereas FI stored for more than 12 months had insufficient vitamin content. Lipid oxidation was acceptable but for six FI presenting excessive peroxide values. Most products were contaminated by low amounts of mycotoxins but only two FI did not abide by the regulation. A strong correlation between peroxide values, hexanal content and time of storage was observed.

Practical applications:

The expiration dates for fortified infant flours commercialized in low income countries should be shortened from 36 to 12 months so to guarantee the nutritional quality of these functional foods and abide by the fortified infant flour legislation. Indeed, FI quality significantly decreased over time of storage. The use of very barrier packaging materials must be generalized, although it is a necessary criterion but not sufficient to ensure the long term stability of FI. Special attention should be given to reduce lipophilic vitamin overages and improve their lipid profile, especially ω6/ω3 ratio, which has to be lower than 15.

INTRODUCTION

Nutrient deficiencies still affect two billion people worldwide, due to health issues, inappropriate diet, poverty, poor hygiene and sanitation [START_REF] Hayashi | Levels and trends in child malnutrition: key findings of the 2018 Edition of the Joint Child Malnutrition Estimates Report[END_REF] . In 2016, 155 million preschool-age children were still affected by stunting [START_REF] Hayashi | Levels and trends in child malnutrition: key findings of the 2018 Edition of the Joint Child Malnutrition Estimates Report[END_REF] . In Africa and South-East Asia, the diet of low-income populations is mainly based on starchy products and do not include enough nutrient-rich foods (i.e. fruits, vegetables, beans or animal products). These diets are lacking in essential micronutrients and in certain macronutrients, such as essential lipids, and children are particularly concerned by this nutritional issue. Lipids play different important roles, in particular energetic, structural and transport [START_REF] Innis | [END_REF] . Moreover, adequate intakes in essential lipids are very important for visual acuity, brain development and lipid metabolism [START_REF] Innis | [END_REF][3][4][5] .

During the 1 000-days between a woman's pregnancy and her child's 2 nd birthday, adequate micronutrient intakes are essential for child's cognitive and physical development. Indeed, during fetus and infant development, inadequate food intake strongly impacts the nutritional status, resulting in stunting with cognitive consequences and increased mortality [6] . As micronutrient deficiencies are public health issues, governments and international organizations have, for decades, implemented three main strategies to solve the problems: diet diversification, supplementation and food fortification [7] . Diet diversification has the advantages to stimulate the local economy by generating incomes for small farmers and to promote the consumption of diversified food with complementary nutritional profiles. But, in some contexts, the cost of a diversified diet seems too high and not reachable for people with low incomes [8] . Supplementation has the advantage of being very specific in the intervention and in terms of dose-adjustment, but expensive and with risk of toxicity, due to low compliance and selfprescription by users [9] . The use of food fortification is an alternative strategy which is considered as the most cost effective to eliminate micronutrient malnutrition [7] . The biological efficacy of fortified food products has been demonstrated in clinical trials. Under controlled environments, the conditions are perfect and the results are encouraging, but they do not reflect the "real food system" in terms of conditions of storage in the supply chain of southern countries and practices at home. Fortified infant flours (FI), mostly cereal-based, have been designed to fulfill the needs of infants and preschool children. FI are used in complement to breastfeeding from the age of six months, under the form of gruel or porridge, consumed on a daily basis. Most FI have adjusted lipid profile, and can be enriched in polyunsaturated fatty acids (PUFA). Enrichment in essential fatty acids (FA) -i.e. linoleic C18:2 (ω6 family precursor) and linolenic C18:3 (ω3 family precursor) FA -and frequently in long chain PUFA that are important for brain and vision development, such as docosahexaenoic acid (DHA, C22:6, ω3 family) [4,10] . Indeed, lipids play several important functions for young children, as they supply most of the calories necessary for growth, contribute to the development of cerebral functions, and to lipophilic vitamin transport [START_REF] Innis | [END_REF] . More specifically, DHA contributes to visual acuity and brain membrane accumulation during the child's first two years of life. Unbalanced ω6/ω3 lipid input during infant growth do not support as satisfactorily infant development than balanced ones [4] .

A previous study conducted in low-income countries, has reported that an adequate consumption of well-formulated fortified cereal-based complementary foods, has a positive impact on the nutritional status of young children [11] . The nutritional quality of many complementary foods sold in African and south east Asian countries have been assessed [12][13][14] , but these studies focused either on the macronutrients, minerals and trace elements, or on the anti-nutrients, and none focused on lipid profile nor reported lipophilic vitamin contents.

Moreover, unsaturated FA and lipophilic vitamins present poor chemical stability during food production, transportation and storage [15] . Vitamin A can be rapidly degraded, especially in food products stored in non-optimal conditions. High losses in Vitamin A have been reported in products stored at moderate temperatures (~40 °C) and when the packaging doesn't display good oxygen and water vapor barrier properties [16,17] . Very recently, more than half of vitamin A fortified flours, used in 20 national fortification programs, did not meet the fortification standards [18] . Performance data on fortification interventions are often missing and regular assessment of fortification programs in "field conditions" are needed [19,20] .

The aim of the present work was to characterize 13 FI, sold and consumed on a daily basis, in four countries in Africa and Asia. FI were collected "in the field" after different storage periods.

Lipid composition (i.e. total and essential fatty acids, lipophilic vitamins), lipid oxidation (peroxide and acid values, volatile compounds), mycotoxins contents and barrier properties of packaging materials were evaluated.

MATERIALS AND METHODS

Collection and Storage of Fortified Infant Flours

Thirteen FI consumed on a daily basis were collected in pharmacies, groceries and markets in four countries in Africa and South east Asia (Table 1). The products were sampled after being stored in "field conditions" in the real supply chain from 1 to 19 months. Storage time is thus the period of time elapsing from the manufacture to the collection (purchase). Products were then shipped to our laboratory (Montpellier, France). The products were produced either locally or imported.

In order to obtain a representative sample, several unit-doses were mixed (achieved average mass ~ 105 -150 g). At opening, products were immediately analyzed for vitamin profiles, dry matter and water activity. The rest of the samples was vacuum-packed in distinct bags and frozen at -80 °C for further analyses (mycotoxins, total and neutral lipids extraction and characterization, volatile compounds).

Each product was labelled with a code FI_X, where X corresponds to a specific brand. The characteristics of the products in terms of formulation, packaging and duration of storage since production date are reported in Table 1.

For two FI brands (FI_2 and FI_3), two distinct batches were characterized. These four products were tested rapidly at reception (i.e. after 1 or 2 month "in field" storage) or stored for two more months in the laboratory at ambient temperature (̴ 20 °C) and again characterized. For these two brands, the products were labelled as follows FI_X_LY_Z to indicate that the FI was produced by a brand (X) with a number of batch (LY) and a specific duration of storage in month (Z).

Products that were stored for two more months under controlled conditions in the laboratory are noted with an asterisk (*): FI_2_L2_3*, FI_2_L1_4*, FI_3_L2_3*, FI_3_L1_4*.

In total thirteen brands of FI were purchased in local groceries and markets in Vietnam, Burkina Faso, Madagascar and Benin. Their production place, time of storage, packaging and composition are detailed in Table 1. The collected products can be considered as representative of the ratio (imported/local) of local products in the supply chain. This ratio, imported/local, was of 3/13. The three imported products had all been produced in the European Union.

FI were formulated with five to 13 ingredients and limited amounts of additives (except in FI_6). FI were based on cereals, either local ones such as millet (Pennisetum glaucum), sorghum (Sorghum bicolor) in African FI, but also wheat (Triticum) in three products. In most FI, lipids were mainly brought by peanuts (Arachis hypogaea), some oleo-proteaginous such as soy (Glycine max) (present in 8 FI) or sesame (Sesamum indicum) and milk. 38% of FI included added "fats" with no other precision. 85% of the formulas included sugar and 23% added salt.

Lipophilic vitamins were brought under the form of mineral and vitamin complex (CMV).

Materials and Chemicals

Solvents (ethanol, diethylic oxide, hexane, chloroform, methanol, acetone, tertbutylethylether), reagents (potassium hydroxide, phenolphatlein, methylate sodium, hydrochloric methanol, potassium iodide, thiodene, sodium thiosulfate) were obtained from Sigma-Aldrich (Saint Quentin Fallavier, France). FAMEs external calibration standards (Mixture ME 100) were obtained from Larodan (Sweden). HPLC standards (α-tocopherol, δ-tocopherol, 𝛾𝛾-tocopherol, 𝛽𝛽-tocopherol, retinol palmitate, retinol acetate, vitamin D2 and D3) were obtained from Sigma-Aldrich (Saint Quentin Fallavier, France) and Biopharm Rhône Ltd (Glasgow, UK). The polytetrafluoroethylene (PTFE) membranes were obtained from Sartorius (Palaiseau, France).

The water used in all the experiments was mQ water (HPLC grade).

Dry Matter and Water Activity Determination

The dry matter (DM) contents were determined in triplicate by drying 3 g of the samples at 105 °C in Memmert heat chamber (modell 100 Schwabach, Germany) until constant weight following method 44-15A [START_REF]Anonymous, AACC Method 44-15A[END_REF] . Samples and their dehydrated residues were precisely weighted on a Mettler AE166 balance (Viroflay, France). Water activity (aw) was determined at 25 °C on approximately 1 g with a water activity meter 4TE AQUALAB (Hopkins, USA).

Determination of Vitamin A and D

The vitamin profiles were determined by liquid chromatography and specific detection by DAD (vitamin A and D) as previously described [START_REF] Hemery | [END_REF] . The UV detection allowed us to quantify two forms of vitamin A (acetate and palmitate) and two forms of vitamin D (cholecalciferol and ergocalciferol).

One gram of flour was mixed with 20 mL water and gently shaken for 10 min [23] . Samples were homogenized in 16 mL of ethanol/hexane (4:3, v/v) for 30 seconds at 30 000 rpm (Ultra-Turrax, Prolabo, France) and then centrifuged (30 min, 4 °C, 13 000 g) (Heraeus Multifuge X1R, Thermo FIher Scientific, Villebon sur Yvette, France). Afterward, the upper layer was transferred into amber glass tubes and dried with a Genevac during 25 min at 30 °C (EZ-2 series, Genevac LTD, Sp Scientific, England). The dried residues were dissolved in 2 mL of acetone, filtered at 0.45 µm PTFE minisart SRP4 membrane (Sartorius) and analyzed by liquid chromatography (Agilent System 1200 series, Massy, France). The column was a polymeric C30 (4.6 mm i.d. × 250 mm, 5 μm particle size, YMC, Inc Wilmington NC) and the injection volume was 20 µL. The mobile phase was based on the blend of two mixes at a flow rate of 1 mL/min and the temperature was 25 °C. Mix A was constituted of methanol and water, 60:40 (v/v), and mix B was constituted of methanol, methyl tert-butyl-ether and water, 28.5:67.5:4.0 (v/v/v). The gradient applied progressed from 100% to 0% (A/B) over a period of 43 min and the column was washed 5 min with ethyl acetate at the end of each run. Chromatograms were recorded with a UV-visible photodiode array detector (Agilent Technologies 1200 series) at the wavelength of maximum absorption of the vitamin A and D in the mobile phase (i.e. 325 and 265 nm respectively). External calibration was realized weekly with standard solutions of the pure chemical in acetone on the range of 0.5 to 25 mg/L. Each sample was analyzed with five repetitions. Vitamin A activity was expressed in retinol equivalents (RE) [START_REF]Conversion factors for vitamin A and carotenoids[END_REF] :

1 µg retinol equivalent = 1.146 µg retinol acetate = 1.832 µg retinol palmitate.

Determination of Vitamin E

Vitamin E was determined on the same extract that had been obtained for vitamin A and D quantification. Fluorescence was used to detect and quantify four distinct tocopherols (𝛼𝛼, 𝛽𝛽, 𝛿𝛿 and 𝛾𝛾). HPLC analysis was performed with an Agilent System 1290 series (Massy, France) equipped with a C18 column (250 mm × 4.6 mm i.d., 5 μm, HALO®-5 column, AMT, Wilmington, Delaware, USA) and a fluorescence detector. The mobile phase consisted of ethanol/methanol (40:60, v/v) in isocratic conditions. The temperature of the column was maintained at 25 °C and flow rate was 0.8 mL/min. Fluorescence detection was set at 296 nm for excitation and 330 nm for emission. The injection volume was 20 μL and the calibration curves were realized with standard solutions from 0.1 to 1.5 mg/L. Each sample were analyzed with five repetitions.

Vitamin E activity is expressed in 𝛼𝛼 -tocopherol equivalent (𝛼𝛼-TE) in mg for 100 g [START_REF] Shils | Modern nutrition in health and disease[END_REF] and calculated as follow:

𝛼𝛼 -𝑇𝑇𝑇𝑇 = (1 × α -T) + (0.7 × α -TA) + (0.4 × β -T) + (0.2 × γ -T) + (0.1 × δ -T) (1)
With 𝛼𝛼 -TE: tocopherol equivalent, T: tocopherol, TA: tocopherol acetate, α: 𝛼𝛼-tocopherol, β : β-tocopherol, 𝛾𝛾: γ-tocopherol, 𝛿𝛿: δ-tocopherol.

Determination of Lipid Content and Fatty Acid composition

The lipid content was determined gravimetrically in triplicate [START_REF] Folch | [END_REF] and each extract was then analyzed in duplicate. Briefly, lipids were extracted from thoroughly homogenized food samples using chloroform/methanol (2:1, v/v). 15 g of sample was rehydrated during 10 min in distilled water and, thereafter, dispersed in a sample/solvent ratio of 1:37 (w/v) for 1 min at 10 000 rpm (Ultra-Turrax T8, IKA Labortechnick, Staufen, Germany). NaCl 0.73% (w/v) was added to the organic phase with thorough shaking. After dephasing, the lower phase was filtered and retrieved. Then, the sample was washed again with NaCl 0.58% (w/v). Once clear, the organic layer was filtered and collected. Solvent was evaporated with a rotavapor at 40 °C until constant weight and residual lipids were precisely weighted (Laborota 400-efficient, Heidolph, Schawabach, Germany).

Fatty acid methyl esters (FAMEs) were obtained by methylation of lipids (~ 200 mg) with 3 mL of sodium methylate for 10 min at 65 °C in heated mantle with saponification sticks under reflux. Then, 3 mL of chloride methanol were added and samples were heated again for 10 min at 64.7 °C. FAMEs were extracted with 8 mL of hexane, washed with 10 mL of distilled water. The column temperature started from 150 °C, then reached 150 °C to 225 °C with a rise of 5 °C/min and was kept at 225 °C during 10 minutes. These chromatographic conditions allowed a correct and rapid separation of all FAMEs from C10:0 to C24:1. FAMEs were identified using as external standards a mixture of methyl esters (Mixture ME 100, Larodan, Sweden). The injector and detector temperatures were 250 °C and 270 °C respectively. FA contents were expressed in g per 100 g of fresh product FA contents were expressed in g per 100 g of fresh product, taking into account the total lipid content determined by Folch extraction.

Peroxide Value Determination

The peroxide values (PV) were determined by iodometric titration [START_REF]Anonymous, Official Methods and Recommended Practices of the American Oil Chemists'Society: Physical and Chemical Characteristics of Oil, Fats and Waxes[END_REF] with slight modifications.

For each FI, average values were calculated from six determinations (three extractions analyzed in duplicate). Approximately 200 mg of oil was dissolved in 1 mL of chloroform. After addition of 1.5 mL of acetic acid and 0.1 mL of saturated potassium iodide, the solution was shaken for 1 min and placed 5 min in the dark. After addition of 7.5 mL of distilled water and iodine indicator, the solution was titrated with Na2S2O3 0.002N until the color disappeared. A blank determination was made, and the PV was calculated using the following equation:

𝑃𝑃𝑃𝑃 = (𝑃𝑃𝑉𝑉 -𝑃𝑃𝑉𝑉) × 𝑁𝑁 × 100 𝑊𝑊 (2)
With PV: mEqO2/kg of lipid, Vs: volume of Na2S2O3 used in sample (mL), Vb: volume of Na2S2O3 used in the blank sample (mL), N: normality of Na2S2O3 (mEq/ mL), and W: weight of lipids (g).

Acid Value Determination

The acid values (AV) were determined by titrimetry [28] and average values were obtained from six determinations (three extractions analyzed in duplicate). A precise quantity of lipid (~200 mg) were dissolved in 0.4 mL ethanol/diethyl oxide (50:50, v/v). After addition of phenolphthalein, the solution was titrated with KOH 0.01N until the pink color persisted for at least 10 seconds. A blank determination was made, and the AV was expressed in oleic acid equivalent and calculated using the following equation:

𝐴𝐴𝑃𝑃 = (𝑃𝑃𝑉𝑉 -𝑃𝑃𝑉𝑉) × 𝑁𝑁 × 282.46 10×𝑊𝑊 (3)
With AV: % lipid (acid oleic eq%), Vs: volume of KOH used in sample (mL), Vb: volume of KOH used in the blank sample (mL), N: normality of KOH, 282.46: molecular weight of oleic acid (g/mol), and W: weight of lipids (g).

Volatile Compound Determination

For each sample, the volatile compounds were extracted in triplicate using headspace solidphase microextraction gaz chromatography [START_REF] Lebrun | [END_REF] . Extraction and analysis were carried out using divinylbenzene/carboxen/polydimethylsiloxane fiber (Supelco, Bellefonte, Pennsylvania, USA), and a tandem gas chromatograph 6890 / MSD 5973 (Agilent Technologies, Palo Alto, USA) / Gerstel Multipurpose Sample MPS-2. Sample (1 g) was placed in headspace vials (10 mL) with addition of benzyl butyrate (5 µL/100 mL) as internal standard for semi Peak identification was realized comparing mass spectra with those of the NIST 14 database.

Co-injection of alkanes from C8 to C20 (Sigma-Aldrich) was used for Kovats retention indice calculations and their comparison with the literature (flavornet and pherobase websites and NIST). The contents of the volatile compounds were expressed in mg equivalent of internal standard (i.e. benzyl butyrate) as previously described [30] .

Determination of Mycotoxins

Five grams of sample was homogenized with 20 mL of acetonitrile/water/ acetic acid (50:50:1, v/v/v). After 10 min of gentle stirring, salts were added as follow: MgSO4 (4 g), NaCl (1 g), SCTD (1 g), SCDS (0.5 g). Samples were again stirred for 10 min and centrifuged (3000 rpm, 10 min). A mix of internal standard was added to 200 µl of supernatant and the overall extract was evaporated under nitrogen at 40 °C. Residue was diluted with 1 mL water/acetic acid 0.5%.

The extract was filtered with 0.45 µm PTFE minisart SRP4 membrane (Sartorius). The extracts were analyzed by ultra-high performance liquid chromatography [31] and injection volume was 20 µL. The pump model was a LC 20 AD Shimadzu (Kyoto, Japan) with an autosampler model: SIL 20 A XR Shimadzu and a column Kinetex 2.6 µm XB-C18 100A (50 mm × 2.1 mm, Phenomenex Inc., California, USA). The oven temperature was 50 °C. The mobile phase A was water/acetic acid 0.5%, and mix B was isopropanol/acetic acid 0.5% at a flow rate of 0.4 mL/min. The elution gradient started from 10% of eluent B, to 55% in 1.5 min, then 85% at 2 min and decreased to 80% in 0.5 min and a stabilization step of 2% during seven min. The tandem mass spectrometry (MSMS) conditions with system LCMS 8040 Shimadzu (Kyoto, Japan) were ionization ESI (positive and negative), MRM mode, ion source temperature (for desolvation line) was set at 250 °C and 400 °C for heater block, gases nebulization at 3 L/min and gases drying at 15 L/min. Standard calibration curves were established with several mycotoxins (aflatoxins, ochratoxins, fumonisins, trichotecenes, zearalenon, beauvericins) (Biopharm Rhône Ltd, Glasgow, UK).

The contents were expressed in µg/100 g of FI and analyses were performed in triplicate.

Packaging Characterization

Packaging was characterized by Fourier Transform Infrared Spectroscopy (Table 1). Spectra were recorded using a Nexus 5700 spectrometer (Thermo Electron Corp., Massachusetts, USA) equipped with the diamond ATR Smart Orbit Accessory inserted. Spectral data were accumulated from 128 scans with a resolution of 4 cm -1 in the range 800-4000 cm -1 . All spectra pretreatments were performed using Omnic v7.3 and TQ Analyst v7.3 softwares (Thermo Electron Corp., Massachusetts, USA). Oxygen and water permeabilities were obtained from the literature for standard polymers [START_REF] Massey | Permeability properties of plastics and elastomers: a guide to packaging and barrier materials[END_REF] . Oxygen transmission rate (OTR) represents the quantity of O2 which goes through the packaging per day and water vapor transmission rate (WVTR) represents the quantity of H2O which diffuses through the packaging per day. OTR and WVTR were calculated according to the packaging surface, the permeability coefficient of the material and the time of storage of the product [START_REF] Massey | Permeability properties of plastics and elastomers: a guide to packaging and barrier materials[END_REF] .

Statistical Analysis

If not stated otherwise, all characterizations were conducted at least in triplicate. Analysis of variance (one-way ANOVA), followed by LSD post hoc tests were performed using Statgraphics plus 5.1 (Virginia, USA) to identify significant differences between samples.

Differences were considered statistically significant for p value <0.05. Still using the same software, correlations between the biochemical composition, time of storages, oxidation markers, oxygen and water transfer rates were evaluated using Principal Component Analysis (PCA).

RESULTS

Dry Matter and Water Activity.

The water contents of the FI ranged from 1.78 ± 0.02% to 6.45 ± 0.30% and aw from 0.06 ± 0.01 to 0.41 ± 0.01 (Table 2).

Lipid Content and Fatty Acid Profiles

A high heterogeneity was observed among FI in terms of lipid contents which averaged 9.1 ± 3.5 g/100 g but ranged from 1.5 to 15.1 g/ 100 g (Table 2). The FI produced in Europe had a lower lipid content in comparison to the locally produced FI (Average 2.9 ± 1.8 versus 10.3 ± 2.6 g/100 g respectively). European Union directive [START_REF]Commission Directive 2006/125/CE on processed cereal-based foods and baby foods for infants and young children[END_REF] requires a maximal lipid content of 3.3 g per 100 Kcal. For the imported products, the highest lipid content was 5.0 ± 1.4 g/100 g corresponding to 1.3 ± 0.4 g/100 Kcal (caloric equivalent: 1 g of lipid = 9 Kcal). Despite this heterogeneity, all the FI were in agreement with the European legislation for the maximal lipid contents.

The FA profiles in the FI were characterized by GC (Figure 1 and Table 2). The main FA were, by decreasing order, linoleic acid C18:2 n-6, oleic acid C18:1 n-9 and palmitic acid C16:0. Their average percentages were respectively 43.3 ± 8.8%, 29.5 ± 7.4% and 17.8 ± 6.7% of total lipids. FI contained on average 22.0 ± 7.3% saturated FA (SFA) with important discrepancies between FI since the lowest value for SFA was 15.7% (FI_3) and highest reached 40.9% (FI_6). Most FI contained a high amount of PUFA (47.8 ± 9.1%), again with discrepancies (MIN= 18.7%, MAX= 60.6%). The ω6/ω3 ratios of FI averaged 12.2 ± 5.9 and were globally in agreement with the international recommendations which indicates an optimal ratio range between five and 15 [3] . However, it is important to underline that for two FI (FI_6 and FI_7), the ratios exceeded largely these recommendations (21.2 ± 3.8 and 31.7 ± 1.0 respectively).

Two FI (FI_2 and FI_3) were analyzed after being stored over two months in the laboratory.

The main fatty acids (i.e. C16:0, C18:1 n-9, C18:2 n-6) did not evolve significantly with the time of storage over this limited period of time (Table S1).

Lipophilic Vitamin Profiles

The lipophilic vitamin contents in FI are displayed according to their time of storage (Figure 2). Most of the FI were not consistent with the European directive [START_REF]Commission Directive 2006/125/CE on processed cereal-based foods and baby foods for infants and young children[END_REF] . For all lipophilic vitamins a significant "time of storage effect" was observed whatever the FI brand or formulation: vitamin contents decreased with time of storage (p<0.001). Globally, the use of vitamin overages, that led to contents above the upper recommended limits, was far more frequent than insufficient contents. Whatever the vitamin, 13 out of 19 analyzed FI were above the upper limits and the excess reached up to 15, 35 and 10 times the recommended upper limits for vitamin A, D and E, respectively. Average amount of vitamin A for FI stored from one to six months reached 378.8 ± 88.0 µg/100 Kcal corresponding to an overage of 210% compared to the authorized upper limit and dropped down to an average value of 100.9 ± 116.6 µg/100 Kcal for FI stored for more than six months (six products). Similarly, values were quite homogeneous with important overages up to five-month-storage, for vitamin D (average value = 13.5 ± 5.2 µg/100 Kcal corresponding to an overage of 450% compared to the authorized upper limit) and for vitamin E (average value= 4.3 ± 2.7 µg/100 Kcal corresponding to an overage of 143% compared to the authorized upper limit). After five months, averaged values dropped down to 3.5 ± 6.3 µg/100 Kcal and 1.4 ± 1.5 µg/100 Kcal, for vitamin D and E respectively.

Seven out of 19 analyzed products were below the lower limits and most of them were close to the expiry date (time of storage > 12 months): three FI for vitamin A, six for vitamin D and four for vitamin E. All the imported products, i.e, FI produced in Northern countries and shipped to Africa (FI_10, FI_11, FI_12) were included in this set of seven products and had an insufficient vitamin content.

When assessing compliance with the nutritional composition indicated on product label, we observed that vitamin contents were not always detailed. Moreover, the products were most of the time not compliant with the contents indicated on the label. To be more precise, for vitamin A, six products out of 13 had a content indicated on the label and two products only were compliant with indications. Regarding vitamin D, four products out of 13 had a content indicated on the label and none was compliant with indications. Regarding vitamin E, three products out of 13 had a content indicated on the label and one product only was compliant with indications. When comparing the two products stored over two months in the laboratory at ambient temperature (̴ 20 °C), no significant difference was observed for any of the vitamins.

A short time of storage, at moderate temperature in the first months after production did not alter the vitamin profile of these fortified foods. However, it also is important to note that these products were packed with multilayer aluminum [START_REF] Moyssiadi | [END_REF] .

Acid Values and Peroxide Values

The acidity values of all the products were acceptable (average value= 0.06 ± 0.04%, range= [0.01; 0.16]%). Indeed, the values were below the maximum limit of 0.6% of total lipids as defined officially [START_REF]Anonymous, Codex Standard for Edible Fats and Oils not Covered by Individual Standards (CODEX STAN 19-1981, Rev. 2017[END_REF] (Figure 3). Regarding peroxide contents, five products did not meet the international recommendations, i.e. were above the limit of 10 meq O2 per kg of lipids [START_REF]Anonymous, Codex Standard for Edible Fats and Oils not Covered by Individual Standards (CODEX STAN 19-1981, Rev. 2017[END_REF][START_REF]Commission Regulation EEC 2568/91 on the characteristics of olive oil and olive-residue oil and on the relevant methods of analysis[END_REF] . These products were those which had been stored for the longest period (i.e. nine months and more). Peroxide contents increased significantly over the time of storage (p<0.001).

When comparing the two products stored over two months in the laboratory (FI_2 and FI_3), the time of storage significantly increased the acid and peroxide values (p<0.001), despite multilayer aluminum packaging.

Volatile Compounds

The main volatile oxidation compounds identified were saturated aldehydes and, by decreasing order, hexanal, pentanal and nonanal (Table 3). These three volatile compounds significantly increased over the time of storage of FI (p<0.001). The highest content was reached with hexanal in the product stored the longest time (1.35e -08 ± 2.19e -09 mg eq benzyl butyrate/100 g in FI_12 after a 19-month-storage). When comparing the two products stored over two months in the laboratory (FI_2, FI_3) an increase in hexanal was observed.

Determination of Mycotoxins

In our experiments, trichotecene, zearalenone, ochratoxin A, beauvericin were not detected.

Low levels of fumonisins (FB1 and FB2) and aflatoxin were detected in 14 FI and only four FI were free of mycotoxins (Table 3). Samples were considered contaminated if the mycotoxin levels exceeded the EU limit [START_REF]Commission Regulation EEC[END_REF] which corresponds to: 0.1 µg/kg for aflatoxin B1 and 200 µg/kg for fumonisins. Among the 19 analyzed products, only one product reached the limit for aflatoxin AFB1 (FI_6, 4.2 ± 0.2 µg/kg) and another for fumonisins (FI_8, FB1= 198.1 ± 3.5 µg/kg and FB2= 40.6 ± 1.1 µg/kg).

Packaging Characterization

The packaging materials used to commercialize the FI were by decreasing frequency of use: aluminum/polyethylene multilayer, polyethylene, polyethylene/polypropylene multilayer and cellophane/epoxy resin (Table 1).

OTR and WVTR were sometimes equal to zero if packaging is structured by an aluminum thin layer which is a very good barrier to oxygen and water transfer (Table 4). Such very good packaging materials were used for seven FI out of 13, particularly for FI stored over long periods of time (> 12 months, i.e. FI_10, FI_11 and FI_12).

Determinants of the Degradation of Lipids and Vitamins

The key determinants of the stability of FI were explored by a correlation approach using Principal Component Analyses (PCA) with the biochemical composition, oxidation level, OTR and WVTR. However, this first analysis was not satisfying because several variables were not well projected in two or three dimensions. It was not surprising because of the great discrepancy between the product formulations, the packaging types and conditions of storage (duration, temperature, etc…). In order to obtain a better representation of the variability of the data, OTR and WVTR data were excluded and a new PCA was realized. As expected for moisture sorption isotherm of starchy products, a positive correlation (0.78) between aw and water content was observed. As a consequence, only water content was integrated in the PCA (Figure 4).

The three components extracted explained 79% of the variability of the data set. The representation of the variables along the first component accounted for 51% of the variability of the data, the second for 18%, and the third one for 10%. Despite the design of the study, triggering high variability in FI's formulation, packaging materials and conditions of storage, the set of analyzed products presented variables very well correlated (negatively or positively) with time of storage. The contents in vitamins A and E were negatively correlated with the time of storage and the correlation was rather strong with R = 0.86 for vitamin A and R = 0.85 for vitamin E. The peroxide content and the time of storage were positively correlated (R = 0.81).

The content in volatile compounds was not correlated to the lipid content of the FI.

DISCUSSION

The composition of FI sold in low-income countries was not always adequate in terms of fatty acid composition, lipophilic vitamins content, peroxide value, and mycotoxins content. The nutritional profiles of the 13 FI greatly differed depending on the formulation and on the location of the producing unit. The FI produced in Africa and in Asia contained three times more lipids than the products from Northern countries. Such difference can be explained by the fact that children in developing countries need to cover a higher level of macronutrients with these fortified foods than children from northern countries that have access to a large choice of food to cover their needs. Indeed, the daily diet of children from southern countries is poorly diversified and can generate nutrients and caloric deficiencies.

Even if the FI lipid content greatly differs, most of them had a similar lipid profiles with three predominant fatty acids (i.e. C18:2 n-6 followed by C18:1 n-9 and C16:0). Lipids are crucial macronutrients that support most of the growth during the first six months of life and represent 40 to 60% of caloric requirements. Then, lipid need gradually decreases to ~35% of the total energy intake at 24 months. Palmitic acid, the third major FA in the fortified FI, plays an important role in infant nutrition [START_REF] Innis | [END_REF] . It is the main saturated FA in breast milk. Nevertheless, its bioavailability will depend on food matrix composition (content in Ca2 + ) and on its position on the triacylglycerol backbone. In breastmilk, palmitic acid is located in sn-2 position in the triacylglycerol, the latter position will favor its absorption and role in the bone mineralization [START_REF] Innis | [END_REF] . In vegetable oils used in our fortified FI, palmitic acid is predominantly located in external positions [START_REF] Innis | [END_REF] . We can thus suspect that the consumption of formulas with high contents of saturated fat from vegetable oils or palm olein will not favor C16:0 absorption, but can be counterbalanced by complementary breast feeding until 24 months. Globally, ω6/ω3 ratios were high in fortified FI and sometimes excessive compared to the recommended range (5 -15). Furthermore, the amounts of essential FA (linoleic acid C18:2 n-6 and α-linolenic acid C18:3 n-3) present in the FI were sometimes too high. These FA represent approximately 43.3 ± 8.8% and 2.8 ± 0.9% of the total FA in the fortified FI, while it represents only 10.5 -12.7% and 0.72 -0.95% of the total FA in human milk [3] . Linoleic acid (LA) and α-linolenic acid (ALA) intake recommendations for six-month-old-infant to five-year-oldchildren are 3.0 -4.5% and 0.5 -0.6% of energy intake respectively [START_REF]Anonymous, Interim Summary of Conclusions and Dietary Recommendations on Total Fat & Fatty Acids Summary of Total Fat and Fatty Acid Requirements for Adults, Infants (0-24 months) and Children (2-18 years[END_REF] , which corresponds to 8.1 -25.2 Kcal/day and 1.4 -3.4 Kcal/day. If the FI analyzed in our study were consumed on a daily basis, LA intakes would be higher than the nutritional recommendations [START_REF]Anonymous, Interim Summary of Conclusions and Dietary Recommendations on Total Fat & Fatty Acids Summary of Total Fat and Fatty Acid Requirements for Adults, Infants (0-24 months) and Children (2-18 years[END_REF] . For a daily consumption of 100 g flours, an average 29.7 ± 11.7 Kcal would be attributed to LA, which is higher than the recommendation, while ALA intakes would be satisfying.

Unbalanced LA intake can decrease blood DHA and cerebral lipids of infants [4] . Excessive intakes of ALA and LA can limit DHA biosynthesis by a competitive inhibition of PUFA bioconversion [3,5] . Conversely, a decrease in ALA contents in infant food complement while maintaining C18:2 n-6/C18:3 n-3 ratio below 5 could promote DHA biosynthesis. Unbalanced ω6/ω3 ratios during infancy and childhood have long term consequences on adipogenesis and lipid metabolism [3,5] .

In most FI, over fortification in vitamins was observed to ensure that vitamins would still remain in the product until its consumption whatever the storage conditions. However, consumption of large amounts of vitamin A over a long period of time can induce liver damage, bone abnormalities and vomiting [START_REF]Vitamin and mineral requirements in human nutrition[END_REF] . Furthermore, in most developing countries, children aged 6 -59 months, are supplemented twice a year with a dose of 100 000 UI. The daily intakes from diet should not exceed 900 µg which is well above the mean requirement of about 200 µg/day for infants [START_REF]Vitamin and mineral requirements in human nutrition[END_REF] . In our experiments, seven FI could be at risk of excessive contents. Risk of hypervitaminosis (D or E) were already documented [START_REF]Vitamin and mineral requirements in human nutrition[END_REF][START_REF] Masterjohn | [END_REF] . In addition, one can wonder about the nature and safety of the lipophilic vitamins overages degradation products. This aspect should be further investigated.

Globally, a strong effect of time of storage was observed on the set of FI despite heterogeneous conditions of storage in the supply-chain. This strong effect of time of storage is an important outcome of our study. For the FI produced in Europe and purchased in Africa with time of storage > 12 months, the vitamin contents were below the recommended amounts. Two hypothesis can be formulated: either the vitamins were not adequately added during the industrial production but this hypothesis is so unlikely that it can be rejected, or the temperature during shipping and storage have activated chemical degradation within the products. There was a clear trend of vitamin degradation and peroxide generation over the storage period (between one and 19 months) in the "real supply chain". The use of high barrier packaging material (ALU / PE) did not modify this trend. An overall adequacy of the FI, with acceptable nutritional profiles and low levels of degraded lipids, was observed up to 12 months, which could be a reasonable expiration date. According to the climatic conditions in tropical countries, the average temperatures are high and the temperature control within supply chain is not always possible. Indeed, vitamin A is susceptible to light and oxygen exposure while vitamin E is more stable. For instance, 90% degradation of vitamin A degradation was observed in fortified wheat flour after a three-month storage at 40 °C [16] . On the contrary, Vitamin E has been reported to be stable over 70 days even after opening a unit dose of infant milk [41] .

According to their aw, the studied FI can be altered during storage mainly by hydrolysis reactions (aw>0.25) and enzymatic activity (aw>0.35). On the contrary, very low aw (<0.2) favors very high oxidation rate so the ideal window in terms of aw is narrow probably (0.2 -0.3). In our set of FI, three products were in this window and six products had aw that exceeded 0.35.

With regards to peroxide and acidity values, they were higher when the storage duration increases, but the products were still acceptable for human consumption up to nine months of storage whatever the packaging used. The degradation reactions are rapid, especially in food matrices in powder form and at low aw.

FI have a powdery structure, with a high surface area between the product and atmosphere which makes them an ideal matrix for the propagation of lipid oxidation [42] . Moreover, reactive oxygen species (ROS) can initiate the oxidation of PUFA and, as a consequence, induce the production of hydroperoxides as well as other oxidation compounds such as aldehydes (hexanal, pentanal and propanal) [START_REF] Frankel | Lipid oxidation[END_REF] breakdown on n-6 FA (hexanal, pentanal) and n-3 FA (propanal) [START_REF] Goicoechea | [END_REF] . These molecules are good markers of infant formula oxidation and participate to the off flavor development [45] .

CONCLUSIONS

The panorama of fortified infant foods collected "in the field" after one to 19 months of storage indicated that their lipid profile and nutritional quality could be improved. Indeed, in most FI stored less than six months, lipophilic vitamin overages were observed. Long time of storages (> 12 months) have deleterious impact on the fortified food nutritional profile despite the use of protective packaging. expiration dates should be shortened in order to guarantee an optimal quality. In addition, ω6/ω3 ratios should be maintained below 15. Such recommendation could improve the biological efficacy of fortified FI and better help preventing deficiencies. In perspectives, it would be very interesting to develop a mathematical model that could predict the degradation of lipophilic vitamins in complex matrices stored under different environmental conditions. This model would help optimizing vitamin levels and limiting overages, so that the level of added vitamins is acceptable from production up to consumption of fortified food products. Such model would improve significantly the vitamin profile of fortified foods and would constitute a helpful tool to abide by the regulation and fulfill infant needs.

ACKNOWLEDGEMENTS

This work was supported by the French Ministry of Sciences and Technology (scholarship program for PhD grant) and by the French Research on Lipid & Nutrition (https://lipides-etnutrition.net/le-gln/). We warmly acknowledge Pierre Villeneuve for welcoming us in his lipid chemistry team (LiFFHeS, Lipids Functions Functionalities in Heterogeneous Systems) and all members of the team for their support and advices in the undertaken work.

CONFLICT OF INTEREST

The authors have no conflicts of interest to declare. The limits are defined by straight lines: Maximal limit of peroxide value: 10 mEqO2/kg of lipid Maximal limit of acid value: 0.6% lipid

5

  µl of samples were analyzed by gas chromatography (Focus GC, Thermo electron corporation, Massachusetts, USA) equipped with a split injector (ratio of 1/20), a CP-Cil 88 Varian capillary column (50 m × 0.25 mm with a 0.2 µm film thickness; Chrompack, Middelburg, The Netherlands) and helium 1 mL/min as the carrier gas. FAMEs were analyzed by flame ionization detector and ChromCard software data system (version 2005; Thermo FIher Scientific, Massachusetts, USA).

  quantification. Samples were left to equilibrate for 15 min and trapped 60 min at 60 °C. DB-Wax UI (J&W Scientific Folsom, CA, USA) fused silica capillary column (30 m × 0.25 mm i.d. × 0.25 µm film) was used with a 1.2 mL/min constant flow of hydrogen. The temperature program for elution was: 3 °C/min from 40 °C to 170 °C, then 10 °C/min up to 240 °C and held for 10 min. The injection was performed in splitless mode injector at 250 °C. Mass spectrum were recorded in EI+ mode at 70eV within 40 to 350 Da. Analyzer and source temperatures were 150 °C and 250 °C respectively. Data were analyzed with MassHunter version B. 06.00 (Agilent Technologies, Palo Alto, USA).

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .Figure 3 .

 23 Figure 2. Content in vitamins of the fortified infant flours according to the time of storage:

Figure 4 .

 4 Figure 4. Principal Component Analysis of the determinants of the stability of the fortified

Figure 1

 1 Figure 1.

Figure 3 Figure 4 .

 34 Figure 3.

Table 1 .

 1 Characteristics of the fortified infant flours. the place of production is indicated when different from the place of purchase. C / Epox: cellophane/ epoxy resin.

	Code	Purchase place (production place) *	Storage date (months) duration (months)/ Expiration	Packaging material	Ingredients	Producer typology
	FI_1	Burkina Faso	5 / 6	PE †	Mil, soy, peanut, sugar, iodized salt, industrial amylase, CMV $ .	Local (national producer)
	FI_2	Madagascar	1-2-3-4 / 12	Alu / PE † †	Corn, rice, soy, peanut, sugar, salt, vitamins, minerals	Local (national producer)
	FI_3	Madagascar	1-2-3-4 / 12	Alu / PE † †	Corn, rice, soya, peanut, sugar, salt, vitamins, minerals	Local (national producer)
	FI_4	Benin	6 / 24	PE †	Cereal sprouts, soy germs, fats, sugar, CMV $	Local (national producer)
	FI_5	Benin	9 / 24	PE †	Corn, mil, tubers, soy, sugar, fats, full milk, carrots, , vanilla, CMV $	Local (national producer)
	FI_6	Benin (Ghana)	12 / 12	Alu / PE † †	Wheat flour, skimmed milk, sugar, palm olein, calcium carbonate, maltodextrin, vitamins, , ferrous fumarate, vanillin, zinc sulfate, bifidus bacteria, sodium chloride, potassium iodide	Local (multi-national producer)
						Local
	FI_7	Benin	2 / 6	PE / PP ∆	Rice, corn, milk, sugar, CMV $	(national
						producer)
						Local
	FI_8	Benin	3 / 6	PE †	Corn, sorghum, soy, sugar, CMV $	(national
						producer)
						Local
	FI_9	Benin	4 / 24	PE †	Cereals, soy, tubers, fats, sugar, CMV $	(national
						producer)
						Imported
	FI_10	Benin (France)	13 / 18	C/ Epox □	Flours (wheat, rice, corn), sugar, CMV $	(multi-national
						producer)
						Imported
	FI_11	Benin (France)	17 / 36	Alu / PE † †	Corn starch, rice flour, maltodextrins, tapioca, sunflower lecithin, CMV $	(multi-national
						producer)

*

∆ PE/ PP: polyethylene/polypropylene. □

Table 2 .

 2 Water content, aw, lipid contents and fatty acid profiles of the fortified infant flours.Number of repetitions (n), * n = 3, $ n=6. aw: water activity. SFA: saturated fatty acid. MUFA: monounsaturated fatty acid. PUFA: polyunsaturated fatty acid. Data are presented as mean ± standard deviation for 100 g of product.Values with distinct lowercase superscript letters in the same column are significantly different (p≤0.05). C / Epox: cellophane/ epoxy resin. ** Aluminum multilayer packaging are considered as total oxygen and water barriers.

	Sample	aW *	Water (g/100 g) *	Lipids (g/100 g) *	SFA (%) $	MUFA (%) $	PUFA (%) $	ω6/ω3 $
	FI_1	0.22 ± 0.00 3.91 ± 0.16	13.6 ± 0.4 f	19.8 ± 0.1 bc	34.1 ± 0.1 ef	46.2 ± 0.2 d	8.5 ± 1.5 a
	FI_2_L2_1	0.35 ± 0.00 5.72 ± 0.27	11.7 ± 3.5 def	16.7 ± 0.2 a	32.6 ± 0.5 def	50.7 ± 0.2 g	8.2 ± 0.5 a
	FI_2_L1_2	0.33 ± 0.01 4.98 ± 0.09	8.7 ± 0.2 def	17.7 ± 0.2 a	33.1 ± 0.3 def	49.3 ± 0.6 g	8.2 ± 0.6 a
	FI_2_L2_3* 0.38 ± 0.00 5.95 ± 0.10	9.9 ± 0.9 def	17.5 ± 0.1 a	32.4 ± 0.4 def	50.3 ± 0.3 g	8.8 ± 4.8 a
	FI_2_L1_4* 0.33 ± 0.00 5.92 ± 0.25	10.0 ± 1.2 def	17.4 ± 0.1 a	33.8 ± 0.6 def	49.6 ± 0.1 g	9.1 ± 1.0 a
	FI_3_L2_1	0.32 ± 0.00 5.09 ± 0.19	15.1 ± 3.2 ef	17.5 ± 0.2 a	33.8 ± 1.1 f	48.8 ± 0.7 ef	8.3 ± 1.0 a
	FI_3_L1_2	0.33 ± 0.00 5.44 ± 0.67	10.6 ± 1.3 ef	15.7 ± 0.1 a	40.3 ± 0.5 f	48.5 ± 0.2 ef	8.2 ± 0.6 a
	FI_3_L2_3* 0.31 ± 0.00 5.66 ± 0.29	10.3 ± 0.4 ef	17.5 ± 0.1 a	33.7 ± 0.1 f	48.8 ± 0.2 ef	9.2 ± 1.5 a
	FI_3_L1_4* 0.35 ± 0.00 4.89 ± 0.16	9.8 ± 0.4 ef	17.8 ± 0.1 a	34.6 ± 0.7 f	48.2 ± 0.1 ef	9.1 ± 1.3 a
	FI_4	0.18 ± 0.01 3.20 ± 0.12	8.8 ± 1.5 cdef	18.3 ±	30.1 ± 0.7 cd 51.7 ± 0.3 gh	10.0 ± 1.1 bc
					0.3 abc
	FI_5	0.15 ± 0.01 1.99 ± 0.13	9.0 ± 0.3 cdef	20.4 ± 2.5 c	29.6 ± 2.1 c	50.2 ± 1.0 fg	11.6 ± 4.0 d
	FI_6	0.20 ± 0.00 2.96 ± 0.13 10.2 ± 0.4 cdef	40.9 ± 0.5 h	42.8 ± 0.9 g	18.7 ± 0.8 a	21.2 ± 3.8 h
	FI_7	0.40 ± 0.01 6.37 ± 0.08	8.8 ± 3.5 cdef	23.6 ± 0.3 d	34.7 ± 0.3 f	41.7 ± 0.4 c	31.7 ± 1.0 i
	FI_8	0.40 ± 0.00 6.45 ± 0.30	6.6 ± 0.7 abcd	17.7 ± 0.1 ab	29.5 ± 0.3 c	52.8 ± 0.2 h	13.5 ± 5.9 e
	FI_9	0.16 ± 0.01 3.07 ± 0.16	7.7 ± 0.2 bcde	18.1 ± 0.1 ab	28.8 ± 0.0 c	53.2 ± 0.1 h	10.7 ± 1.8 cd
	FI_10	0.40 ± 0.01 5.49 ± 0.02	5.0 ± 1.4 abc	25.7 ± 0.4 de	14.1 ± 0.2 a	60.6 ± 0.6 i	14.8 ± 5.4 f
	FI_11	0.28 ± 0.00 4.46 ± 0.52	1.5 ± 0.4 a	32.3 ± 0.4 f	20.4 ± 0.2 b	47.4 ± 0.7 de	16.4 ± 5.9 g
	FI_12	0.41 ± 0.01 5.75 ± 0.14	2.5 ± 1.1 ab	27.1 ± 2.9 e	13.6 ± 9.3 a	59.3 ± 6.5 i	14.9 ± 0.4 f
	FI_13	0.06 ± 0.01 1.78 ± 0.02	13.5 ± 0.7 f	36.3 ± 0.3 g	30.6 ± 0.6 cde	33.0 ± 0.3 b	8.9 ± 3.5 ab
	Average	0.29 ± 0.1	4.69 ± 1.44	9.1 ± 3.6	22.0 ± 7.3	30.6 ± 7.5	47.8 ± 9.1	12.2 ± 5.9
	min	0.06	1.78	1.5	15.7	13.6	18.7	8.2
	max	0.41	6.45	15.1	40.9	42.8	60.6	31.7

∆

PE / PP: polyethylene/polypropylene. □

PERMISSION STATEMENTS

The manuscript does not contain experiments using animals.

The manuscript does not contain human studies. 5.25e -10 ± 1.41e -11a 6.53e -10 ± 1.33e -10a 115.7 ± 3.0 b --FI_2_L1_4*

3.54e -09 ± 5.39e -10b 6.15e -10 ± 8.28e -11a 6.05e -10 ± 4.83e -11a 118.5 ± 2.1 b --FI_3_L2_1 9.69e -10 ± 1.46e -10c 1.89e -10 ± 1.87e -11b 3.80e -10 ± 3.12e -11b 121.9 ± 3.6 bc --FI_3_L1_2

1.00e ± 3.90e -10c 2.43e -10 ± 1.07e -10bc 1.63e -10 ± 2.06e -10b 117.5 ± 3.0 bc --FI_3_L2_3* Data are presented as mean ± standard deviation for 100 g or kg of fresh product.

Values with distinct lower case superscript letters in the same column are significantly different (p≤0.05).

-: not detected.