Ahlem Khlass
email: ahlem.khlass@orange.com

Thomas Bonald
email: thomas.bonald@telecom-paristech.fr

Salah Eddine Elayoubi
email: salaheddine.elayoubi@orange.com

Analytical Modeling of Downlink CoMP in LTE-Advanced

Keywords: Coordinated Multi-point transmission, LTE-Advanced, Flow-level modeling, Queuing theory, Simulations

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I. INTRODUCTION

LTE-Advanced is the current development trend of mobile communications, with a performance in terms of peak data rates expected to reach the values of 1 Gb/s in downlink and 500 Mbit/s in uplink. This is enabled with the introduction of advanced radio technologies such as enhanced multiple-input multiple-output transmission techniques. However, inter-cell interference remains a very limiting factor, especially in the context of high resource reuse and complex cellular structures.

Several interference mitigation techniques have been investigated in order to overcome this problem of inter-cell interference [START_REF]Evolved universal terrestrial radio access (E-UTRA); further advancements for E-UTRA physical layer aspects (3GPP release9)[END_REF]. A promising candidate that is investigated in this paper is the Coordinated multi-point (CoMP) transmission technique [START_REF] Hossain | Cooperative cellular wireless networks[END_REF]. The CoMP feature has been introduced in release 11 of LTE/LTE-Advanced systems [START_REF]Technical specification group radio access network; coordinated multi-point operation for LTE physical layer aspects (release 11)[END_REF] in order to improve cell-edge throughput and system capacity. It can be seen as an evolution of multiple-input multiple-output (MIMO) technique which enables multiple points to share their antennas and to coordinate with each other in such a way that the transmission signals from/to other points do not interfere or can even be converted into a useful signal, especially at the cell edge where performance may be degraded [START_REF] Marsch | Coordinated Multi-Point in Mobile Communications: from theory to practice[END_REF], [START_REF] Gesbert | Multi-cell mimo cooperative networks: A new look at interference[END_REF].

The CoMP transmission technique has been the focus of many studies in 3GPP for LTE-Advanced networks (e.g. [START_REF] Sawahashi | Coordinated multipoint transmission/reception techniques for lte-advanced[END_REF] and references therein). In [START_REF] Lee | Coordinated multipoint transmission and reception in LTE-advanced: deployment scenarios and operational challenges[END_REF], several deployment scenarios and operational challenges were addressed. System-level performance has been conducted in [START_REF] Brueck | Centralized scheduling for joint transmission coordinated multi-point in lte-advanced[END_REF]. Although such finite buffer simulations provide useful insights into the efficiency of coordination schemes, they are computationally intensive, especially when stability issues are addressed. Hence, the analytical methods are more interesting, especially when considering dynamic settings with flow arrivals and departures.

In this work, we analyze the flow level performance of the downlink CoMP transmission technique. We estimate the potential benefits on average and at cell edge in comparison to a classical transmission without cell coordination. This paper is organized as follows. First, we introduce the principle of CoMP transmissions in section II. In section III, we present the network layout. We introduce in section IV the blind beamforming system as a reference; then we provide flow-level analysis of the coordinated beamforming, basic and enhanced joint transmission schemes in sections V, VI and VII, respectively. Performance results under a variety of realistic network settings are provided in section VIII. Finally, conclusions and further work are drawn in section IX.

II. PRINCIPLE

The main idea of CoMP is as follows: when a user is in the cell-edge region, it may receive several strong signals from neighboring cells in addition to that from the serving cell. Given that, if the transmitted signals are coordinated by either silencing some or letting simultaneous transmissions, the downlink performance can be increased significantly. Indeed, this coordination enables to reduce interference or even to convert it into a useful signal in order to improve not only the users' experience but also the overall downlink system performance.

Two main techniques are possible for downlink CoMP: Coordinated beamforming/scheduling and Joint processing/transmission.

• Coordinated beamforming/scheduling (CB/CS) : The scheduling and beamforming decisions to serve one or multiple users are taken within a CoMP set (i.e. the cells involved into the CoMP transmission). However, the data is only available and transmitted by a single cell (i.e. with best channel conditions). • Joint processing/transmission (JP/JT): The idea of joint processing/transmission is described by the the simultaneous transmission of data from multiple cells to a single user on the same time/frequency resource. This technique is similar to the multi-flow transmission proposed for HSPA+ systems [START_REF]technical specification group radio access network; high speed packet access (HSDPA) multipoint transmission[END_REF]. These schemes have high potential to improve users' experience and the overall system capacity by reducing interference and increasing the signal strength. However, implementation issues are still constraining [START_REF] Lee | Coordinated multipoint transmission and reception in LTE-advanced: deployment scenarios and operational challenges[END_REF] (e.g. due to feedback requirements for inter-site CoMP ).

III. NETWORK LAYOUT

We consider a homogeneous single-layer beamforming system. We assume that each BS can provide N spaced beams per sector (i.e. fixed codebook) and that each MS associates to its preferred beam that provides the best signal (i.e. maximum received power). An illustration is given in figure 1 with N = 4 beams and K = 3 sectors.

Note that it is out of our scope to investigate the optimal beamforming weights as done in several studies for downlink CoMP (e.g. [START_REF] Dahrouj | Coordinated beamforming for the multicell multi-antenna wireless system[END_REF] and references therein).

We propose in the following a flow-level analysis of intrasite coordination using coordinated beamforming and joint transmission schemes where there are no concerns about data availability or signaling overhead and latency between cells, since all operations are done locally within the same site.

IV. BLIND BEAMFORMING

As a reference, we start by investigating the blind beamforming (BB) system in the presence of N serving beams per sector.

We consider only elastic traffic. We assume that data flows arrive according to a Poisson process of intensity λk in sector k. Each flow stays in the system as long as the corresponding data have not been successfully transmitted to the User Equipment (UE). Flow sizes are assumed to be independent and exponentially distributed with mean σ bits, although all our results are approximately insensitive to the flow size distribution beyond the mean.

We consider an arbitrary set C of classes of UEs indexed by i to reflect the different radio conditions (i.e., locations) in the considered site and C k the subset relative to sector k with k ∈ {1, .., K}. All UEs of the same class have approximately the same location and thus the same serving BS and the same data rate when scheduled. We denote by Cn,k the classes of users covered by beam n of sector k with n ∈ {1, .., N } in the presence of N serving beams. Since class-i flows arrive at rate λ i , the corresponding load is:

ρ i = λ i σ R i ,
where R i denotes the transmission rate at class-i with a beamforming system.

A. Blind scheduling algorithm

We consider a centralized scheduler per radio site. According to a blind beamforming system, the scheduler selects a user at random in each sector. This latter is served alone and blocks all other users in the corresponding sector.

Although such Round Robin-based scheduler is simple and does not take into account the radio channel conditions, it remains a good approximation of any opportunistic scheduler like proportional fair (e.g. [START_REF] Yu | Multicell coordination via joint scheduling, beamforming, and power spectrum adaptation[END_REF]) when the channel variations are limited or too fast to be exploited.

B. Flow-level analysis

We denote by B n,k (t) the total number of users in beam n of sector k at time t and B(t) the corresponding vector. Whenever B(t) = b, the scheduler selects a user in beam n of sector k a fraction of time of:

φ n,k ( b) = b n,k |b k | ,
where |b k | denotes the total number of users in sector k.

The arrival rate per beam λn,k is expressed by

λn,k = i∈ Cn,k λ i ,
and the harmonic mean transmission rate:

Rn,k = i∈ Cn,k p i i∈ Cn,k pi Ri , with i∈C k p i = i∈C k λ i / λk = 1.
The queuing system is described by the following transition rates of the Markov process B(t) from state b to state b ′ :

q( b, b ′ ) =    λn,k for b ′ = b + e n,k , φ n,k ( b) Rn,k σ for b ′ = b -e n,k , (1)
where e n,k denotes the unit vector on component n, for n ∈ {1, .., N } and k ∈ {1, .., K}.

The system corresponds to three independent multi-class processor sharing queues with total load ρk = N n=1 ρn,k where

ρn,k = λn,k σ Rn,k . ( 2
)
Under the stability condition in each sector expressed by ∀k ∈ K, ρk < 1, we deduce the stationary distribution describing the number of flows in the system:

π( b) = K k=1 (1 -ρk ) |b k |! N n=1 b n,k ! n ρb n,k n,k , (3)
Using Little's law, we derive the mean duration τ i of class-i flows:

τ i = E(b n,k ) λ i .
With the mean number of class-i flows given by:

E(b n,k ) = ρ i 1 -ρk ,
we deduce the flow throughput (in bit/s) in beam n of sector k defined as the radio of the mean flow size (in bits) to the mean flow duration (in s):

γ n,k = Rn,k (1 -ρk ), (4)
Then the mean throughput in the sector k is given by:

γk = Rk (1 -ρk ). (5)
V. COORDINATED BEAMFORMING When coordinated beamforming is enabled, users are selected under additional constraints in order to avoid high interference states caused by serving cell-edge users.

A. Fixed coordinated beamforming

A way of ensuring less intra-site interference is by activating the same beam in each sector. The scheduler selects a user in beam n of sector k a fraction of time of:

φ n,k ( b) = K k=1 b n,k |b| ,
where |b| denotes the total number of users in the whole site.

The system corresponds to a set of N × K coupled processor-sharing queues with state-dependent service rates. The queuing system can be described by a Markov process whose transition rates are given by:

q( b, b ′ ) =    λn,k for b ′ = b + e n,k , φ n,k ( b) R′ n,k σ for b ′ = b -e n,k , (6)
where R′ n,k refers to the transmission rate in beam n of sector k when coordinated beamforming is performed. This Markov process is reversible and equivalently, the queuing system corresponds to a Whittle network. The stationary distribution of the Markov process B(t) is given by:

π( b) = π( 0) b K k=1 b 1,k , ..., K k=1 b N,k 3 k=1 N n=1 ρb n,k n,k ,
under the stability condition verified in each sector k:

N n=1 ρn,k < 1,
where ρn,k denotes the load per beam defined in [START_REF] Hossain | Cooperative cellular wireless networks[END_REF].

For illustration purpose, we restrict the number of beams to N = 2 per sector and we suppose that all beams have the same load such that ρn = ρ, ∀n ∈ {1, .., N }. We deduce the stationary distribution of the Markov process such that:

π(0) = (-1 + 2 ρ) 5 (1 -4 ρ + 10 ρ2 -12 ρ3 + 6 ρ4 )
.

The flow throughput of users covered by beam n is then given by: γn = R′ n (1 -6 ρ + 18 ρ2 -32 ρ3 + 30 ρ4 -12 ρ5 ) 3 -6 ρ + 12 ρ2 -12 ρ3 + 6 ρ4

B. Flexible coordinated beamforming scheme

A more advanced coordinated beamforming scheme will avoid high interference states while optimizing the scheduling opportunities. Indeed, with a flexible scheme, a minimum separation between active beams is ensured without having a fixed scheduling scheme. Accordingly, the scheduler selects a user in beam n of sector k a fraction of time of:

φ 1,k ( b) = b 1,k |b| + |b| -|b k | -b N,k-1 |b| × b 1,k |b k | , φ N,k ( b) = b N,k |b| + |b| -|b k | -b N,k+1 |b| × b N,k |b k | , φ n,k ( b) = b n,k |b k | , ∀n ∈ {1, .., N } \ {1, N },
The system corresponds to a set of N × K coupled processor-sharing queues with state-dependent service rates. The queuing system can be described by the Markov process whose transition rates are given in ( 6) by replacing the fractions of time φ n,k by their corresponding values. This Markov process is no more reversible. Therefore, the stationary distribution of the number of active flows can not be derived analytically. The performance of such process is deduced numerically by resolution of the corresponding Markov process.

VI. BASIC JOINT TRANSMISSION SCHEME

The basic joint transmission technique enables a user in the overlapping area between two cells to be jointly and simultaneously served by both.

We suppose that the site is divided into six zones: Let Z(t) be the vector of the number of flows in each zone. When Z(t) = z, the considered scheduler selects UEs in zone 1 a fraction of time:

φ 1 ( z) = z 1 + z 23 |z| + z 2 |z| z 1 + z 3 z 1 + z 3 + z 31 + z 3 |z| z 1 + z 2 z 1 + z 2 + z 12 (8)
and UEs in zone 12 a fraction of time:

φ 12 ( z) = z 12 |z| + z 3 |z| z 12 z 1 + z 2 + z 12 , (9)
where |z| denotes the total number of users in the whole site. We obtain [START_REF]technical specification group radio access network; high speed packet access (HSDPA) multipoint transmission[END_REF] for instance by observing that a UE in zone 12 is either selected first by the scheduling algorithm, with probability z 12 /|z|, or after the selection of a UE in zone 3, with probability z 3 /|z|; in the latter case, only UEs in zones 1, 2 or 12 can be selected in the same timeslot. Expression ( 8) can be derived in the same way, and the timeslot allocation in the other zones follow by symmetry.

The system corresponds to a set of six coupled processorsharing queues with state-dependent service rates. The analytical performance in terms of flow throughput can be deduced from our previous work on multi-flow transmission for HSPA+ systems [START_REF] Khlass | Flow-Level performance of intra-site coordination in cellular networks[END_REF] . We obtain:

∀n, Cn ⊂ C 1 , γn ≈ Rn (1 -ρ1 -ρ31 -ρ12 ) ∀n, Cn ⊂ C 12 , ( 10
)
γn ≈ R′ n (1 -ρ12 ) 1 + ρ1 + ρ31 1 -ρ1 -ρ12 -ρ31 + ρ2 + ρ23 1 -ρ2 -ρ12 -ρ23
, under the stability condition:

ρ1 + ρ12 + ρ31 < 1, ρ2 + ρ12 + ρ23 < 1, ρ3 + ρ31 + ρ23 < 1.
Note that R′ n denotes the transmission rate in beam n when joint transmission is performed.

VII. ENHANCED JOINT TRANSMISSION SCHEME

Considering an enhanced scheme where coordination is only performed when resources are available. Indeed, each sector can transmit data to a cell-edge user located in an adjacent sector while scheduling its own users. This means that only beams involved in the JT will be blocked and leaves the possibility for another user to be scheduled in a given sector.

We consider the same system model and notations except that we now differentiate between zone 12, consisting of classes in the coordination region served by BS 1, and zone 21, consisting of classes in the coordination region served by BS 2, and so on for all the coordination zones. We denote by z j the number of users in zone j for j ∈ {12, 1, 21, 2, 23, 3, 32, 13, 31} and by y k the total number of users in sector k. Z and Y refer to their corresponding vectors, respectively.

According to the enhanced JT scheme, the service in each coordination zone depends on the state of the other zones. We propose to decouple the system by replacing the statedependent service rates in each zone by their mean. Accordingly, the system behaves as three independent multi-class processor-sharing queues. The queuing system is described by the following transition rates of the Markov process Z(t)

q( z, z ′ ) =        λj for z ′ = z + e j , ∀j φ j ( z) Rj σ for z ′ = z -e j , j = {1, 2, 3} φ j ( z) β Rj σ for z ′ = z -e j , ∀j \ {1, 2, 3}
with φ j ( z) = zj y k , and where λj and Rj denote the arrival rate and the transmission rate per zone j. The term β refers the coordination gain obtained by averaging over all possible states of neighboring sectors, it is expressed in zone 12 by :

β12 = R′ 12 R12 [P (Y 2 = 0) + E( Z 23 Y 2 |Y 2 > 0)] + E( Z 21 Y 2 |Y 2 > 0) + 1 2 1 - R′ 12 R12 E( Z 32 Y 3 |Y 3 > 0)[P (Y 2 = 0, Y 3 > 0) + E( Z 2 Y 2 |Y 2 > 0)],
and so on for the other zones. Indeed, a UE in zone 12 benefits from coordination if both sector 2 and sector 3 are empty. If sector 2 is empty and UEs in zones 12 and 32 are scheduled, we assume that BS 2 selects to coordinate users in zone 12 or in zone 32 uniformly at random, hence the factor 1 2 . However, when sector 2 is not empty, coordination can be performed when a UE in zone 32 is scheduled or when a UE in zone 2 is scheduled and BS 2 selects to coordinate UEs in zone 12.

VIII. NUMERICAL RESULTS

We present in this section a numerical analysis where the developed models take as input realistic rates from an LTEadvanced system simulation. 2 , Am)

(3GPP model) θ 3dB = 30 • , Am = 20

A. Achievable rates with intra-site coordination

Considering the system parameters summarized in table I, we calculate the peak transmission rates (i.e. stand-alone throughput) achievable at different positions of the reference site on the basis of 100 independent network states using the Shannon formula given by:

R i = W log(1 + SIN R i ),
with W denotes the system bandwidth. The transmission rates are given in table II and table III under several intra-site coordination schemes and in two network settings: i) a network with ideal beams and ii) a network with non-ideal beams where the direction of each beam is perturbed uniformly at random of [-25 o , 25 o ] around the original direction.

We first note that the blind beamforming enables to achieve higher transmission rates compared to a classical system without beamforming since the transmitted energy of such system is confined into directional beams. We see also that the gains of intra-site coordination either with coordinated beamforming or joint transmission are too limited in a network with ideal beams since the intra-site interference is naturally avoided with ideal beams. However, in a network with non-ideal beams, we see that the coordinated beamforming either with a fixed or a flexible scheme enables to achieve an improvement of 10% in transmission rates compared to the blind beamforming since the intra-site interference is better controlled. With the basic JT scheme, the peak rates are improved by 12% on average and 20% at cell edge. The enhanced JT achieves less data rates compared to the basic JT due to the presence of a second user that shares the same resource.

B. Performance results

For various traffic intensities, we plot in figure 2 the performance of several CoMP schemes. Results are obtained by simulation of 10 6 jumps of their corresponding Markov process in terms of mean throughput. The first observation we can make is that there are no gains from intra-site coordination in a network with ideal beams since the intra-site interference is naturally avoided. However, with non-ideal beams, we notice that the performance gains of intra-site coordinated beamforming are limited in comparison to a blind beamforming system. The flexible coordinated beamforming enables to better improve the average throughput, especially at low loads, by avoiding to serve two celledge users. Besides, we see that the basic joint transmission enables to achieve higher throughput at low loads, but makes the system instable at high loads. However, the enhanced joint transmission provides an improvement on average throughput and in system stability since each sector can coordinate its neighbors' transmissions without blocking its own users.

IX. CONCLUSION Throughout this paper, we investigated several CoMP schemes by combining flow-level analysis with network simulations. We evaluated the performance in terms of average user throughput achievable under different traffic intensities. Results with non-ideal beams showed that intra-site coordination achieves significant gains over the blind beamforming system, and particularly the enhanced joint transmission scheme which improves the throughput as well as the system stability since each sector can help its neighbors while serving its own users. This can not the case with ideal beams, since intra-site interference is naturally avoided.

As future work, we intend to investigate the performance of CoMP transmission in a multi-user environment with enhanced physical-layer considerations.

Fig. 1 .

 1 Fig. 1. System model.

  With non-ideal beams Fig.2. Mean throughput vs. traffic intensities with fully loaded neighbors.

  Coordination zones where users are served simultaneously by two BSs noted Z 12 , Z 23 and Z 31 . We denote by C12 ⊂ C the set of classes in zone 12; UEs of class i ∈ C12 are served simultaneously by BS 1 and 2 at rate R ′ i . The sets C1 = C 1 \ C12 and C2 = C 2 \ C12 define zones 1 and 2 of sectors 1 and 2, respectively, where UEs are not subject to coordination; UEs of class i ∈ Cj are served by BS j at rate R i , for j ∈ {1, 2}.

• Non-coordination zones where users are served exclusively by a unique BS noted Z 1 , Z 2 and Z 3 . •


Mabrouk Hamadache
email: mhamdeche@yahoo.fr

Othmane Benkortbi
email: benkortbi_oth@yahoo.fr

Salah Hanini
email: s_hanini2002@yahoo.fr

Abdeltif Amrane
email: abdeltif.amrane@univ-rennes1.fr

Latifa Khaouane
email: latifa_khaouane@yahoo.fr

Cherif Si Moussa
email: simoussa_cherif@yahoo.fr

A Quantitative Structure Activity Relationship for acute oral toxicity of pesticides on rats: Validation, Domain of Application and Prediction

Keywords: Acute toxicity, Pesticides, QSAR, Prediction, External validation QSAR, quantitative structure-activity relationship, LD50, lethal dose 50, ANN, artificial neural networks, BFGS, Quasi-Newton back propagation algorithm, RMS, root mean square error, REACH, registration, evaluation, authorization and restriction of chemicals, OECD, organization for economic cooperation and development, LOO, leave-one-out, CV, cross-validation, AD, applicability domain, VIF, variation inflation factors, MLP, multi-layer perceptron

Quantitative Structure Activity Relationship (QSAR) models are expected to play an important role in the risk assessment of chemicals on humans and the environment. In this study, we developed a validated QSAR model to predict acute oral toxicity of 329 pesticides to rats because a few QSAR models have been devoted to predict the Lethal Dose 50 (LD50) of pesticides on rats. This QSAR model is based on 17 molecular descriptors, and is robust, externally predictive and characterized by a good applicability domain. The best results were obtained with a 17/9/1 Artificial Neural Network model trained with the Quasi Newton back propagation (BFGS) algorithm. The prediction accuracy for the external validation set was estimated by the Q 2 ext and the Root Mean Square error (RMS) which are equal to 0.948 and 0.201, respectively. 98.6% of external validation set is correctly predicted and the present model proved to be superior to models previously published. Accordingly, the model developed in this study provides excellent predictions and can be used to predict the acute oral toxicity of pesticides, particularly for those that have not been tested as well as new pesticides.

Introduction

Pesticides are widely used in agriculture for plant protection and for increasing production yields and quality of agricultural products but also in domestic applications. They are also used to slow the spread of insects, to maintain lawns, recreational areas and highways.

Pesticides have also contributed to the control of many human diseases transmitted by insects.

The most common pesticides are herbicides, insecticides and fungicides. However, despite these advantages, pesticides have a major drawback such as toxicity [START_REF] Speck-Planche | Predicting multiple ecotoxicological profiles in agrochemical fungicides: A multi-species chemoinformatic approach[END_REF]. Due to the excessive use of these products, they are found as well as residue in the environment (water, soil, air) than in terrestrial and aquatic food chains [2, 3]. In addition, they also pose a threat to the environment, humans, animals and other organisms [START_REF] Regueiro | A Review on the Fermentation of Foods and the Residues of Pesticides-Biotransformation of Pesticides and Effects on Fermentation and Food Quality[END_REF][START_REF] Wan | Ecological risk of pesticide residues in the British Columbia environment: 1973-2012[END_REF]. Many studies made internationally highlight the environmental pollution by pesticides. The consequences of this pollution are the widespread presence of residues in air, water, soil and foodstuffs [6-13].

Long-term exposure to pesticides can cause harm to human life and can disrupt the functioning of various organs in the body. This significant relationship between exposure to pesticides and some chronic diseases has been the subject of several scientific publications.

Exposure to these persistent pesticides has been associated with health effects including cancer, headache, skin and eye irritation, immune system problems, stomach, kidney, Parkinson and Alzheimer's disease, reproductive difficulties, birth defects, diabetes, cataracts and anemia [14-

17].

As seen, humans and the environment are exposed to thousands of pesticides. This pollution caused by pesticides has become an important issue affecting the survival and development of humain being. It is evident that risk assessment for pesticides can provide a precaution against the corresponding pollution. One of the procedures currently used for human and environmental risk assessment is the determination of the acute toxicity of pesticides [START_REF] Lagunin | A new approach to QSAR modelling of acute toxicity[END_REF].

Unfortunately, experimental determination of the toxicity takes time, requires a high expense and poses an ethical problem (demands to reduce or abolish the use of animals). Also, there is a very large body of research going on in many countries with the aim of replacing in vivo tests by in silico prediction methods according to the European Directive on the Protection of Laboratory Animals [START_REF] Golbamaki | Comparison of in silico models for prediction of Daphnia magna acute toxicity[END_REF] and the Registration, Evaluation, Authorization and restriction of Chemicals (REACH) regulation [START_REF] Cassotti | Validation and extension of a similarity-based approach for prediction of acute aquatic toxicity towards Daphnia magna, SAR 2[END_REF]. Despite being significantly cheaper than in vivo study, in vitro tests are still costly compared with in silico methods [START_REF] Sazonovas | Estimation of reliability of predictions and model applicability domain evaluation in the analysis of acute toxicity (LD50)[END_REF]. The use of in silico predictive methods, based on computer tools, offers a rapid, cost-effective and ethical alternative to testing toxicity of chemical substances in animals [START_REF] Sullivan | Building on a solid foundation: SAR and QSAR as a fundamental strategy to reduce animal testing[END_REF]. These methods include the Quantitative Structure-Activity Relationship (QSARs) models. To establish a QSAR model, three elements are necessary. The first relates to the biological activity (eg toxicity) measured for a set of molecules. The second concerns the descriptors. Finally, the third must be a statistical learning method that is used to connect the first two elements.

The acute toxicity still remains the object of interest in QSAR model building. To date, a large number of QSARs models for predicting the acute toxicity of chemical substances have been developed [START_REF] Cheng | In silico ADMET prediction: recent advances, current challenges and future trends[END_REF][START_REF] Dulin | Interpretation of honeybees contact toxicity associated to acetylcholinesterase inhibitors[END_REF]. Unfortunately, few studies have been devoted to the acute toxicity of pesticides on rats. For example, Enslein et al. [25,[START_REF] Enslein | A Predictive Model for Estimating Rat Oral LD50 Values[END_REF] developed regression analysis models using two large data sets (425 and 1851 various chemicals, respectively). The R 2 value for the test set is 0.33, which means that these models are characterized by low power external prediction. A very marked improvement in R The initial database that included 907 pesticides was rigorously reviewed and "cleaned" by removing pesticides whose LD50 was not experimentally determined or whose LD50 was not determined in the same experimental conditions. A total of 329 pesticides with experimental data were selected to form the final database (Table 1). The basis of 329 pesticides was divided into 2 lots. The first with 258 pesticides was dedicated to develop the QSAR model. The second which included 71 pesticides that had not been used for the development of the QSAR model, was left for the external validation.

Materials and method

Molecular descriptors

One important step in obtaining a QSAR model is the numerical representation of the structural features of molecules, which were named molecular descriptors. Nowadays, there are more than 4000 of molecular descriptors which can be used to solve different problems in Chemistry, Biology and related sciences [START_REF] Speck-Planche | Predicting multiple ecotoxicological profiles in agrochemical fungicides: A multi-species chemoinformatic approach[END_REF]. In the specific case of this study, for each molecule, 1664 molecular descriptors were calculated, which belong to many classes. All descriptors were obtained through the online program E-Dragon 1.0 (http: //www.vcclab. org/lab/edragon).

To avoid the phenomenon of overfitting, the number of descriptors must be reduced.

Several methods to simplify a database are used. The method used to select the most significant descriptors was described previously [START_REF] Hamadache | Prediction of Acute Herbicide Toxicity in Rats from Quantitative Structure-Activity Relationship Modeling[END_REF]. In the first step, invariant descriptors, namely those with absent values (represented by the code ''999''), were manually removed. Next, any descriptor that had identical values for 75% of the samples and any descriptors with a relative standard deviation < 0.05 were removed. Finally, half of the descriptors showing an absolute value of the Pearson correlation coefficient > 0.95 were also removed. The number of descriptors obtained after the selection was 95. For relevant descriptors selection, stepwise regression was then used [START_REF] Xu | Comparison of different methods for variable selection[END_REF]. Twenty nine descriptors were selected.

Model development

In this work, all calculations were run on a Sony personal computer with a Core (TM) i3 and windows XP as operating system. The Artificial Neural Networks (ANN) which has extensive applicability in solving non-linear systems was employed to build the QSAR model between the molecular relevant descriptors and the toxicity of pesticides. A three-layer feed-forward neural network utilizing back-propagation algorithm was employed. The typical backpropagation network consists of an input layer, an output layer and at least one hidden layer.

Each layer contains neurons and each neuron is a simple micro-processing unit which receives and combines signals from many neurons.

The use of a neuronal regression goes through the choice of the input parameters but also by optimizing the architecture of the neural network itself. The optimization of both the distribution of the database, the number of hidden layers, the number of neurons per hidden layer, the transfer functions as well as algorithms was carried after extensive testing. The design of the neural model is to evaluate the components of the network according to the desired performance modeling. Model performance is evaluated in terms of root mean square error (RMS) [START_REF] Wang | Prediction of impact sensitivity of nitro energetic compounds by neural network based on electrotopological-state indices[END_REF] and was calculated with the following equation:

𝑅𝑀𝑆 = √ ∑ (𝑦 𝑖 𝑒𝑥𝑝 -𝑦 𝑖 𝑝𝑟𝑒𝑑 ) 2 𝑛 𝑖=1 𝑛 ( 1
)
where n is the number of compounds in the dataset, and 𝑦 𝑖 𝑝𝑟𝑒𝑑 , 𝑦 𝑖 𝑒𝑥𝑝 are the predicted and the experimental values, respectively.

Model validation

For the validation of the predictive power of a QSAR model, two basic principles (internal validation and external validation) are available. The quality is always judged by the statistical parameters, for instance, the squared R (R 2 ) and root mean square error (RMS). These parameters mainly reflect the goodness of fit of the models. However, recent studies [START_REF] Wang | Prediction of impact sensitivity of nitro energetic compounds by neural network based on electrotopological-state indices[END_REF] have indicated that the internal validation is considered to be necessary for model validation. In the present study, we took the leave-one-out (LOO) cross-validation (CV) for the internal validation to evaluate the internal predictive ability of the developed model, and its result was defined as Q 2 LOO, which could be calculated according to the following equation [START_REF] Wang | Prediction of impact sensitivity of nitro energetic compounds by neural network based on electrotopological-state indices[END_REF]:

𝑄 𝐿𝑂𝑂 2 = 1 - ∑ (𝑦 𝑖 𝑒𝑥𝑝 -𝑦 𝑖 𝑝𝑟𝑒𝑑 ) 2 𝑡𝑟𝑎𝑖𝑛𝑖𝑛𝑔 𝑖=1 ∑ (𝑦 𝑖 𝑒𝑥𝑝 -𝑦 ̅) 2 𝑡𝑟𝑎𝑖𝑛𝑖𝑛𝑔 𝑖=1 (2)
where 𝑦 𝑖 𝑒𝑥𝑝 , 𝑦 𝑖 𝑝𝑟𝑒𝑑 and 𝑦 ̅ are the experimental, predicted, and average log (1/LD50) values of the samples for the training set, respectively. A value of Q

𝑄 𝑒𝑥𝑡 2 = 1 - ∑ (𝑦 𝑖 𝑒𝑥𝑝 -𝑦 𝑖 𝑝𝑟𝑒𝑑 ) 2 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛 𝑖=1 ∑ (𝑦 𝑖 𝑒𝑥𝑝 -𝑦 𝑡𝑟 ̅̅̅̅̅) 2 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛 𝑖=1 (3)
where 𝑦 𝑖 𝑒𝑥𝑝 , 𝑦 𝑖 𝑝𝑟𝑒𝑑 are the experimental and predicted log(1/LD50) values of the samples for the prediction set, and 𝑦 𝑡𝑟 ̅̅̅̅ is the mean experimental log(1/LD50) values of the samples for the training set.

Applicability domain

Even the most comprehensive and validated models cannot predict reliably properties for all existing compounds. The QSAR model is not intended to be used outside its domain of applicability, that is to say, outside of the chemical space covered by the training set. Also, the applicability domain (AD) of models must be defined and the predictions of the molecules in this area can be considered admissible. The determination of AD is therefore of great importance [START_REF]OECD principles for the Validation, for Regulatory Purposes, of (Quantitative) Structure-Activity Relationship Models[END_REF].

The AD is a theoretical region in the space defined by the descriptors of the model and the modeled response, for which a given QSAR should make reliable predictions. This region is defined by the nature of the compounds in the training set, and can be characterized in various ways. In our work, the AD was verified by the leverage approach. The leverage hi is defined as follows [41]:

h 𝑖 = 1 𝑛 + (𝑥 𝑖 -𝑥̅ ) 2 ∑ (𝑥 𝑖 -𝑥̅ ) 2 𝑛 𝑖=1 (4)
Where xi is the descriptor value of the ith object, and 𝑥̅ is the average value of the descriptor in the training set, and n is the number of substances in the training set. The warning leverage h* is, generally, fixed at 3(p + 1)/n, where n is the total number of samples in the training set and p is the number of descriptors involved in the correlation.

The applicability domain (AD) of QSAR model is defined from the Williams plot. The plot of leverage values versus standardized residuals (Williams plot) was used to give a graphical detection of both the response outliers (Y outliers) and the structurally influential compounds (X outliers). In this plot, the two horizontal lines indicate the limit of normal values for Y outliers (i.e. samples with standardized residuals greater than 3.0 standard deviation units, ±3.0s); the vertical straight lines indicate the limits of normal values for X outliers (i.e. samples with leverage values greater than the threshold value, h > h*). For a sample in the external test set whose leverage value is greater than h*, its prediction is considered unreliable, because the prediction is the result of a substantial extrapolation of the model. Conversely, when the leverage value of a compound is lower than the critical value, the probability of accordance between predicted and experimental values is as high as that for the compounds in the training set [42].

Results and discussion

Selection of relevant descriptors

To select the most important descriptors and the optimal number, the influences of the number of descriptors on the correlation coefficients [R 2 and adjusted R 2 (R 2 adj)] and the RMSE were investigated for 1-29 descriptors. R 2 and R 2 adj increased with increasing number of descriptors. However, the values of RMSE decreased with increasing number of descriptors. Models with 18-29 descriptors did not significantly improve the statistics of the model. For these reasons, the number of descriptors used to develop the model was 17. Let us note that n / k is greater than 5 [START_REF] Tropsha | The importance of being earnest: validation is the absolute essential for successful application and interpretation of QSPR models[END_REF] where n (258) and k [START_REF] Van Maele-Fabry | Occupational exposure to pesticides and Parkinson's disease: a systematic review and meta-analysis of cohort studies[END_REF] are respectively the number of compounds and the number of descriptors used in the QSAR model.

Multi-collinearity between the 17 descriptors was detected by calculating their variation inflation factors (VIF). If VIF falls into the range of 1-5, the related model is acceptable. All the descriptors have VIF values < 2.873, indicating that the obtained model has statistical significance, and the descriptors were found to be reasonably orthogonal. Order to study the correlation between the selected descriptors, the correlation matrix has been established using the XLSTAT software. The results show that these descriptors are not correlated owing to the fact that the greatest value of the correlation coefficient is 0.512. The list of descriptors used in the development of QSAR model is given in Table 2.

QSAR modeling

The main objective of this phase of the study is to find the optimal architecture of the neural network to predict the acute oral toxicity of pesticides on rats. A typical multilayer perceptron (MLP) three-layered network with an input layer, a hidden layer and an output layer is adopted in this work. Increasing the number of the hidden layers decreases the learning accuracy. Theoretical works have shown that a single hidden layer is sufficient for the ANN to approximate to any complex nonlinear function and many experimental results seem to confirm that one hidden layer may be enough for most forecasting problems [START_REF] Othman | Reservoir inflow forecasting using artificial neural network[END_REF]. The use of a neuronal regression requires the selection of input parameters, but also the optimization of the neural network architecture. Before training the network, the database distribution, the activation functions (for hidden neurons and output neurons), the number of neurons in the hidden layer and the learning algorithms were optimized after many trials. The optimal model performance is evaluated in terms of root mean square error (RMS) [START_REF] Lee | Back-propagation neural network for the prediction of the short-term storm surge in Taichung harbor, Taiwan[END_REF][START_REF] Sedki | Evolving neural network using real coded genetic algorithm for daily rainfall-runoff forecasting[END_REF]. The results of this study and the ANN network optimal adopted are given in Table 3.

The selected parameters (Table 3) were used to develop nonlinear model. The seventeen relevant descriptors were used as inputs to the network. Before training the network, the number of nodes in the hidden layer was optimized, because it is an important parameter influencing the performances of the ANN. Thus, a 17-9-1 network architecture was obtained after trial and error procedure. The main performance parameters of MLP-ANN model are shown in Table 4.

The predictive results from the MLP-ANN model for the entire dataset (329 compounds) are obtained and presented in Table 1. Figure 1 Fig. 1 and Fig. 2 indicates that there is a significant correlation between experimental values and predicted values of log (1/ LD50). As can be seen from Table 4, the non-linear MLP-ANN model give good results with higher correlation coefficients (R 2 and R 2 ext ), lower RMS, as well as better robustness (Q 2 ) in both training set and validation set, which indicated that the MLP-ANN not only performed well in model development, but also had excellent prediction. This fact suggested a non-linear correlation between the acute toxicity and the relevant descriptors. In addition, the residual of the predicted values of the toxicity data against the experimental values for the present model is shown in Fig. 3. As most of the calculated residuals are distributed on two sides of the zero line, a conclusion may be drawn that there is no systematic error in the development of the present model.

To see the importance of each descriptor for the prediction of LD50 oral toxicity of pesticides towards rats, the relative contributions [47] of the seventeen descriptors to the MLP-ANN model were determined and are plotted in Fig. 4. The contribution of the descriptors decreased in the order: HATS0m (12.81%) > E1u (7.98%) > MATS2p (7.74%) > HATSe (7.63%) > Mor15m (7.14% > RDF030e (6.48%) > H6m (6.27%) > Mor23u (6.12%) > Du (5.88%) > nS (5.58%) > PJI3 (5.10%) > N-072 (4.68%) > RDF020e (4.29%) > MATS1m (3.47%) ≈ nArX (3.45%) > Mor26u (2.93%) > H-046 (2.45%). The most significant descriptor in the model was therefore HATS0m. It should be noted that for the majority of the descriptors, the difference between two descriptors contribution was not significant, indicating that all selected descriptors were needed in the development of QSAR predictive model. It is obvious that the descriptors in this category have major significance in the toxicity of pesticides

Applicability domain

The applicability domain of the model was analysed using a Williams plot (Fig. 5), where the vertical line is the critical leverage value (h*), and the horizontal lines are 3s the cut off value for Y space. As seen in Fig. 5, one can observe that none of the pesticides compounds in the training set and validation set have a leverage higher than the warning h* value of 0.16.

In the Williams plot, three pesticides can be considered as response outlier (in the Y-response space). In the training set, one pesticide (Pyrazophos: 225) was overestimated, while another pesticide was underestimated (Oxycarboxine: 201). However, in the region of underestimated pesticides, Pyrazophos (329) was from the validation set. These three response outlier (in the Y-response space) could be associated with errors in the experimental values.

It should be noted that 98.6% of the domain was covered by the model when it was applied to predict the acute oral toxicity of the 71 pesticides in the validation set. Thus, these results show that MLP-ANN model complies with the third principle of the OECD.

Accordingly, the model developed in this study provides excellent predictions for 329 pesticides. It can be used to predict the acute oral toxicity of pesticides, particularly for those that have not been tested as well as new pesticides.

Comparison with different models

As indicated in the introduction, there are a limited number of QSAR models available in the literature for predicting the oral acute toxicity of pesticides to rats. The evaluation of their advantages and disadvantages is quite difficult, because each published study used different data sets and a different modeling approach (chemical descriptors, algorithms, etc.). However, it would be worthwhile to evaluate the performance of our model (present work) in light of the few QSAR models published in the literature over the last few years. Our main aim is to compare the predictive power of each model, which gives an estimation of the fitting of the model and its robustness.

It should be noted that the most of these QSAR models were obtained using small databases [33] and generally with structurally similar chemicals such as amide herbicides to other works. However, the complexity of the modeling approach, while being interesting and promising, renders these models little useful in practice.

The statistical parameters of the results obtained from the present study and studies published in the literature are shown in Table 5. It is possible to observe that all of those models could give high prediction ability (correlation coefficient R 2 , Q 2 ). However, our model exceeds the previously published models in all statistical indices available for comparison. Indeed, it gives the higher correlation coefficient and the lower RSM error if compared to the other models. It can be seen that the database for this study (training set and validation set) was wider than that of previous models with the exception of the base used by Zhu et al. [62]. According to these results, the present model can be promisingly used for predicting the toxicity of new chemicals, thus contributing to the risk assessment, saving substantial amounts of money and time.

Conclusion

The aim of the present work was to develop a QSAR study and to predict the oral acute toxicity of pesticides to rats. This study involved 258 pesticides with an additional external set of 71 pesticides modelled for their oral acute toxicity on rat based on the artificial neural network (multi-layer perceptron: MLP-ANN) with descriptors calculated by Dragon software and selected by a stepwise MLR method. The seventeen selected descriptors showed that the electronic properties and the structure of the molecule play a main role in the toxicity activity of the pesticides. The built MLP-ANN model was assessed comprehensively (internal and external validations). It showed good values of R 2 = 0.963 and Q 2 LOO = 0.962 for the training set and high predictive R 2 ext and Q 2 ext values (0.950 and 0.948) for the validation set. All the validations indicate that the built QSAR model was robust and satisfactory. Based on the comparison with models previously published, the proposed QSAR model achieved good results and provided 98.6% predictions that belong to the applicability domain. In conclusion, the model developed in this study meets all of the OECD principles for QSAR validation and can be used to predict the acute oral toxicity of pesticides, particularly for those that have not been tested as well as new pesticides and thus help reduce the number of animals used for experimental purposes.

(

  62 herbicides) for the R 2 coefficient. The conclusion which can be draw from these studies is that most QSAR models developed are distinguished by two major shortcomings: lack of validation test on the one hand, and a limited field of application because these studies included a relatively small number of pesticides on the other hand.Since the prediction of potential risks to human health is based on the assumption that test results seen in high-dose animal tests are predictive of effects that will occur in human populations exposed to much lower levels [34], our main goal in this work is to establish a robust QSAR model to predict acute toxicity (log [1/LD50]) of pesticides on rats. The database used consists of 329 pesticides. The QSAR model established by using artificial neural networks and molecular descriptors satisfies the guidelines required by the Organisation for Economic Cooperation and Development (OECD), namely: (1) a defined endpoint; (2) an unambiguous algorithm; (3) a defined domain of applicability; (4) appropriate measures of goodness of fit, robustness, predictability; (5) a mechanistic interpretation, if possible.

2. 1

 1 Data set It is well known that high-quality experimental data are essential for the development of high quality QSAR models [35]. If they are unreliable, the model will be unreliable. The rat lethal dose 50 (LD50 -rat, male via oral exposure) values were retrieved from Pesticide Properties Database [36]. The LD50 correspond to the concentration (mg/kg) of pesticide that lead to the death of 50% of rat. All values of oral acute toxicity were first converted into mmol/kg and then translated to log [1/ (mmol/kg)].

  and 2 shows the regression line of the model equation, i.e. predicted vs experimental results for the training and validation set highlighted by different symbols.

  Generally, QSAR models are functions of a molecule's structure, electronic properties and hydrophobicity [48]. In the present model, HATS0m, E1u, Mor15m, H6m, Mor23u, Du, nS, PJI3, N-072, MATS1m, nArX, Mor26u and H-046 involve the structure while MATS2p, HATSe, RDF030e and RDF020e represent the electronic properties. Descriptors used in our model have been used in previous QSAR models in the literature. Hamadache et al. [32] have used MATS2p, HATSe, HATS0m, nS, E1u and N-072 in their MLR and ANN models to predict rat oral acute toxicity of 62 herbicides. In a study by Habibi-Yangjeh and Danandeh-Jenagharad [49], the MATS1m, H-046, Mor23u and PJI3 descriptors were used for global prediction of the toxicity of 250 phenols to Tetrahymena pyriformis in a linear and nonlinear model. In a QSAR model of acute toxicity LD50 for rats caused by aromatic compounds, Bakhtiyor et al. [50] found that the descriptor MATS2p significantly contributes to the toxicity of these compounds. In a study on the penetration of the blood-brain barrier, the human intestinal absorption and the hydrophobicity, Soto et al. [51] proposed linear and nonlinear QSAR/QSPR models that include the descriptor MATS2p. A QSA(P)R model with high internal and external statistical quality for predicting toxicity was developed by Borges [52] with MATS2p for a set of 28 alkyl (1-phenylsulphonyl)-cycloalkanecarboxilates. A QSAR model on rat oral LD50 data of 58 per-and polyfluorinated chemicals developed by Bhhatarai and Gramatica [53] employed E1u; the authors concluded that E1u is one of the most important descriptors.Moreover, some authors [48, 54-57] found that among the descriptors that affect the toxicity of the compounds studied, a substantial number belong to the categories of WHIM descriptors, GETAWAY descriptors, 2D autocorrelations, and Atom-centered fragments. In our study, a large number of descriptors involved in the present model also belong to this category.

  benzimidazoles herbicides [59] or phenylurea herbicides [60]. Also, the number of statistical parameters used for validation of this QSAR models is limited, especially in old publications. Devillers [61] developed a QSAR model for acute oral toxicity in rodents (rats). He used artificial neural networks (ANN) to predict the LD50 values of organophosphate pesticide. The 51 chemicals of the training set and the nine compounds of the external testing set were described by a set of descriptors. The acute toxicities (1/log LD50) were converted to mmol/kg and a series of 8 descriptors has been used. The best results were obtained with an 8/4/1 ANN model. The root mean square error (RMS) values for the training set and the external testing set equaled 0.29 and 0.26, respectively. This study demonstrated the usefulness of descriptors such as lipophilicity and molar refractivity. Structure-toxicity relationships were studied for a set of 47 insecticides with three-layer perceptron and use of a backpropagation algorithm [29]. A model with three descriptors showed good statistics in the artificial neural network model with a configuration of 3/5/1 (r = 0.966, RMS = 0.200 and Q 2 = 0.647). The statistics for the prediction on toxicity [log LD50, oral, rat)] in the test set of 20 organophosphorus insecticides derivatives was r = 0.748, RMS = 0.576). The model descriptors indicate the importance of molar refraction toward toxicity of organophosphorus insecticides derivatives used in this study. Otherwise, different topological descriptors were used by Garcia-Domenech et al. [31] in the prediction of the oral acute toxicity (LD50) of 62 organophosphorus pesticides on rats. The LD50 values were expressed in mmol/kg with a logarithmic transformation before use. A model with eight variables (r = 0.906, Q 2 = 0.701) was generated. Zhu et al. [62] have developed a number of QSAR models for acute oral toxicity in rats using large datasets (7385 compounds). Several sets of descriptors and different modeling methods were used. It should be noted an improvement of the prediction compared

27], Eldred and Jurs [28], Zahouily [29],

  2 coefficient was obtained following the QSAR models developed with 44, 54, 67, 30 and 62 pesticides by Zakaria et al. [Guo et al. [30] and Garcia et al. [31] respectively. Recent studies devoted to pesticides [32, 33] have proposed QSAR models with values of 0.93 (27 herbicides) and 0.96

Table 1 .

 1 Observed (experimental) log (1/LD50). predicted log (1/LD50) and leverage of pesticide compounds.

	No.	Compound	Type	log [1/LD50] (mmol/kg) -1	Leverage (hi)
				Observed Predicted
			Training set
	1 1,2-Dichloropropane	Insecticide -1.24	-1.26	0.010
	2 2,4,5-Trichlorophenol	Herbicide -0.62	-0.30	0.005
	3 2,4-DB		Herbicide -0.55	-0.53	0.005
	4 2,4-Dimethylphenol	Fongicide -0.30	-0.28	0.004
	5 2-Amino butane	Fongicide -0.68	-0.59	0.005
	6 Acephate	Insecticide -0.71	-0.73	0.006
	7 Acetamiprid	Insecticide 0.02	-0.08	0.003
	8 Acetochlor	Herbicide -0.85	-0.84	0.007
	9 4-CPA		Herbicide -0.66	-0.63	0.005
	10 Acrolein	Herbicide 0.29	0.32	0.003
	11 Alachlor	Herbicide -0.54	-0.71	0.005
	12 Alanycarb	Insecticide 0.08	0.12	0.003
	13 Aldicarb	Insecticide 2.31	2.41	0.024
	14 Aldrin		Insecticide 0.97	0.94	0.006
	15 Allyxycarb	Insecticide 0.49	0.27	0.004
	16 Alpha-endosulfan	Insecticide 1.03	0.90	0.007
	17 Amicarbazone	Herbicide -0.62	-0.75	0.005
	18 Amidithion	Insecticide -0.34	-0.08	0.004
	19 Aminocarb	Insecticide 0.84	0.82	0.006
	20 Amiprofos-methyl	Herbicide -0.01	-0.04	0.003
	21 Amitraz	Insecticide -0.44	-0.37	0.004
	22 Ancymidol	Herbicide -0.83	-0.77	0.006
	23 Anilazine	Fongicide -1.22	-1.41	0.010
	24 Anilofos	Herbicide -0.11	0.13	0.003
	25 Asomate	Fongicide 0.11	0.21	0.003
	26 Azaconazole	Fongicide -0.01	0.02	0.003
	27 Azametiphos	Insecticide -0.56	-0.59	0.005
	28 Azinphos-methyl	Insecticide 1.55	1.48	0.012
	29 Benalaxil	Fongicide -0.32	-0.65	0.004
	30 Bendiocarb	Insecticide 0.82	0.83	0.005
	31 Benfuracarb	Insecticide 0.30	0.00	0.003
	32 Benquinox	Fongicide 0.38	0.36	0.003
	33 Bentazone	Herbicide -0.32	-0.27	0.004

Table 2 .

 2 List of descriptors used in the development of QSAR model.

	Category	Descriptor	Description
	2D Autocorrelations	MATS2p	Moran autocorrelation of lag 2 weighted by polarizability
	indices	MATS1m	Moran autocorrelation of lag 1 weighted by mass
	Atom-centred	N-072	RCO-N</>N -X = X
	fragments	H-046	H attached to C0(sp3) no X attached to next C
	Geometrical descriptors	PJI3	3D Petitjean shape index
		H6m	H autocorrelation of lag 6/weighted by mass
	Getaway descriptors	HATSe	Leverage-weighted total index/weighted by Sanderson electronegativity
		HATS0m	Leverage-weighted autocorrelation of lag 0/weighted by mass
	RDF descriptor	RDF020e RDF030e	Radial distribution function-020/weighted by Sanderson electronegativity Radial distribution function-030/weighted by Sanderson electronegativity
		Mor15m Signal 15/weighted by mass
	3D-Morse descriptor	Mor23u	Signal 23/unweighted
		Mor26u	Signal 26/unweighted
		Du	D total accessibility index/unweighted
	Whim descriptors	E1u	1st component accessibility directional WHIM index/unweighted
	Functional group counts	nArX	Number of X on aromatic ring
	Constitutional indices nS	Number of sulfur atoms

Table 3 .

 3 Selected parameters of the optimal multi-layer perceptron.

	Parameters studied	MSE (minimum value)	Selected parameters
	The database distribution
	Training (80%) and validation (20%)	0.0311
	Training (79%) and validation (21%)	0.0317
	Training (78.5%) and validation (21.5%)	0.0295	Training (78.5%) and validation (21.5%)
	Training (78%) and validation (22%)	0.0345
	Training (77%) and validation (23%)	0.0382
	Activation functions (hidden neurons/output neurons)
	Sigmoid-sigmoid	0.0291
	Sigmoid-linear	0.0293
	Sigmoid-tangent hyperbolic 0.1054
	Tangent hyperbolic-sigmoid 0.1719
	Tangent hyperbolic-linear 0.0290 Tangent hyperbolic-tangent hyperbolic 0.0293	Tangent hyperbolic-linear
	Linear-sigmoid	0.1563
	Linear-tangent hyperbolic 0.0306
	Linear-linear	0.0299
	Number of neurons in the hidden layer
	1-16	0.0290	9 Neurons
	Learning algorithms
	Quasi-Newton back propagation (BFGS)	0.0290
	Levenberg-Marquardt (LM) 0.0293 Scaled conjugate gradient (SCG) 0.0395	Quasi-Newton back propagation (BFGS)
	Conjugate gradient descent (CGP)	0.0346

Table 4 .

 4 Performance of MLP-ANN model for pesticides.

		R 2		0.963
	Training set (n = 258)	Q 2	LOO 0.962
		RMS 0.164
		R 2	ext 0.95
	Validation set (n = 71)	Q 2	ext 0.948
		RMS 0.201


N Benzaoui
email: benzaoui@alcatel-lucent.com

Y Pointurier

T Bonald

Q Wei

S Bigo

Mobility support in optical slot switching-based next-generation mobile backhaul networks

We propose a new CoS-aware mechanism to support User-Element mobility at optical layer in optical slot switching-based next-generation mobile backhaul network. This new mechanism allows supporting 30% additional network load and up to halves latency compared with naive mechanism.

Introduction

With the evolution of the optical transport technologies, energy-efficient solutions for the transport in the radio access part of cellular backhaul networks have become available. In this paper, we consider the use of a fine granularity optical transport solution: optical slot switching (OSS), an energy-efficient 1 , lowlatency switching technology [START_REF] Benzaoui | Optical Slot Switching Latency in Mobile Backhaul Networks[END_REF] (thanks to optical transparency for transit traffic.), where user packets are encapsulated into fixed duration containers called slots, to interconnect base stations (eNodeBs denoted eNBs) in an LTE-A mobile backhaul network. Here, optical slot switching is applied at the metro level for backhaul networks with a few (and up to a few dozens) of nodes (eNBs): Fig. 1 shows one example of LTE-A mobile backhaul network with eNBs interconnected in a ring structure. We focus on Packet Optical Add/Drop Multiplexer, an implementation of OSS for ring networks.

By shifting the support of User Element (UE) mobility (from one cell to another one) to optical layer, OSS has the potential to dramatically reduce the total handover (HO) duration by 50-70% as shown in 3 , assuming (conservatively) a queuing delay of 2ms in the OSS backhaul.

In this paper, for the first time, we propose and evaluate four optical transport mechanisms that will effectively support the mobile OSS backhaul to fulfill the afore-mentioned decrease in handover duration. The first two are naive mechanisms. The first naive approach based on slot copy and forwarding, optimizes latency while the second one, based on intermediate reencapsulation, optimizes capacity. The non naive approaches are adaptive: the first essentially removes the previous trade-off while the second adaptive and CoS-aware is the enabler for an ultra-low latency (<500 µs for real-time, traffic even when it is forwarded), capacity-efficient (above 80%) next generation mobile backhaul network.

Naive traffic forwarding mechanisms

A typical (X2-based) LTE-A handover procedure [START_REF] Shayea | Advanced handover techniques in LTE-Advanced system[END_REF] is depicted in Fig. 2, where a user receives traffic from Node 1 and is moving from a cell (Node 2) to another cell (Node 3), both served by same service gateway. During handover procedure, the data is first received by Node 2, which forwards it to Node 3. When the handover is complete, Node 1 sends data directly to Node 3.

In an OSS-based LTE-A backhaul, user packets are encapsulated in slots according to their destination eNB. Therefore, slots sent from Node 1 to Node 2 contain user packets with destination Node 2 but also packets that have to be forwarded from Node 2 to Node 3. Information about the intermediate and final destinations of client frames is carried by an outof-band control channel, which is synchronous with the data channels. Based on this information and without further user packet processing, Node 2 knows which slots should be forwarded. Latency during handover is thus essentially impacted by the forwarding mechanism in the optical layer. Thanks to the ring structure, the optical forwarding mechanisms proposed here also apply to the multicast types of traffic such as IPTV or CoMP 5 , a cooperation technique that requires cell cooperation and very low latency (1 ms end to end, i.e., less than 500 µs within one access ring) to increase user capacity at cell edges. Such strict latency constraints are enforced in POADM by sending slots even when they are not full upon timer expiration. However this may induce sending partially-full slots and thus network capacity wastage. We now first present 2 naive mechanisms to support mobility directly at the optical layer.

Naive Mechanism N1: Electronic forwarding without intermediate re-encapsulation:

As illustrated in Fig. 2, if an eNB (Node 2) receive a slot containing user packets that should be forwarded to another eNB (Node 3), the slot is 1) received by Node 2; and 2) forwarded without any modification to Node 3, after optoelectronic conversions. The slot is decapsulated at Node 3, which discards irrelevant packets whose destination is not Node 3.

The advantage of this mechanism is that small channel re-insertion latency is added by Node 2 to mobility traffic. This is done by using a higher priority for forwarded traffic at Node 2. However, since forwarded slots contain user packets which destination is not Node 3, some channel capacity between Nodes 2-3 is wasted.

Naive Mechanism N2: Electronic forwarding with intermediate re-encapsulation:

As illustrated in Fig. 3, and contrary to Mechanism N1, after slots de-capsulation at Node 2, user packets that have to be forwarded to Node 3 are re-encapsulated with user packets sent from Node 2 to Node 3. The advantage of this mechanism is that, since slots sent from Node 2 to the Node 3 contain only user packets with destination Node 3, no capacity is wasted. The disadvantage is that, due to the reencapsulation at Node 2, forwarded traffic may observe substantial additional latency, which may adversely affect real-time (RT) traffic.

Naive forwarding mechanisms evaluation

We simulate an OSS ring with 7 eNBs each connected to an OSS node (Fig. 1); a selected OSS node (e.g., Node 0) acts as a traffic hub and collects traffic to/from backbone or other rings. Traffic characteristics are shown in Tab. 1. OSS rings are dimensioned to ensure the support of such traffic demand using a custom algorithm. We allocate transponders for each node, starting with the most loaded node (allocating resources for unicast traffic first at a given node), and use first fit for wavelength allocation. CoS-management is performed by encapsulating RT and non-real-time (NRT) traffics in separated slots, and giving priority to RT slots at the channel insertion. The slot duration is 8 µs, and timers are set to 450 and 900 µs for RT and NRT traffic, respectively. We assume geographically uniform user mobility. Fig. 5 shows the latency (queuing and insertion) for all four proposed mechanisms, for RT and NRT traffic forwarded by any intermediate node and mean packet loss ratio for all traffics. Load 1 (100%) corresponds to the load for which the dimensioning algorithm is run.

The electronic forward mechanism without intermediate re-encapsulation keeps the latency low for the forwarded traffic but causes offered channel capacity waste. As shown in Fig. 5, the maximum supported network load is only ~50% for a packet loss ratio (PLR) below 10 -3 (above this limit the netwotk is considered unstable). In contrary, all the offered channel capacity is used (supported load: RT up to 100%, NRT up to 80%) with the forwarding mechanism with intermediate re-encapsulation, at the expense of high latency for the forwarded traffic, which then becomes larger than the 500 µs target for RT traffic even for low loads. This is because the RT forwarded traffic experiences up to 2 RT timer durations: at source and intermediate nodes. (Using lower timer values would reduce latency but also maximum carried load.)

Mechanism M3: Adaptive forwarding mechanism

Mechanism M3 is described in Fig. 4a. The reencapsulation process (N2) is used at Node 2 only when the channel load is high (and network is congested) and capacity should not be wasted. When the channel load is low, N1 is used and capacity (which is then abundant) is leveraged to reduce latency. Because the load is likely to vary in a real network scenario, the re-encapsulation decision is taken dynamically, slot by slot. M3 is distributed: each node independently assesses network congestion by counting the number of slots locally queued for insertion; a pre-defined number of queued slots (threshold T) indicates network congestion.

Mechanism M4: CoS-aware adaptive forwarding

M4 is depicted in Fig. 4b. To further ensure a limitation on latency for very sensitive mobile traffic such as CoMP, we propose to enhance the new adaptive mechanism by introducing two levels of network congestion detection, as shown in Fig. 4b. A first congestion threshold T1 applies to NRT slots, and a second threshold T2>T1 applies to RT slots. This mechanism keeps the latency for forwarded RT traffic as low as possible by saving channel capacity by reencapsulating NRT forwarded traffic when the network is congested. M4 is also distributed.

Adaptive forwarding mechanisms evaluation

We evaluate the 2 proposed mechanisms using the same scenario described previously, and taking T1=1 slot, T2=40 slots. Using the adaptive forwarding mechanisms the network benefits from each electronic forwarding mechanism depending on the network load: low latency and high supported load. With M3, the strict latency limit of 500 µs for RT traffic is met for load up to ~55% only. With M4, by differentiating the processing for RT and NRT traffic, we are able to ensure very low latency below 500 µs for the forwarded traffic at low loads and save offered channel capacity at high loads. M4 ensures that RT forwarded traffic meets the latency constraint for load up to 80%, and is generally able to support a total network load of at least 95% with a negligible PLR for RT traffic (all losses reported on NRT traffic thanks to CoS-management. Hence, M4 divides latency by up to factor 2 compared to N2 (Figs. 5a andb) and supporting 30% additional network load compared with N1 (Fig. 5c).

Conclusions

Our proposed CoS-aware adaptive forwarding mechanism presents the best trade-off between latency and offered channel capacity in optical slot switching-based mobile backhaul networks, where eNBs need to forward traffic from one cell to another e.g. upon user element mobility. We ensure a total network supported load of up to 80% while meeting the strict latency constraint of next generation mobile backhaul networks.

Fig. 1 :

 1 Fig. 1: OSS-based LTE-A backhaul network with 7 cells.

Fig. 2 :Fig. 3 :

 23 Fig. 2: Electronic forwarding without re-encapsulation

Fig. 5 :

 5 Fig. 5: Comparison between electronic forwarding mechanisms N1, N2, M3 and M4. Dashed curves: PLR>10 -3 .

Acknowledgement

Work supported by Celtic+ SASER project.


N Benzaoui

Y Pointurier

T Bonald

Q Wei

M Lott

Optical Slot Switching Latency in Mobile Backhaul Networks

We show that an optical slot switching network fulfills the strict latency constraints of a next generation LTE advanced switching mobile backhaul network. The impact of class-of-service handling when aggregating client data into slots is also quantified.

Introduction

With the evolution of the optical transport technologies, energy-efficient solutions for the transport in the radio access part of cellular backhaul networks have become available. In this paper, we consider the use of fine granularity optical transport solutions -optical slot switching (OSS), an energy-efficient switching technology 1 , to interconnect the eNodeBs in an LTE mobile backhaul network. Here, optical slot switching is applied at the metro level for backhaul networks with a few (and up to a few dozens) of nodes (eNodeBs): Fig. 1 shows LTE base-stations (eNodeBs) interconnected by a mobile backhaul network.

We focus on Packet Optical Add/Drop Multiplexer (POADM 3 ; see top of Fig. 1), an implementation of OSS for physical ring networks. POADM provides sub-wavelength switching granularity, and is designed to minimize the power consumption thanks to optical transparency for the transit traffic Direct node-to-node communication [START_REF] Wei | Multicast in Mobile Backhaul with Optical Packet Ring[END_REF] can be efficiently leveraged to transport Coordinated MultiPoint (CoMP) traffic, which is used in the LTE standards to improve coverage, cell-edge throughput, and system efficiency.

This paper quantifies for the first time the latency of an OSS-based LTE advanced backhaul network using real traffic demand. Specifically, we show that the overall latency is compatible with LTE advanced requirements. In addition, we investigate the impact of class of service (CoS) handling at the slot level to support additional real-time traffic, at the expense of a reduction of the maximum amount of non-real-time traffic that can be carried before losses occur.

Support of differentiated classes of service

Traffic in an LTE advanced mobile backhaul network is described in Tab. 1. In this work we consider 2 classes of service: real-time (RT) and non-real-time (NRT).

RT traffic is latency sensitive and consists of (some) data traffic, Voice over IP (VoIP), and signaling for CoMP, while NRT (or best effort) traffic consists of (some) data traffic, data for the CoMP mechanism, and handover (HO) signaling. The most strict latency requirement comes from CoMP signaling, which should experience less than 1 ms end-to-end latency. Given that such traffic may traverse one node in the backbone network to ensure communication between 2 eNodeBs in two different mobile backhaul networks (here, rings), the per-ring maximum latency for RT traffic is thus at most 500 μs. This paper quantifies the impact of CoS management during slot formation on traffic latency. We first describe how slots are formed in a non-CoS managed network.

Scenario description

We consider a POADM ring connecting 7 eNodeBs; each base-station is connected to a POADM node. As described in Fig. 4 the traffic sent between base-stations, belonging to the same ring, remains inside the ring. The traffic exchanged with base-stations on other rings or with the Internet (via the backbone) is transmitted via a selected OSS node, which we call "hub" and denote by H. As mentioned earlier we consider 6 types of traffic. Each type of traffic has a specific pattern: centralized traffic is between any node and the backbone (i.e., it transits via H) while peer-to-peer traffic is between any two eNodeBs. The pattern and per-flow demands for each type are summarized in Tab. 1.

The dimensioning of the POADM ring that ensures the support of such traffic demand is computed using algorithm [START_REF] Uš | Optimal dimensioning of the WDM unidirectional ECOFRAME optical packet ring[END_REF] and results in a 6-wavelength ring with 3 transponders on the hub and 1 transponder on every other node.

Performance evaluation

First we evaluate the performance of the POADM solution with no CoS management in the 7-node mobile backhaul network. The slot duration is set to 8 μs and client traffic is assumed to be Poisson.

A load of 1 corresponds to the demand of Tab. 1 and other loads are generated by scaling this reference load. Propagation (a few μs in a 7-node mobile backhaul ring) and insertion/extraction on the medium (1 slot duration each) are small compared with the target real-time traffic latency (500 μs) such that queuing delays, which are reported here, are representative of the latency experienced by client data within the ring.

We first set the (global) timer to 500 μs; Fig. 5 shows the mean queuing delay for each traffic type. Seemingly counter-intuitively, the queuing delay decreases as load increases for low loads; this is because queuing delay is then dominated by the time to actually fill the optical slots 5 . At higher loads the queuing delay mainly depends on channel congestion and queuing delay increases, as expected. Fig. 5 shows that the mean queuing delay of all traffic classes is well below the timer limit for load up to 0.88. The ~10% wasted load is due to the impossibility to fully fill slots with client data. This problem can be solved by allowing segmentation of client packets in several slots; this is out of the scope of this work. Note that there is no loss up to load 0.85 and we measured a client frame loss below 1e-3 up to load 0.9.

In Fig. 6 we show the impact of CoS management. We consider that half of the data traffic is RT and the other half is NRT. We keep a timer of 500 μs for RT traffic and set a timer of 1 ms for NRT traffic. Both RT and NRT queuing delays are higher than in the no-CoS management scenario. The queuing delays remain below the respective timer values. However, as we can see in Fig. 6, the CoS management policy gives an advantage to RT traffic, since we can achieve a load close to 1 for a packet loss probability below 1e-3. This is at the expense of a lower maximum amount of NRT traffic that can be carried in the network for a given client frame loss rate. Indeed in Fig. 6; NRT traffic can still achieve a load of 0.85 but beyond this value the queuing delay is higher with than without CoS management: RT traffic experiences almost no loss while NRT traffic experiences high losses. Figs. 5 and6, show that, whichever CoS management policy is used, the proposed optical slot switching ring fulfills the strict latency constraints of LTE advanced mobile backhaul network. Fig. 7 shows the impact of the timer (no CoS management: global timer; CoS management: RT timer) on the maximum achievable load for each traffic class. Without CoS management we can reach a load of 0.8 while ensuring a queuing delay for any traffic of 50 μs. Using CoS management we can still achieve a load close to 1 with a timer of 100 μs and load>0.8 using a timer of 50 μs. For very short timers (<200 μs) the maximum load achieved for NRT traffic is impacted by the prioritization of RT traffic but remains >0.7 for a timer of 50 μs, and >0.8 for a timer of 100 μs.

Conclusions

We showed that an optical slot switching network fulfills the latency constraints of a next generation LTE advanced switching mobile backhaul network, which can reach as low as a few hundreds of microsecond in the considered segment.

Even without differentiated CoS handling, real-time traffic can be supported with load up of to 88%. When CoS handling is used while forming slots it is possible to support even more real-time traffic, at the expense of a reduced non-real-time maximum carried load. Without CoS management, we showed that we can ensure a queuing delay of 50 μs while reaching a load of 80% for both RT and NRT traffic; with CoS management we can ensure a queuing delay of 100 μs while reaching a load of nearly 100% for RT and 80% for NRT traffic.

Figure 1 :

 1 Figure 1: POADM mobile backhaul ring.

Figure 4 :

 4 Figure 4: Traffic pattern: (a) centralized; (b) peer to peer.

Figure 3 :Figure 2 :

 32 Figure 3: Optical slot formation with CoS management.

Figure 6 :Figure 5 :

 65 Figure 6: Mean queuing delay with CoS management.

Figure 7 :

 7 Figure 7: Max. achievable load for packet loss rate < 1e-3.

Table 1 :

 1 Traffic characteristics.

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Acknowledgements

Work supported in part by CELTIC+ SASER project.