Neila El Heni
email: neila.elheni@enst-bretagne.fr

Xavier Lagrange
email: xavier.lagrange@enst-bretagne.fr

Multicast vs multiple unicast scheduling in high-speed cellular networks

Packet scheduling is one of the key features in dataoriented radio interfaces of cellular networks like HSDPA (High Speed Downlink Packet Access). It has been primarily designed for unicast applications. Nevertheless, unicast may not optimise the resource usage when the same content has to be transmitted to several users in the same cell. In this paper, we compare the performance of multicast and unicast scheduling considering both a theoretical generic system and an HSDPA system. We prove the benefit of deploying multicast which is found to have merits when the average channel quality is good enough. Results show that the better the average channel quality is, the more users are allowed to receive the service simultaneously.

I. INTRODUCTION

Packet scheduling is the functionality that distributes radio resources between users. It tries to serve them fairly while maximising the system throughput. Intensive research has been conducted on the performance of unicast schedulers in cellular networks, especially in the context of HSDPA (e.g. [START_REF] Al-Manthari | Fair channel qualitybased scheduling scheme for HSDPA system[END_REF], [START_REF] Braga | Packet scheduling for VoIP over HSDPA in mixed traffic scenarios[END_REF], [START_REF] Liu | A framework for opportunistic scheduling in wireless networks[END_REF]). During a service session, users may experience different channel conditions from a slot to another. The packet scheduler uses the reported channel qualities and chooses at each Transmission Time Interval (TTI) the user to serve with the suitable modulation and coding scheme. Here, we consider an opportunistic scheduler which serves the user having the best Signal to Noise Ratio (SNR).

In some multimedia applications (e.g. video streaming), it may be interesting to transmit the same content to several users within the same cell. The standard way to manage these applications is to duplicate transmission to the different User Equipments (UEs). This may however considerably waste radio resource as only one user is served at each time slot. In this paper, such an approach is called multiple unicast. An interesting alternative is to multicast data on high capacity channels like the High Speed-Downlink Shared Channel (HS-DSCH) and deliver the same content to several users at the same time. Though not defined in the HSDPA standard, multicast may be implemented on the HS-DSCH by use of group identifier; the protocol modification details are not in the scope of this work. In order to avoid packets loss, the multicast scheduler must consider the worst case; i.e. adapt the transmission bitrate to the mobile that has the lowest SNR. Hence, the gain of using such a conservative multicast scheduling instead of the multiple unicast scheme of the standard systems is not easily predictable. Our objective is then to quantify the gain of using multicast instead of the conventional multiple unicast. More precisely, we compare the performance of a discontinuous service using the maximum bitrate capacity to a continuous service using the lowest supported bitrate (Fig. 1). The study can be applied to any type of service (e.g. file transfer, video streaming, etc.).

It is noteworthy that other multicast schedulers can be used such as MPF and IPF [START_REF] Won | Multicast scheduling in cellular data networks[END_REF]. However, although these algorithms allow higher multicast bitrates, packet losses are frequent and resulting retransmissions may decrease the system performance. Forward Error Correction (FEC) has to be applied to scalable video coding to properly alleviate this problem.

This paper is organized as follows. In Section II, the system model and assumptions are given. Section III compares multiple unicast and multicast strategies considering a theoretical generic system using Shannon [START_REF] Shannon | A mathematical theory of communication[END_REF] with the Knopp&Humblet [START_REF] Knopp | Information capacity and power control in single-cell multiuser communications[END_REF] channel model. In Section IV, we verify the coherence with the HSDPA context using a different radio channel model [START_REF]Eurane website[END_REF]. The multicast gain simulations for HSDPA are analyzed in Section V. Conclusions are drawn in Section VI.

II. THE SCENARIO DESCRIPTION

We restrict our study to a cell where N equivalent users require the same service. Users have the same average carrier to interference ratio. Considering equivalent UEs remains realistic (e.g. UEs grouped at a stadium or at a concert) and simplifies the evaluation of the used models.

Let γ i be the carrier to interference ratio for user i. Due to the radio channel variations, γ i is a random variable. Assuming the Node B is serving user UE i , we define β i as the largest transport block size supported by UE i . Let g be the function that relates β i to the reported γ i of the served user i (β i = g(γ i )), it is easy to see that g is a strictly increasing function. Let h be the associated inverse function (i.e. γ i = h(β i )).

Let P X (x) be the cumulative distribution function (CDF) of a random variable X. Similarly, p X (x) denotes the probability distribution function (PDF) of X. The CDF of β i is then

P βi (x) = P γi (h(x)).
(1)

A. Multiple unicast scneario

The advantage with unicast is the possibility to adjust transmission to the users radio conditions. At each TTI, the scheduler serves the UE that has the maximum bitrate capacity. Let δ u be the maximum block size of the current transmission, we have then

δ u = Max {i=1..N } (β i ). (2)
As UEs are equivalent, the bandwidth is fairly shared among them. Each user is served every N TTIs on average. Note that no code multiplexing is used, i.e. the scheduler serves only one UE per TTI. The average bitrate per unicast user R u,ucast is then easily calculated to be

R u,ucast = E[δ u ] ND T T I . ( 3
)
where D T T I is the duration of a TTI. We recall that the average of a random positive variable X is given by

E[X] = ∞ 0 (1 -P X (x))dx. (4)
As {β i } i=1..N are independent random variables and according to equation ( 2), the CDF of δ u is given by

P δu (x) = P N β (x). (5)
Combining equations (3), ( 4) and ( 5), we can deduce the average bitrate per unicast user

R u,ucast = 1 ND T T I ∞ 0 (1 -P N β (x))dx. (6)
Using equation ( 1), we reformulate equation ( 6) as follows

R u,ucast = 1 ND T T I ∞ 0 1 -P N γ (h(x)) dx. ( 7
)

B. Multicast scenario

We suppose all the UEs of the cell clustered in the same group. We use a conservative multicast approach to avoid packet losses for mobiles with low SNRs. Thus, at each TTI, the Node B serves all the UEs with the lowest bitrate capacity. Let δ m be the lowest supported block size within the multicast group, we have then

δ m = Min {i=1..N } (β i ) (8)
We define R u,mcast as the average bitrate per multicast user

R u,mcast = E[δ m ] D T T I . ( 9
)
Referring to equation ( 8), we compute the CDF of δ m

P δm (x) = 1 -[1 -P β (x)] N . ( 10
)
Combining equations ( 4), ( 9) and (10), we can deduce the average bitrate per multicast user

R u,mcast = 1 D T T I ∞ 0 [1 -P β (x)] N dx. ( 11
)
From equation ( 1), it follows that

R u,mcast = 1 D T T I ∞ 0 [1 -P γ (h(x))] N dx. ( 12
)

C. Multicast gain

To compare multicast and multiple-unicast, we define Γ m as the multicast gain

Γ m = R u,mcast R u,ucast . ( 13
)
The multicast gain can be also formulated as

Γ m = N E[δ m ] E[δ u ] . ( 14
)

III. STUDY OF A THEORETICAL GENERIC SYSTEM

We consider a generic system independently of the radio technology applied. To this end, we use the Shannon formula [START_REF] Shannon | A mathematical theory of communication[END_REF] that gives the maximum reachable system capacity.

A. Shannon formula

Shannon supposes a perfect error correcting system. It allows the computation of the maximum bitrate depending on the SNR ratios. If W is the available bandwidth, the maximum bitrate is then

R max (bps) = W log 2 (1 + γ). ( 15
)
The transport block size is then derived as follows

g(γ) = W D T T I log 2 (1 + γ). ( 16
)
Next, we can deduce the function h below

h(x) = 2 x W D T T I -1. (17)

B. Knopp-Humblet (K&H) model

In [START_REF] Knopp | Information capacity and power control in single-cell multiuser communications[END_REF], K&H have proposed a reference radio channel model based on the following exponential distribution for γ

p γ (x) = 1 γ exp( -x γ ) if x > 0 0, otherwise
where γ is the average received SNR. We recall that the CDF of γ can be deduced by integrating its PDF. Hence

P γ (x) = 1 -exp( -x γ ). (18)
Then, combining equations ( 7) and (18), we can compute the mean bitrate per unicast user

R u,ucast = 1 ND T T I ∞ 0 1 -[1 -exp( -h(x) γ )] N dx. ( 19
)
In the multicast case, equation ( 12) can be written as follows

R u,mcast = 1 D T T I ∞ 0 exp -Nh(x) γ dx. ( 20
)
Using Shannon, we can substitute for h from equation (17) into equations ( 19) and (20). The mean bitrate per unicast user is then

R u,ucast = 1 ND T T I ∞ 0 (1-[1-exp( -2 x W D T T I + 1 γ )] N )dx.
(21) as for the individual mean multicast bitrate

R u,mcast = 1 D T T I ∞ 0 exp( -N 2 x W D T T I + N γ )dx. ( 22
)
C. Multicast gain using Shannon with K&H Fig. 2 and Fig. 3 show the multicast gain for W and D T T I fixed to 5 MHz and 2ms, respectively.

1) gain vs γ: Fig. 2 presents Γ m vs γ for various N . We see that the larger γ, the more gain there is from multicast scheduling. It is also observed that the larger γ becomes, the greater the span in system gain becomes between different multicast group sizes.

2) gain vs N : Fig. 3 shows Γ m vs N for different values of γ. For N =1, it is trivial that Γ m is equal to 1 whatever γ is. When N increases, the behavior of Γ m depends on γ values. Two regions can be studied:

For low γ values: the greater N is, the smaller the gain. In fact, if N increases for poor channel quality, the probability of having a very low bitrate capacity within the multicast group is higher. Since the multicast strategy is conservative, the obtained mean bitrates are therefore close to zero. On the other hand, when N increases, the individual unicast bitrates become lower since the bandwidth is split between more users and then a lower bandwidth fraction is allocated to serve each unicast user. When the channel quality is bad, the group bitrate decrease has a higher impact than the reduction of unicast bandwidth fraction. Thus, multicast is less competitive than unicast and the resulting Γ m is below 1.

For high γ values: the gain increases with N . In this case, multicast bitrate no longer suffers from frequent very small transport blocks. The increase of N affects unicast more since the bandwidth will be split between more users. On the other hand, if N increases, the minimum supported block size within a multicast group decreases too. When channel conditions are good enough, the decrease in the bandwidth fraction allocated to a unicast user is more dominant than the decrease of the supported bitrate within the multicast group, resulting in higher Γ m values.

IV. STUDY OF THE HSDPA SYSTEM

In this section, we no longer consider a generic system. The used transport blocks sizes are those defined in the HSDPA specification [3]. We also consider a more complex radio channel model. That is to verify the coherence between the theoretical model and a more realistic model.

A. The considered radio channel model

The used radio channel model has been proposed in "Enhanced UMTS Radio Access Network extension for ns-2" (Eurane) simulator [START_REF]Eurane website[END_REF]. Let P i be the transmit power to user i. The received power, denoted as P r , is then given by

P r = P i h ij χ ij (23)
where h ij is the path gain (including shadowing, distance loss and antenna gain) between user i and Node B j and χ ij is the fast fading between user i and Node B j. The variable χ ij is a random variable which represents Rayleigh fast fading, it has therefore an exponential distribution. The average of χ ij is set equal to 1. The shadowing standard deviation is set equal to zero. Given these assumptions, all the users have the same signal average and the choice of the user to serve depends mainly on the random fast fading phenomenon. The signal to interference ratio received by user i connected to the reference Node B (j=0) is

γ i = P i h i0 χ i0 I intra-cell,i + I inter-cell,i + N th ( 24
)
where I intra-cell,i and I inter-cell,i represent the intra-cell and inter-cell interference received by a user i, respectively. N th is the background noise, it will be neglected. The internal interference received by UE i at Node B 0 is

I intra-cell,i = α(P max -P i )h i0 χ i0 ( 25
)
where α is the orthogonality factor and P max is the total transmit power of each cell in the system. The received intercell interference is

I inter-cell,i = M j=1 P max h ij χ ij ( 26
)
where M is the number of neighboring cells. The variable I inter-cell,i is the sum of exponential laws, so it tends to a Gaussian law when M is high. For simplicity, we assimilate it to a constant C. Finally, the received SNR reduces to

γ i = P i h i0 χ i0 α(P max -P i )h i0 χ i0 + C (27) Let f (x) be f (x) = P i h i0 x α(P max -P i )h i0 x + C (28)
f is bijective on R + and its inverse is given by

f -1 (x) = Cx P i h i0 -α(P max -P i )h i0 x (29)
The CDF of γ is given by

P γ (x) = P χ (f -1 (x)). ( 30
)
As the fast fading χ has an exponential distribution, equation ( 30) is reformulated as follows

P γ (x) = 1 -exp -Cx P i h i0 -α(P max -P i )h i0 x . (31)

B. Bitrate calculations considering an HSDPA system

The objective is to deduce the block size (β) from the SNR (γ) considering an HSDPA system. The rule is to derive the channel quality indicator (CQI) from γ and then β from CQI. Here, we detail the aforementioned steps:

The function that relates CQI to γ is given in [START_REF]Eurane user guide[END_REF]. A new formulation denoted as qual is obtained when switching from a linear to a logarithmic scale and from a piecewise constant function to a continuous one

qual(γ) =    0 if γ ≤ 0.025 10 log(γ) 1.02 + 16.62 if 0.025 < γ < 25.11 30 if 25.11 ≤ γ
Then, the block size (β) is computed for a given CQI. A mapping is defined in [3]. Using a quadratic approximation, we can express this mapping in form of a function M .

M (CQI) =    183 if CQI < 2 (4.24CQI -9.78) 2 + 182.2 if 2 ≤ CQI < 22 7154 if 22 ≤ CQI ≤ 30
Some adaptations have been done to make the function M continuous. Then, the function g that relates β to γ is deduced For the sake of simplicity, we define the following intermediate function

g(γ) = M (qual(γ)). (32)
g(γ) =    183 if γ < 0.
I(x) = Ch(x) P i h i0 -α(P max -P i )h i0 h(x) (34)
Then, according to equations ( 31) and (33), equation ( 7) becomes

C. Multicast gain with HSDPA Fig. 4 shows Γ m vs N for different distances UE-Node B. The parameter P i is fixed to 6.3. We note that Γ m is the highest when UEs are near the Node B and gets lower when approaching the cell border. The multicast gain exceeds 1 when the distance-loss is low enough. This is coherent with the results of the theoretical case of Shannon/K&H in which Γ m is higher than 1 for quite high SNR values (above around 3 dB).

To better assess performance, it is interesting to evaluate the limiting case of high average channel quality for which

lim γ→∞ Γ m = N (37)
In fact, when the channel quality is high enough, the supported block sizes reach a threshold value (7168 in HSDPA [3]). In this case, δ m equals δ u . Then, according to equation ( 14), we deduce that Γ m tends to N .

D. Forecast of the propagation environment impacts

When we fix N in equation ( 14), the multicast gain Γ m increases if E[δ u ] decreases while E[δ m ] increases, which is equivalent to a reduction in the standard deviation of SNR. This may occur when the propagation environment is characterized by a fast fading having a low dynamicity. Tests considering different environments (Pedestrian A, rural, Typical Urban (TU) etc.) will confirm this statement.

V. SIMULATION RESULTS FOR HSDPA

A. Simulation parameters

Simulation parameters are listed in Table I. The "Enhanced UMTS Radio Access Network extension for ns-2" (Eurane) simulator [START_REF]Eurane website[END_REF] has been used. It implements the channel model and the bitrate derivation mechanism described in Sections IV-A and IV-B, respectively.

B. Simulated multicast gain with HSDPA

Fig. 5 shows the multicast gain for different distances from the Node B. As it has been found in the HSDPA analytical model (section IV), the gain is the highest when UEs are near the Node B and gets lower when moving toward the cell border. At 100 m, SNR values are mapped to the maximum block size value (7168 bits/TTI [3]) for both unicast and multicast. Thus, Γ m reaches 20 with 20 users. When terminals go further, the gain from using multicast decreases. At the cell border (500m), multicast brings no tangible interest compared to unicast, Γ m is around 1. Fig. 5 shows that Γ m increases with N for low distance-loss values, which is coherent with the results of the analytical model for HSDPA and also Shannon with K&H model. Simulations of Γ m for different propagation environments are shown in Fig. 6. Gains are higher for environments with low channel dynamicity (like Ped. A and Indoor A). In fact, the standard deviation of fast fading is less important in these environments (2.19 and 2.86 dB in Ped. A and Indoor A, respectively) than in the TU (5.81 dB), rural (5.81 dB) and vehicular (4.36 dB) cases. This leads to a low standard deviation of the SNR and then a higher multicast gain.

VI. CONCLUSIONS

In this study, we have compared multiple-unicast to conservative multicast scheduling in the framework of both a generic theoretical system and an HSDPA system. Taking the mean bitrate per user as the performance metric, we have shown that multicast can largely outperform unicast for acceptable channel quality. Having proved the merits of multicast scheduling, we have laid out the foundation of the necessity to investigate more in multicast schedulers design.

In summary, we have verified that the multicast gain depends on the multicast group size, the mean SNR (equivalently the distance from the Node B) and also the propagation environment. Future work will generalize the study to UEs with different average SNRs by using a convenient group clustering and evaluate more enhanced scheduling schemes.

Fig. 1 .

 1 Fig. 1. Multiple unicast vs multicast scheduling considering 2 UEs

Fig. 2 . 2 NFig. 3 .

 223 Fig. 2. Γm vs γ for different N

Fig. 4 .

 4 Fig. 4. Γm vs N for different d UE-NodeB : numerical resolution of the analytical model for HSDPA

1 -

 1 (1 -exp (-I(x))) N dx. (35) As for equation (12), it becomes R u,mcast = 1 D T T I 7154 183 exp (-NI(x))dx.

Fig. 5 .

 5 Fig. 5. Γm vs N for different distance-loss (simulations in a TU env.)

Fig. 6 .

 6 Fig. 6. Γm for different environments (at 400 m)

  032 (41.5 log γ + 60.68) 2 + 182.2 if 0.032 ≤ γ < 4.43 7154 if 4.43 ≤ γ Function g is continuous and strictly increasing within [0.032,4.43]. Then, its inverse h on this range is

	h(x) = 10	√	x-182.2-60.68 41.5	if 183 < x < 7154 (33)


R Lefort

R Fablet

J.-M Boucher

L Berger

S Bourguignon

Automatic fish school classification for acoustic sensing of marine ecosystem

With the human demand for fish and the global warming effects, we know that marine populations are changing. Developing methods for observing and analyzing the spatio-temporal variations of marine ecosystems is then of primary importance. In this context, underwater acoustics remote sensing has a great potential. Operational systems mainly rely on expert interpretation of echograms acquired by sonar echosounders. In this works, we propose new algorithms for the analysis of acoustic survey regarding the inference of species mixing proportion. They rely on the definition and training of probabilistic school classification models from survey data.

Sonar echosounders are commonly used to observe and analyse the spatio-temporal evolutions of marine ecosystems [START_REF] Maclennan | Fisheries acoustics[END_REF]. For instance, echosounders mounted on fishing vessels allow Scientifics to assess fish stock for pelagic species such as anchovy or herring [START_REF] Scalabrin | Acoustic detection of the spatial and temporal distribution of fish shoals in the bay of biscay[END_REF]. It typically relies on the interpretation of sonar echograms by experts to assign the backscattered acoustic energy to fish species biomass. All the aggregations in the water column are viewed by echosounders. The backscattering strength allows to build either a 3D picture (figure 1) when a multi beam sensor is considered or a 2D picture (figure 2) considering a single beam sensor. These echograms are analysed by experts to discriminate species when it is possible. Several studies have examined the responses of different fish species and the capability to be discriminated in terms of morphological and spatial features (figure 2) [START_REF] Scalabrin | Acoustic detection of the spatial and temporal distribution of fish shoals in the bay of biscay[END_REF] The development of methods and algorithms automating or aiding this interpretation task would greatly contribute to improve the quality of expert estimation [START_REF] Korneliussen | The bergen echo integrator post-processing system, with focus on recent improvements[END_REF], as it should reduce the dependence on experts' subjectivity and provide better characterization of estimate uncertainties. Previous studies have been applied to automate the school classification [START_REF] Korneliussen | The bergen echo integrator post-processing system, with focus on recent improvements[END_REF] [START_REF] Haralambous | Artificial neural networks as a tool species identification of fish schools[END_REF]. However, these methods are based on a supervised learning scheme that remains uncommon as representative labelled training sets are usually not available. The labelling is achieved by the correspondence between trawl catches data and associated echograms (figure 1). The trawl catches most frequently provide a mixture of species. So, one school can not be associated with a given species. The originality of our methods proceeds from the association between a mixture proportion coming from the trawl catches and the schools extracted from the echograms. It is a weakly supervised learning strategy (figure 1). The paper is organized as follows. Section 2 presents the methods and introduces the notations for the probabilistic model. In section 3 we present the two probabilistic models based on the conditional model and the Bayesian model. Performances of these models tested with real and synthetic data are presented in section 4. Finally, concluding remarks are given in section 5.

Global methods and notation

In this section the weakly supervised learning strategy and the notation of the probabilistic model are presented. An oceanographic survey provides two kinds of data set: N T r echograms associated with N T r trawls catches given the proportion π n , 1 ≤ n ≤ N T r for each echogram and N T t echograms without trawl catch (figure 3). The first one is the training data set that allows us to build our probabilistic classification model (equation 1). All the non labelled schools of the second data set are classified independently using this model.

Considering a probabilistic school-based setting, we aim at evaluating the likelihood of observed school to be assigned to a given class. The term class refers to fish species or group of species. Let us denote by X nj ∈ R D the observation vector for the j th school in the n th echogram, where D is the number of descriptors per schools. For any

p (y njk |X nj , π n ) (1)
Note that for the training data set (i.e. for echograms associated to trawl catches) variable π n is known. The first step of the method consists in estimating model parameters Θ (see the section 3 for details) from echograms for which π n is known (i.e. echograms at trawled sites). In the second step, the trained model can be applied to any echograms.

To evaluate the performance of the proposed algorithms, datasets with known ground truth is built. Then, we compare the class found for each school with the real class. As there is a lack of mono specific trawl catch, it is hard to build the ground truth dataset. In practical terms, the method involves selection of haul having more than 90% of a determined species. Afterwards the mono specific set of fish schools is mixed according to the type of echograms wanted. Then the composition and the species proportion of each echogram are known that allows us to test classification algorithms and compare classification results with real composition. Echograms comprising mixture with one, two, three, or four classes are simulated. Note that if there is one specie per echogram, it leads to the supervised case. As statistical variables must be evaluated from a mixing proportion, it is easy to understand that the higher is the number of species in echograms, the less the classification model is suitable.

In this paper, only 2D data are processed. Simulated echograms are built with four classes of data either coming out from the campaign (Sardina: 179 schools, Anchovy: 478 schools, Horse Mackerel: 1859 schools, Blue Whiting: 95 schools) or simulated with the acoustic fish school software OASIS [START_REF] Diner | Correction on school geometry and density: approach based on acoustic image simulation[END_REF] developed by the IFREMER institute (Anchovy: 1360 schools, Sardina: 1187 schools, Horse Mackerel: 1859 schools). While the fish school simulator provides big data base for any specie acoustic campaign does not. For instance, the statistical variables will not be correctly evaluated with the 95 Blue Whiting schools of the campaign. Once echograms are built, descriptors are extracted with a software [START_REF] Diner | Ines-movies: a new acoustic data acquisition and processing system[END_REF]. 20 descriptors are used: the depth, the minimum depth, the relative altitude, the minimum altitude, the backscattering strength, the mean of acoustic echo, the maximum of acoustic echo, the standard deviation of acoustic echo, a coefficient describing the variation of echo, the maximum school height, the mean school height, the length, the area, the elongation, the fractal dimension, the circularity, the total energy, the mean energy, and the index of the amplitude dispersion. Note that these descriptors are not necessarily discriminative between them.

Models of classification

The two models of classification are presented in this section. The conditional model and the Bayesian model for weakly supervised learning have been considered and extended to our problem. Stated in [START_REF] Bishop | Generative versus discriminative methods for object recognition[END_REF] for binary labelling, an extension to mixing proportion data is considered.

• The conditional models can be viewed as a probabilistic setting of discriminative models. In the linear case, it consists in parametrizing a probabilistic decision from the signed distance to the decision hyperplane:

p (Y njk |X nj , π n ) ∝ f (< W k , X nj > +b k ),
where < W k , X nj > +b k = 0 is the equation of the hyperplane separating the class k from the others and f is the exponential function. Exponential function weights the observation as a function of the distance to the hyperplan. Model parameters Θ = {W, b} are estimated from a gradient-based minimization of the total proportion estimation error. An minimum error criterion is considered:

Θ = arg min Θ n D(π n (Θ), π n ) (2)
where πn (Θ) is the vector of the estimated priors of the acoustic energies relative to the different species classes: πn (Θ) = j E nj p (y nj |x nj , Θ), E nj equals one if these proportions are computed as relative object occurrences, and D a distance between the observed and estimated priors. Among the different distances between likelihood functions, the Battacharrya distance is chosen. An extension to non-linear models is proposed here using the kernel trick [START_REF] Schölkopf | Learning with kernels[END_REF]. The non linear model consists in a projection of the original feature space in a new kernel space. Then a Principal Component Analysis is carried out.

• For the Bayesian model, we develop p (y njk |X nj , π n ) according to Bayes relation:

p (y njk |X nj , π n ) = p(Y njk |π n )p (X nj |Y njk , π n ) l p(Y njl |π n )p (X nj |Y njl , π n )
where p(Y njk |π n ) is depending on the proportion π n into the n th echogram (the expression is given into [START_REF] Bishop | Generative versus discriminative methods for object recognition[END_REF]) and p (X nj |Y njk , π n ) is a Normal M-mixture distribution of the form:

p (X njk |Y njk , π n ) = M m=1 ρ k,m N (µ k,m , Σ k,m ) (3)
Where ρ k,m is the mixing prior for class k, µ k,m and Σ k,m are the Gaussian parameters. Models parameters Θ = {ρ k,m , µ k,m , Σ k,m } are estimated by an Expectation Maximization procedure [START_REF] Bishop | Generative versus discriminative methods for object recognition[END_REF]. A diagonal pooled variance-covariance matrix is chosen to avoid problems when the inverse matrix is calculated. This implicates that we suppose that there is no dependence between descriptors.

Results

Figure 4 shows the improvement brought by considering mixing proportion data for training compared to presence/absence data [START_REF] Bishop | Generative versus discriminative methods for object recognition[END_REF]. The presence/absence case considers that the proportion is unknown and replaces it by a binary value indicating 1 if the class is present in the echogram and 0 if the class is absent. The correct classification rate is shown as a function of the complexity of the proportion in the echogram. A complexity value of zero means that one class is dominating in the echogram and a complexity of one means that the proportion is the same for all the classes. With a simulated database and for the three classification models, the classification rate of the proportion method is better compared with the presence/absence method.

Figure 5 shows algorithms performance for real and simulated data. The rate of correct classification is shown as a function of the complexity of the training dataset from mono specific echograms (i.e. in the supervised case) to three or four class mixture. This allows the behaviour changes of the methods to be evaluated. The implementation of the different proportion complexity is done with a random number computer selection on the mono specific database. A part of the data base is randomly selected for the training and the remaining part is used to evaluate the classification of the trained model. This procedure is carried out one hundred times and the mean of the correct classification rates gives the global rate of correct classification. The higher is the number of species, the less the results are suitable. Reported results show that the proposed conditional model outperforms the Bayesian model. The Bayesian model performance decreases faster when proportions are more complex. The difference between the linear and the non linear conditional model is difficult to evaluate and depends on the dataset but the non linear conditional model dominates. Additional results also point out that correct classification rate depends on the number of descriptors used for the classification. Figure 6 presents the correct classification rate as a function of the complexity when four descriptors are considered. We picked out from the twenty descriptors those that are more discriminant. Results show that the Bayesian model is not robust. Indeed, performance decreases faster when proportions are more complex but the rate of correct classification dominates now (more than 10% for real data) compared with conditional model when the number of species per echogram is limited. We conclude that the Expectation Maximization algorithm doesn't converge with higher system dimension.

Conclusion

This paper considers an original algorithmic method for studying marine ecosystem. Previous works tried to clas- sify species using a supervised learning scheme that is not adapted to oceanographic survey. Our algorithm takes into account the observation labels coming from trawl catches give proportion information.

With regards to lack of ground truth, a procedure has been developed to test and evaluate the classification results. Before analyze the methods comportments we notice the result improvement when proportion label is considered compare to presence/absence label. Performance of the method depends on the classification model, the origin of database, and the number of parameters the methods haves to estimate. Concerning the classification results and considering all the descriptors, non linear conditional model seems to be the more adapted to the weakly supervised method. Robustness and superiority of the model are deduced from the high level of correct classification and the regularity against the number of species complexity per echogram. Finaly, we observed that the Bayesian model is sensitive to the number of descriptors.

Figure 1 .

 1 Figure 1. Weakly supervised learning: sonar echosounder provides a 3D image (echogram) composed of fish schools. Trawl catches the proportion of species mixture.

  [3] [4].

Figure 2 .

 2 Figure 2. Geometric descriptors like the depth, the length and the height of the school are used. In the bidimensional echogram, six horse mackerel schools are observed.

Figure 3 .

 3 Figure 3. Example of an oceanographic vessel route in the bay of Biscay. The learning set is composed of echograms obtained at trawled sites. It provides labelled data necessary to evaluate the classification model. The oceanographic vessel route provides echograms continuously. All schools in these unlabelled echograms are classed.

  fish school, we used geometrics and energy descriptors (figure 2) [3] [4], but temporal or geographical descriptors [2] could be used too. Let us denote by y njk the value indicating that the j th school in image n belongs to the class k. y njk = 1 if the class is k. y njk = 0 if the class is different from k. Introducing in addition the global random variable π n corresponding to class mixing proportion at the echogram level provided by the trawl catch, this leads to the definition of likelihood:

Figure 4 .

 4 Figure 4. Correct classification rate for Simulated database as a function of the complexity of the class proportion in the training echogram. Comparison between the proportion case (dashed line) and the presence/absence case (solid line) for the three classification model (Bayesian, Linear conditional and non-linear conditional).

Figure 5 .

 5 Figure 5. Classification performance for real fish school data (top) and simulated acoustic fish school data (bottom). The rate of correct classification is reported for the M=5 mixture Bayesian model (solid), the non-linear conditional model (dashed) with and the linear conditional Model (dotted).

Figure 6 .

 6 Figure 6. Classification performance for real (top) and simulated (bottom) fish school database using the four descriptors the most discriminant. The rate of correct classification is reported for the M=5 mixture Bayesian model (solid), the non-linear conditional model (dashed) and the linear conditional Model (dotted) as a function of the proportion complexity.


Thuc-Huy Duong

Mehdi A Beniddir

Grégory Genta-Jouve

Huu-Hung Nguyen

Dinh-Phuoc Nguyen

Thi-Anh-Tuyet Nguyen

Dinh-Hung Mac

Joël Boustie

Kim-Phi-Phung Nguyen

Warinthorn Chavasiri

Pierre Le Pogam

Further Terpenoids from Euphorbia tirucalli

Keywords: Euphorbia tirucalli L., Euphorbiaceae, Sesquiterpene, Cadalene, Triterpenes, Tirucallane, Euphane. Graphical

The phytochemical investigation of Euphorbia tirucalli L. (Euphorbiaceae) yielded four new compounds, including a rare cadalene-type sesquiterpene (tirucadalenone), two tirucallane triterpenoids, euphorol L and euphorol M, with the latter being described as an epimeric mixture, and a euphane triterpene, namely, euphorol N, together with 7 known compounds. Their structures and absolute configurations were elucidated from analysis of 1D (1H, J-modulated 13 C) and 2D NMR (HSQC, HMBC and NOESY), high-resolution mass spectrometry (HRESIMS), optical rotation, and GIAO NMR shift calculation followed by CP3 analysis, along with comparison with literature reports. All these compounds were tested for cytotoxicity against K562, MCF-7 and/or and HepG2 tumor cell lines. Only tirucadalenone displayed a mild cytotoxic activity.

Introduction

Euphorbia is among the largest 'giant genera' of flowering plants with close to 2.160 recognized species being renowned for their remarkably diverse growth forms, making it the third largest genus of angiosperms, second only to Astragalus (Fabaceae) and Psychotria (Rubiaceae) [START_REF] Frodin | History and concepts of big plant genera[END_REF][START_REF] Ernst | Rønsted, Global medicinal uses of Euphorbia L. (Euphorbiaceae)[END_REF]. Euphorbia plants are easily distinguishable by their irritant milky latex and their specialized inflorescences (cyathia) [START_REF] Horn | Phylogenetics and the evolution of major structural characters in the giant genus Euphorbia L.(Euphorbiaceae)[END_REF]. The chemical diversity of Euphorbiaceae is mainly related to their isoprenoid constituents. In particular, diterpenoids account for the majority of the metabolites reported in this genus with more than 650 metabolites being recorded, falling into more than twenty core frameworks including casbanes, jatrophanes, daphnanes, tiglianes, and ingenanes series alongside triterpenoids and sesquiterpenoids [START_REF] Vasas | Euphorbia Diterpenes: Isolation, Structure, Biological Activity, and Synthesis[END_REF]. As such, several Euphorbia terpenes endowed with promising pharmacological properties were reported during the last decade including ingenol-3-angelate that was approved by the FDA in 2012 and by EMA in 2013 for actinic keratosis treatment [START_REF] Vasas | Diterpenes from European Euphorbia Species Serving as Prototypes for Natural-Product-Based Drug Discovery[END_REF] while other phorbol and ingenane derivatives are currently under clinical investigations [START_REF] Kissin | Therapeutic targeting of TRPV1 by resiniferatoxin, from preclinical studies to clinical trials[END_REF][START_REF] Sanchez-Duffhues | Activation of latent HIV-1 expression by protein kinase C agonists. A novel therapeutic approach to eradicate HIV-1 reservoirs[END_REF]. In this privileged taxa, Euphorbia tirucalli L. is a shrub or small tree endemic to tropical areas with pencil-like branches from which derives its vernacular name of pencil tree [START_REF] Mwine | Euphorbia tirucalli L.(Euphorbiaceae): the miracle tree: current status of available knowledge[END_REF]. E. tirucalli L. is widely distributed in the Pantropical region of Madagascar, The Cape region (South Africa), East Africa, and Mainland Southeast Asia and is grown as garden plant in various tropical countries. Despite being widely regarded as a toxic plant, its various parts are highly valued for their medicinal properties in local medicine [START_REF] Khan | Cycloeuphordenol, a new triterpene from Euphorbia tirucalli[END_REF]. It is used in African folk medicine against warts, cough, sexual impotence, haemorrhoids, epilepsy and cancer [START_REF] Van Damme | Het traditioneel gebruik van Euphorbia tirucalli[END_REF][START_REF] Schmelzer | Medicinal plants[END_REF]. In India, this plant is used for the treatment of cancer, asthma, leprosy and leucorrhoea [START_REF] Van Damme | Het traditioneel gebruik van Euphorbia tirucalli[END_REF].

The bark and the latex of this plant exhibit a variety of significant pharmacological activities such as antibacterial [START_REF] Lirio | Note antibacterial activity of medicinal plants from the Philippines[END_REF][START_REF] Upadhyay | Ethno-Medicinal, Phytochemical and Antimicrobial Studies of Euphorbia tirucalli L[END_REF], antiherpetic [START_REF] Betancur-Galvis | Cytotoxic and antiviral activities of Colombian medicinal plant extracts of the Euphorbia genus[END_REF], and anti-mutagenic [START_REF] Rezende | Efeito antimutagênico do látex de Euphorbia tirucalli no sistema metionina em Aspergillus nidulans[END_REF]. Furthermore, E. tirucalli latex exerts pesticidal properties against various pests including mosquitoes [START_REF] Yadav | Larvicidal activity of latex and stem bark of Euphorbia tirucalli plant on the mosquito Culex quinquefasciatus[END_REF][START_REF] Rahuman | Larvicidal activity of some Euphorbiaceae plant extracts against Aedes aegypti and Culex quinquefasciatus (Diptera: Culicidae)[END_REF], molluscs [START_REF] Jurberg | Molluscicide activity of the" Avelós" plant (Euphorbia tirucalli, L.) on Biomphalaria glabrata, the mollusc vector of schistosomiasis[END_REF][START_REF] Tiwari | Toxicity of Euphorbia tirucalli plant against freshwater target and non-target organisms[END_REF]. Exposure to Euphorbia tirucalli has been proposed to be a cofactor in the genesis of endemic Burkitt's lymphoma as suggested by the coincidence between this condition and human exposure to this plant in the lymphoma belt of Africa [START_REF] Macneil | Activation of the Epstein-Barr virus lytic cycle by the latex of the plant Euphorbia tirucalli[END_REF]. E. tirucalli is also widely used for poison fishing in tropical Africa [START_REF] Neuwinger | Plants used for poison fishing in tropical Africa[END_REF] as corroborated by its strong piscicidal effects towards the catfish Heteropneustes fossilis [START_REF] Kumar | Toxicity of aqueous extract of Euphorbia tirucalli latex on catfish, Heteropneustes fossilis[END_REF]. Owing to the high amounts of triterpenes and sterols of E. tirucalli, it was also suggested that this plant might be used for rubber fractionation so that it was investigated for its diesel oil properties [START_REF] Hastilestari | Euphorbia tirucalli L.-Comprehensive characterization of a drought tolerant plant with a potential as biofuel source[END_REF].

As a continuation of our research focused on the diversity of bioactive metabolites from Vietnamese medicinal plants [START_REF] Duong | Two novel diterpenes from the roots of Phyllanthus acidus (L.) Skeel[END_REF], we herein report on the structure elucidation of a rare cadalenetype sesquiterpene [START_REF] Frodin | History and concepts of big plant genera[END_REF], two tirucallane-type triterpenes (2, 3a and 3b) and an euphane-derived triterpenoid (4), along with 7 known compounds.

A C C E P T E D

M A N U S C R I P T

Results and Discussion

Dried whole plants of Euphorbia tirucalli were extracted with ethanol. As the crude extract evaporated in vacuo, a precipitate was formed, which was filtered off prior to any further phytochemical processing. Both filtered ethanol extract and precipitate were successively extracted with n-hexane, EtOAc and n-BuOH. Further purifications were performed using a combination of chromatographic techniques including silica gel and preparative thin-layer chromatography. Through this phytochemical study, four undescribed terpenoids (1-4) were isolated, elucidated through NMR and mass spectrometric analyses and then assessed for their cytotoxicity against tumor cell lines (Fig. 1).

FIGURE 1

Tirucadalenone (1) was isolated as a white amorphous solid and its molecular formula was represent oxygenated sp 3 quaternary carbons. A pertinent way to meet all these requirements is to bridge C-5 and C-12 through a peroxy bridge, resulting in an 1,2-dioxane system. This structure is supported by the chemical shift value of C-12 which is typical of a peroxydated carbon [START_REF] Banskota | Cytotoxic cycloartanetype triterpenes from Combretum quadrangulare[END_REF][START_REF] Banskota | Thirteen novel cycloartanetype triterpenes from Combretum quadrangulare[END_REF][START_REF] Aichour | Terpenoids and other constituents from Euphorbia bupleuroides[END_REF] while the carbon resonance of C-5 is reminiscent of the value reported from cyclic peroxyhemiketalcontaining terpenoids [START_REF] Chen | Sinugibberosides A-E, new terpenoids with cyclic peroxyhemiketal from the soft coral Sinularia gibberosa[END_REF]. Therefore, the structure of compound 1 was elucidated as depicted in Fig. 1.

FIGURE 2 TABLE 1

Compound 1 displays the 1,7-dimethyl-4-isopropyldecalin skeleton typical of the so-called cadinane sesquiterpenes lato sensu, with further sub skeletons being distinguished according to the stereochemistry of the ring linkage [29]. This archetypal substitution pattern is related to their biogenesis proceeding from either a bisabolane or a germacrane cation [START_REF] Faraldos | A 1, 6-ring closure mechanism for (+)-δ-cadinene synthase?[END_REF]. One or both cadinane rings can subsequently aromatize. Calamene-type sesquiterpenes contain one benzenoid ring while cadalenes incorporate the whole naphthalene bicycle [START_REF] Breitmaier | Terpenes: Flavors, Fragrances, Pharmaca, Pheromones[END_REF]. Some tricyclic analogues of cadinane sesquiterpenes also extended the chemical diversity of this structural class, leading to introduce a fused five or six-membered oxygenated heterocycle [START_REF] Hiramatsu | Cadinane sesquiterpenoids, strobilols L and M, from Strobilurus ohshimae[END_REF][START_REF] Bunyapaiboonsri | Cadinane sesquiterpenoids from the basidiomycete Stereum cf. sanguinolentum BCC 22926[END_REF][START_REF] Pailee | Bioactive Cardinane Sesquiterpenes from the Stems of Alangium salviifolium[END_REF] Nevertheless, the 6/6/6-fused tricyclic ring skeleton of tirucadalenone comprising an 1,2-dioxane core is an unprecedented structural feature.

The para-disposition of the 5-OH group moiety to the carbonyl group at C-2 suggests that 1 might stem from a para quinone precursor. A variety of ortho [START_REF] Letcher | O-Naphthoquinones from the heartwood of Azanza garckeana[END_REF][START_REF] Puckhaber | Thespesenone and Dehydrooxoperezinone-6-methyl Ether, New Sesquiterpene Quinones from Thespesia populnea[END_REF] and para quinones [START_REF] Takahashi | Parviflorene A, a novel cytotoxic unsymmetrical sesquiterpene-dimer constituent from Curcuma parviflora[END_REF][START_REF] Stipanovic | Gossypolhemiquinone, a dimeric sesquiterpenoid identified in cotton (Gossypium)[END_REF] were indeed reported within cadalene sesquiterpenes. Accordingly, a convenient starting point to access 1 would be a C-12 hydroperoxide of the known cadalenequinone [START_REF] Toume | novel cytotoxic unsymmetrical sesquiterpene-dimers with three backbone skeletons from Curcuma parviflora[END_REF]. Even though this specific derivative of cadalenequinone has not been reported so far, terpenes' hydroperoxidations are of considerable generality [START_REF] Schmidt | Terpene hydroperoxides. IV. The thermal decomposition of pinane hydroperoxide[END_REF]. Thereafter, an intramolecular nucleophilic attack of the peroxide group onto the putative C-5 carbonyl group could straightforwardly afford the final peroxyhemiketal function, based on a reactivity widely described elsewhere [START_REF] Sander | General acid and base catalysis of the reversible addition of hydrogen peroxide to aldehydes[END_REF][START_REF] Calandra | Terpene hydroperoxide chemistry in citrus oils; reaction with endogenous aldehydes to form peroxyhemiacetals[END_REF], and as earlier proposed to step in the biosynthesis of cyclic peroxyketal metabolites [START_REF] Chen | Sinugibberosides A-E, new terpenoids with cyclic peroxyhemiketal from the soft coral Sinularia gibberosa[END_REF]. The lack of optical activity hinted the racemic nature of 1, as further backed up by the lack of any Cotton effect in the ECD spectrum. This would be related to the

A C C E P T E D M A N U S C R I P T

6 proposed biosynthetic scenario according to which the access to the cyclic peroxyhemiketal would merely be driven by chemical reactivity and most likely involve no enzyme in the process, thereby not awaiting any stereoselectivity to be introduced at this stage. Among the scarce number of natural products comprising such peroxyhemiketal or peroxyketal groups, some were reported as epimeric mixtures such as sinugibberosides from the soft coral Sinularia gibberosa [START_REF] Chen | Sinugibberosides A-E, new terpenoids with cyclic peroxyhemiketal from the soft coral Sinularia gibberosa[END_REF] and xestins from the marine sponge Xestospongia [START_REF] Quinoa | Heterocycles from the marine sponge Xestospongia sp[END_REF]. The hemiketal nature of C-5 may render its configuration labile throughout phytochemical processing [START_REF] Kotoni | Thermodynamic and kinetic investigation of monoketo-aldehyde-peroxyhemiacetal ( MKA ), a stereolabile degradation product of dihydroartemisinin[END_REF][START_REF] Chan | Evaluation and optimization of synthetic routes from dihydroartemisinin to the alkylamino-artemisinins artemiside and artemisone: A test of N-glycosylation methodologies on a lipophilic peroxide[END_REF]. Cadinane-group sesquiterpenes, lato sensu, are being subdivided based on the nature of the ring fusion and the orientation of the isopropyl group at C-7, dividing them into four structural classes : cadinanes, muurolanes, bulgaranes, and amorphanes [START_REF] Bordoloi | Naturally occurring cadinenes[END_REF].

Regarding the specific example of tirucadalenone, the subsequent aromatization of the skeleton prevents ascribing it to one of these basic skeletons. This compound was detected unambiguously from the crude n-hexane extract, hinting that this compound should be a genuine natural product (see supporting information). This does not formally exclude the possibility of a peroxidation artifact, which may occur during extraction.

Euphorol L (2) was isolated as a white gum with a molecular formula of C30H48O5 ( 7 along with seven methylene carbons, three further methine carbons and five quaternary carbons

(including an oxygenated one). Spectroscopic features described so far account for three units of desaturation (two olefinic moieties and one ketone), thus determining the structure to be tetracyclic.

The structure of the fused ring moiety was entirely confirmed by HMBC experiments as displayed in triterpenes isolated from plants display this configuration [START_REF] Takahashi | Structural Revision of Terpenoids with a (3 Z)-2-Methyl-3-penten-2-ol Moiety by the Synthesis of (23 E)-and (23 Z)-Cycloart-23-ene-3β, 25-diols[END_REF]. Altogether, these data led to characterize the 2D structure of 2 as displayed in Fig. 1. consistently with NMR data reported elsewhere on related scaffolds [START_REF] Wang | Euphane and Tirucallane Triterpenes from the Roots of Euphorbia kansui and Their in Vitro Effects on the Cell Division of Xenopus[END_REF][START_REF] Zhang | Chemical Constituents from Euphorbia kansui[END_REF].

FIGURE 3

The large coupling constants of H-3 [δH 3.27, dd, (J = 11.0, 6.0)] indicated its axial α-position, thus deducing the equatorial β-position of 3-OH moiety [START_REF] Kamperdick | Apotirucallane and Tirucallane Triterpenoids from Luvunga sarmentosa[END_REF][START_REF] Makino | Tirucallane-type triterpenes from Juliania adstringens[END_REF][START_REF] Wang | New triterpenoids from the latex of Euphorbia resinifera Berg[END_REF]. The stereochemistry of the tetracyclic nucleus and the orientation of the side chain could be further inferred from the key NOE correlations emphasized in Fig. 4. These configurations were consistent with either a euphane or a tirucallane triterpene that only differ by the configuration of C-20 [START_REF] Giner | Stereochemical investigations of the Tetrahymena cyclase, a model system for euphane/tirucallane biosynthesis[END_REF]. NMR spectral data of tetracyclic triterpenes indicate that carbon resonances are too similar between euphane (20R) and tirucallane (20S) triterpenoids to afford a clear-cut discrimination between these structural classes on this sole basis, which led to several erroneous structural reports [START_REF] Liu | Tirucallane triterpenes from the roots of Ozoroa insignis[END_REF]. A reliable spectroscopic approach to differentiate between these structural classes is the nuclear Overhauser effect of H-21 with H-16α,β in euphanes and with H-12α in tirucallanes [START_REF] Akihisa | Tirucalla-5, 24-dien-3β-ol [(13α, 14β, 17α, 20 S)-lanosta-5, 24-dien-3β-ol] and three other Δ 5-unsaturated tirucallanes from the roots of Bryonia dioica Jacq.: the first naturally occurring C-10 methylated tetracyclic triterpene alcohols with a Δ5-monounsaturated skeleton[END_REF][START_REF] Akihisa | Helianol [3, 4-seco-19 (10→ 9) abeo-8α, 9β, 10α-eupha-4, 24dien-3-ol], a Novel Triterpene Alcohol from the Tabular Flowers of Helianthus annuus L[END_REF][START_REF] Akihisa | Isohelianol: a 3, 4seco-triterpene alcohol from Sasanqua oil[END_REF][START_REF] Mohamad | Tirucallane triterpenes from Dysoxylum macranthum[END_REF][START_REF] Wang | Euphane and Tirucallane Triterpenes from the Roots of Euphorbia kansui and Their in Vitro Effects on the Cell Division of Xenopus[END_REF][START_REF] Chen | Tirucallane Triterpenoids from the Stems of Brucea mollis[END_REF]. Compound 2 revealed the key NOESY correlation H-21/H-12α determining it as a tirucallane triterpenoid, as further suggested by the NOESY cross-peak between H3-18 and both H-20 and H3-21 (Fig. 4).

FIGURE 4

At last, the negative optical rotation of 2 (-92.3) was a further clue indicating that 2 pertained to the tirucallane triterpenes rather than to the euphane series [START_REF] Itoh | Tirucalla-7, 24-dienol: a new triterpene alcohol from tea seed oil[END_REF][START_REF] Benosman | Tirucallane triterpenes from the stem bark of Aglaia leucophylla[END_REF]. Thus, the structure of 2, namely euphorol L, was determined as indicated in Fig. 1. Both 1 H and 13 C NMR chemical shift values of 2 were consistent with those reported from the identical tetracyclic scaffold of tirucalla-8,24-diene-3β,11β-diol-7-one [START_REF] Zhang | Chemical Constituents from Euphorbia kansui[END_REF].

Euphorol M (3) was isolated as an optically active white amorphous solid, the molecular applied in structural validation and revision in cases when the NMR data of a pair of diastereomers are available [START_REF] Smith | Assigning the stereochemistry of pairs of diastereoisomers using GIAO NMR shift calculation[END_REF][START_REF] Beniddir | Resolving the (19 R) Absolute Configuration of Lanciferine, a Monoterpene Indole Alkaloid from Alstonia boulindaensis[END_REF]. Taking into account both 1 H and 13 C NMR spectroscopic data for CP3 probability analysis led to assign the configuration of C-24 as S for the major form 3a (see supporting information) since the CP3 parameter results in respective values of 0.46 and -0.37 for the correct and incorrect assignments. Jointly with Bayes' theorem, this leads to define a quantifiable confidence of 67.9%.

Compound 3 was therefore determined to be a mixture of diastereoisomers with the major form (24S)

and the minor form (24R) in a 6:4 ratio. Although the determined side chain is fairly common among various triterpene series such as lanostanes [START_REF] Bernardi | Fungal metabolites. IX. Triterpenes from Naematoloma sublateritium[END_REF] or cycloartanes [START_REF] Anjaneyulu | Triterpenoids from Mangifera indica[END_REF], it is herein first being reported on a tirucallane scaffold.

Euphorol N (4), isolated as a white amorphous solid, was determined as C30H52O3 from the HRESIMS deprotonated molecular peak at m/z 459.3809 (calcd for C30H52O3-H, 459.3844), making it an isomer of 3. The comparison of NMR data indeed supported that these two metabolites were very closely related to each other, with a common planar structure and identical configurations, except for the side chain moiety. The key NOE cross-peak between H3-18/H-11α, H319/H-11ß, and H3-21/H-16α defined a euphane-type triterpene [START_REF] Akihisa | Helianol [3, 4-seco-19 (10→ 9) abeo-8α, 9β, 10α-eupha-4, 24dien-3-ol], a Novel Triterpene Alcohol from the Tabular Flowers of Helianthus annuus L[END_REF][START_REF] Jiang | The first euphane-type triterpene tridesmosides and bisdesmoside from Rhoiptelea chiliantha[END_REF]. and tirucallane series, as aforementioned. Thus, neither the diagnostic optical rotation value nor the key NOESY correlations to reliably discriminate between these two structural series were discussed, making the structural assignment rather uncertain. Likewise, the co-isolation of euphol from Clusia columnaris is not a relevant argument since both euphane and tirucallane series can arise from the same enzymatic system [START_REF] Giner | Stereochemical investigations of the Tetrahymena cyclase, a model system for euphane/tirucallane biosynthesis[END_REF], making these structural series often associated within a single plant, as reported here. The few NMR chemical shift values discrepancies between the currently reported structure and those appearing in Compagnone et al. may indicate that this euphane is herein first described due to a former misidentification and reported as a single molecule with fully assigned spectroscopic data. The chemical shifts of 4 were in excellent agreement with those of 3a, thus determining a (24S) stereochemistry for this former compound as well. Altogether, these spectroscopic data determined 4 as shown in Fig. 1.

A C C E P T E D M A N U S C R I P T 10

Seven known compounds were also isolated from the ethanol extract of E. tirucalli and identified as the triterpenes euphorol D [START_REF] Wang | New triterpenoids from the latex of Euphorbia resinifera Berg[END_REF], euphol [START_REF] Pascual Teresa | Triterpenes from Euphorbia broteri[END_REF], and lupanone [START_REF] Wenkert | Carbon-13 nuclear magnetic resonance spectroscopy of naturally-occurring substances-LVII Triterpenes related to lupane and hopane[END_REF], the sterol ergosterol peroxide [START_REF] Kim | Anticomplementary activity of ergosterol peroxide from Naematoloma fasciculare and reassignment of NMR data[END_REF], the terpene alcohol vomifoliol [START_REF] Bercht | Isolation of vomifoliol and dihydrovomifoliol from Cannabis[END_REF], the coumarin scopoletin [START_REF] Banthorpe | Two unexpected coumarin derivatives from tissue cultures of Compositae species[END_REF] and the anthraquinone aloe-emodin [START_REF] Danielsen | NMR study of some anthraquinones from rhubarb[END_REF]. The structures of these compounds were determined based on the thorough analysis of their 1D and 2D NMR spectra, mass spectrometry data, alpha D values and GIAO NMR shift calculations with subsequent CP3 probabilities; as well as on comparisons with literature data.

In this study, compounds 1-4 were evaluated for their cytotoxicity against K562 (chronic myelogenous leukemia), MCF-7 (breast cancer) and/or HepG2 (liver hepatocellular carcinoma) cell lines. Compound 1 exerted a mild activity against both K562 and HepG2 cell lines with respective IC50 values of 22 (± 1.4) and 89 (± 1.2) µg/mL (i. e. respective values of 84.6 (± 5.4) and 342 (± 4.6) µM).

Other compounds failed to reveal any cytotoxicity on HepG2 and MCF-7 cell lines.

Conclusions

The present study reports the isolation and identification of four new terpenic compounds with cadalene, tirucallane and euphane skeletons from whole plant extracts of Euphorbia tirucalli. As far as can be ascertained, the 6/6/6-fused tricyclic ring of the cadalene sesquiterpene tirucadalenone

(1) incorporating a 1,2-dioxane ring is unprecedented in nature. The complexity of the studied extract might stem from this phytochemical investigation being conducted on whole plants rather than specific organs.

Experimental section

General experimental procedures

Optical rotations were measured on a Jasco DIP-370 digital polarimeter at 293 K. Electronic circular dichroism were recorded using a Jasco J-815 ECD spectrometer. UV spectra were obtained using a Perkin Elmer Lambda 25 UV-Vis spectrometer. The IR spectra were acquired using a Shimadzu FTIR-8200 infrared spectrophotometer. NMR spectra were measured on a Bruker Avance III (500 MHz

Extraction and isolation

The clean, air-dried and ground material (3.5 kg) was extracted by maceration with EtOH (10 L

x 2) at 70°C. A precipitate occurred as the crude extract was being evaporated under reduced pressure, which was filtered off to be further processed separately, affording 250.4 g of precipitate P. The filtered solution was evaporated to dryness to yield 290.3 g of crude ethanol extract. The dry residue of this latter extract was subsequently dissolved using solvents of increasing polarities: n-hexane (H, 94.2 g), EtOAc (EA, 61.8 g) and n-BuOH (B, 27.0 g). Extract H (94.2 g) was applied to silica gel CC using a nhexane/EtOAc/Acetone gradient system (12:1:1 to 5:1:1; v/v/v) to afford three fractions. Among these, fraction H2 (15.7 g) was fractionated by Sephadex LH-20 CC using MeOH to yield three subfractions (H2.1-H2.3). Sub-fraction H2.1 (4.1 g) was applied to normal phase silica gel CC and eluted isocratically with the solvent system n-hexane/EtOAc/EtOH/Acetic acid (9:2:1:0. For 1 H and 13 C NMR (chloroform-d1) spectroscopic data, see Table 2 For 1 H and 13 C NMR (chloroform-d1) spectroscopic data, see Table 2.

Biological assays

Cytotoxic activities of the formerly unreported metabolites against the HepG2 (liver hepatocellular carcinoma) and K562 (chronic myelogenous leukemia) tumor cell lines. These two cell lines were cultured in RPMI 1640 medium or in DMEM medium, respectively, supplemented with 10% fetal bovine serum (FBS), 100 IU/mL penicillin, 100 μg/mL streptomycin and maintained at 37 °C and 5% CO2 with 95% humidity. Viable cells were counted and inoculated in 96-well plate with density of 10 4 cells/100 μL/well for HepG2 and 10 5 cells/100 μL/well for K562. After 24 hours, the cells were treated with the compounds and doxorubicin (positive control) diluted in culture media at 100, 50, 25, 12.5, 6.25, 3.125 and 0 µg/mL concentration containing 1, 0.5, 0.25, 0.125, 0.0625, 0.03125, 0%

dimethyl sulfoxide (DMSO), respectively. DMSO in culture media was used as negative control. In addition, culture medium without cells was used as blank. All experiments were done in triplicate. The plates were incubated in 5% CO2, 95% humidity at 37 °C for 72 h. 10 µL of 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT, 5 mg/ml stock solution) was added into each well and incubated in 37 °C in 5% CO2 for 3.5 hours. 70 µL of Detergent Reagent (10% SDS) was added into each well and the plate was maintained in 37 °C for 16 h. The optical density of each well was read by using a scanning multiwall spectrophotometer (Sunrise) at wavelength of 595 nm. Cell survival was measured as the percentage absorbance compared to the negative control (DMSO-treated cells). All spectra were recorded a in acetone-d6; b in chloroform-d1; c Overlapped; d Inverse detection by HMBC.

  established as C15H16O4 (corresponding to an index of hydrogen deficiency of 8) based on the sodiated ion peak at m/z 283.0968 ([M+Na] + , calcd. 283.0941). The 1 H NMR data of 1 showed two ortho aromatic protons (H 7.42, 1H, d, J = 8.0 Hz and 7.30, 1H, d, J = 8.0 Hz), one hydroxy group (H 6.67), one olefinic proton (H 6.13, q, J = 1.0 Hz), four methyl groups [H 2.58, 2.08, 1.61, 1.56 (each 3H, s)]. The 13 C NMR and HSQC spectra revealed 14 different carbon resonances comprising one ketone carbonyl group, four methyl groups, three sp² methine carbons, two oxygenated sp 3 tertiary carbons and four sp² quaternary carbons. Long-range heteronuclear correlations led to define a first aromatic ring that comprised the two ortho-coupled aromatic protons and a first methyl group. In particular, H-9 revealed key HMBC cross-peaks with C-7 (δC 137.4), C-8 (δC 128.6) and C-10 (δC 138.7). The CH3-15 moiety was connected to C-10 as evidenced by the HMBC correlations from these protons to C-9 (δC 133.1) and C-10. A third HMBC cross-peak of equal intensity connected these protons to what seemingly corresponded to C-8, which would stand for a 4 J HMBC correlation. Instead, it could rather be supposed that this correlation might be associated to the missing quaternary carbon C-1 (δC 128.6).Subsequently, HMBC correlations from both CH3-13 and CH3-14 to C-12 and C-7 were diagnostic of the attachment of an isopropyl moiety on this latter carbon. This connectivity is also supported by the H-8/C-12 HMBC cross peak. A second nucleus, the so-called B-ring, could be elucidated from long-range heteronuclear correlations originating from H-3, H3-11 and OH-5. The CH3-11 moiety could be located on C-4 based on the HMBC correlation from these protons to C-3, C-4 and C-5. Likewise, the C-5 position of the hydroxy group could be deduced from its HMBC correlations to C-4, C-5 and C-6, consistently with the H-3/C-5 HMBC cross-peak. The structure of the remaining part of this nucleus could be determined based on H-3/C-1 and H3-11/C-2 HMBC cross-peaks. Most interestingly, the determined position of the ketone moiety is in line with the 4 J HMBC coupling from H3-15 to C-2. The downfield chemical shift of C-4 (δC 154.0) further backed up the defined α,β-unsaturated ketone moiety. Finally, owing to C-1, C-6 and C-7 being three sp² quaternary carbons and due to all the other carbons of the molecules being already assigned at this stage, the C-1-C-6-C-7 connectivity could be deduced to afford a two fused six-membered ring. The spectroscopic features described so far represent seven indices of hydrogen deficiency, still leaving one to be added while two oxygen atoms also have to be incorporated into the structure. The 13 C NMR data also indicate that both C-5 and C-12

  indices of hydrogen deficiency) as indicated by the [M-H] -peak at m/z 487.3416 (calcd. for C30H47O5, 487.3429) in the HRESIMS spectrum. The 1 H, J-modulated and 13 C NMR data exhibited resonances for a disubstituted double-bond (δH 5.61 (2H), δC 137.3 and 128.7), an α,β-unsaturated ketone (δC 199.7, 140.3 and 163.0), a secondary alcohol methine [δH 3.27, dd, (J = 11.5, 6.0) ; δC 78.1], one secondary methyl [δH 0.96, d (J = 6.5)] and seven tertiary methyl groups (δH 0.76, 0.91, 0.98, 1.13 and 1.27 (x3))

Fig. 3 .

 3 Fig.3. The quaternary carbon C-25 was deduced to bear a hydroperoxy group as evidenced by the value of its chemical shift at δC 80.0[START_REF] Banskota | Cytotoxic cycloartanetype triterpenes from Combretum quadrangulare[END_REF][START_REF] Banskota | Thirteen novel cycloartanetype triterpenes from Combretum quadrangulare[END_REF][START_REF] Aichour | Terpenoids and other constituents from Euphorbia bupleuroides[END_REF] against ca. 70 ppm in the case of an alcohol moiety[START_REF] Mohamad | Tirucallane triterpenes from Dysoxylum macranthum[END_REF][START_REF] Wang | Euphane and Tirucallane Triterpenes from the Roots of Euphorbia kansui and Their in Vitro Effects on the Cell Division of Xenopus[END_REF].Accordingly, the signals related to the side chain were superimposable to those of known tetracyclic triterpenes having the Δ23, 25-hydroperoxide moiety: inoterpene C[START_REF] Nakamura | Absolute stereostructures of inoterpenes A-F from sclerotia of Inonotus obliquus[END_REF], floralginsenosides B and D-F[START_REF] Yoshikawa | Medicinal flowers. XI. Structures of new dammarane-type triterpene diglycosides with hydroperoxide group from flower buds of Panax ginseng[END_REF] and floralquinquenosides A and C[START_REF] Nakamura | Medicinal flowers. XVII. New dammarane-type triterpene glycosides from flower buds of American ginseng, Panax quinquefolium L[END_REF]. The signals related to the olefinic protons resulted in a multiplet at δH 5.6 that could not be resolved by obtaining a spectrum of 2 in other deuterated solvents, precluding the straightforward assignment of the geometry of the double bond based on the magnitude of the vicinal coupling constant value. Accordingly, the geometry of the side chain was established as E primarily based on comparison of the13 C NMR spectroscopic data of analogues with similar side chain[START_REF] Leong | 20R, 23E)-Eupha-8, 23-diene-3β, 25-diol from Tripetalum cymosum[END_REF][START_REF] Xu | Chemical constituents of the roots of Euphorbia micractina[END_REF][START_REF] Pettit | Isolation and Structure of Cancer Cell Growth Inhibitory Tetracyclic Triterpenoids from the Zimbabwean Monadenium lugardae[END_REF] and further backed up by biosynthetic considerations since most related

  formula of which was established as C30H52O3 based on its negative-ion mode HRESIMS data (m/z 459.3803, calcd for C30H52O3-H, 459.3844). As for compound 2, a 3β-hydroxy-Δ 8 tetracyclic scaffold could be assigned based on 1 and 2D NMR spectral data. Some slight differences could nevertheless be observed between the fused ring structures of 2 and 3. These could be related to the reduction of the C-7 ketone group to give rise to a further diastereotopic methylene signal, also being in line with the upfield shift of the vicinal carbon C-6 (δC 19.1) and of the olefinic carbons C-8 and C-9 (δC 133.7 and 134.2, respectively). The relative configuration of 3 was determined to be similar to that of 2 from both 1 H NMR chemical shift values and NOESY correlations. At first, the large magnitude of the vicinal coupling constant of H-3 established the equatorial position of the 3β-hydroxy group. Subsequently, the significant NOE correlations: H-3/H-5, H-3/H3-28, H3-18/H-20, H3-18-H-22, H3-29/H3-19 and H3-A C C E P T E D M A N U S C R I P T 8 30/H-17 defined a similar stereochemistry of the tetracyclic triterpene core. The NOE correlations from the diastereotopic methylenic protons at C-11 (H3-18/H-11α and H3-19/H-11ß) revealed the antifacial orientations of the methyl groups CH3-18 and CH3-19, ruling out the possibility of a lanostane triterpene. As to the side chain, NMR data revealed that the double bond was reduced and that a hydroxy substituent was introduced on C-24. At last, the chemical shift of C-25 (δC 73.3) indicates that its hydroperoxy substituent was replaced by an alcohol group. Compound 3 exhibited NOE correlations between H3-18 and both H-20 and H3-21 as well as between H-12 and H3-21 that are possible only in case of (S)-configuration at C-20, leading to assign 3 a tirucallol skeleton as well, as further backed up by the negative optical rotation of 3 (-121.0). Having determined the planar structure of 3, a detailed inspection of the 1 H and 13 C NMR data revealed noticeable shifts in C-24 chemical shift value (δH 3.35 and 3.29; δH 79.8 and 78.9) leading to the surmise that 3 might indeed represent a mixture of C-24 epimers. Doubling of carbon resonances of adjacent carbons is in line with this inference. For further verification, Smith and Goodman's CP3 parameter method was undertaken to demonstrate the epimeric relationship of 3a and 3b and individually assign NMR data. This strategy has been extensively

The 1 H

 1 NMR chemical shift of CH3-21 (0.85, d, 5.5 Hz), along with the positive optical rotation of 3 (+ 17.0) further confirmed that this metabolite pertained to the euphane rather than the tirucallane series[START_REF] Arai | Fern constituents: Three new skeletal triterpenoid hydrocarbons isolated from Polypodiodes niponica[END_REF][START_REF] Abe | Enzymic cyclization of 2, 3-dihydrosqualene and squalene 2, 3-epoxide by squalene cyclases: from pentacyclic to tetracyclic triterpenes[END_REF][START_REF] Mishra | Euphane triterpenoid and lipid constituents from Butea monosperma[END_REF]. Such euphane derivatives were formerly reported to occur within Clusia columnaris but were isolated as a mixture of C-24 epimers[START_REF] Compagnone | Flavonoids, benzophenones and a new euphane derivative from Clusia columnaris Engl[END_REF]. The structure elucidation of this compound by Compagnone et al. can be regarded as dubious since it was determined based on the A C C E P T E D M A N U S C R I P T 9 sole basis of chemical shift values which usually do not afford a clear-cut distinction between euphane

for 1 H

 1 NMR and 125 MHz for13 C NMR) spectrometer with TMS as internal standard. Proton chemical shifts were referenced to the solvent residual signal of CD3COCD3 at δH 2.05 or of CDCl3 at δH 7.18. The 13 C-NMR spectra were referenced to the central peak of CD3COCD3 at δC 29.4 or of CDCl3 at δC 77.8.The HR-ESI-MS were recorded on a HR-ESI-MS Bruker microTOF Q-II. TLC analyses were carried out on precoated silica gel 60 F254 (Merck) and spots were visualized by spraying with 30% H2SO4 solution followed by heating. Gravity column chromatography was performed with Silica gel 60 (0.040-0.063 mm, Himedia). Samples were analysed using an Agilent LC-MS system comprising an Agilent 1260 Infinity HPLC hyphenated with an Agilent 6530 Q-TOF-MS fitted with an ESI source operating inA C C E P T E D M A N U S CR I P T 11 positive-ion mode. A Sunfire analytical C18 column (150 x 2.1mm; i.d. 3.5 µm, Waters) was used, with a flow rate of 250 µL/min. HPLC analyses were performed by elution gradient using the following parameters: A (0.1% formic acid in water) and B (acetonitrile); T, 0-2 min 5% B; 2-20 min, 100% B linear; 20-30 min, 100 % B; 30-31 min, 5% B linear. ESI conditions were set with the capillary temperature at 320°C, source voltage at 3.5 kV, and a sheath gas flow rate of 10 L/min. 4.2 Plant material Whole plants of Euphorbia tirucalli L. (Euphorbiaceae) were collected from Hong Son village, Ham Thuan Bac, in Binh Thuan province (11.129754 o N, 108.143550 O E) in July 2014 (wet season). The botanical sample was identified by Dr. Pham Van Ngot, Department of Botany, Faculty of Biology, Ho Chi Minh University of Pedagogy. A voucher specimen (No UP002) is deposited in the herbarium of the Department of Organic Chemistry, University of Science, Ho Chi Minh City.

  .

4. 4 . 4 .

 44 Euphorol N (4) White amorphous solid; [α] 20 D +17 (c 0.1, MeOH); UV (CHCl3) λmax (log ε) 227 (3.63) nm; vmax 3438, 2940, 1645, 1070, 1060, 1030 cm -1 ; HRESIMS m/z 459.3809 [M-H] -(calcd for C30H51O3, 459.3844).

Fig. 1 .

 1 Fig. 1. Structures of compounds 1-4.

Fig. 2 . 20 Fig. 3 . 4 .Fig. 4 .

 220344 Fig. 2. Key HMBC correlations of compound 1.

Fig. 1 . 4 .Fig. 2 .Fig. 3 . 4 .Fig. 4 .

 142344 Fig. 1. Structures of compounds 1-4.

Table 1 1

 1 H (500 MHz) and13 C (125 MHz) NMR data for 1 (acetone-d6).

	Position	δc	δH mult.(J in Hz)
	1	128.6
	2	186.8
	3	131.5	6.13, q (1.0)
	4	154.0
	5	94.1
	6	137.8
	7	137.4
	8	128.6	7.42, d (8.0)
	9	133.1	7.30, d (8.0)
	10	138.7
	11	16.1	2.08, s
	12	80.9
	13	28.8	1.56, s
	14	25.0	1.61, s
	15	21.6	2.58, s
	5-OH		6.67, br s

Table 2 1

 2 H (500 MHz) and13 C (125 MHz) NMR data for 2-4.

	N	2 a		3a b		3b b		4 b
		δH mult. (J in Hz)	δC	δH mult. (J in Hz)	δC	δH mult. (J in Hz)	δC	δH mult. (J in Hz)	δC
	1α	1.66, m	34.2	1.20, m	35.4	1.20, m	35.4	1.19, m	35.4
	1β	2.54, m		1.77, m		1.77, m		1.75, m
	2	1.72, m	28.4	1.61-1.69, m	27.8	1.61-1.69, m	27.8	1.62-1.68, m	27.8
		1.68, m						1.62-1.68, m
	3α	3.27, dd (11.5, 4.5)	78.1	3.23, dd (11.5, 4.5)	79.2	3.23, dd (11.5, 4.5)	79.2	3.23, dd (12.0, 4.5)	79.2
	4		39.8		39.1		39.1		39.1
	5	1.72, m	50.2	1.11, m	51.1	1.11, m	51.1	1.11, m	51.1
	6α	2.38-2.41, m	36.4	1.67, m	19.1	1.67, m	19.1	1.66, m	19.1
	6β	2.38-2.41, m		1.41, m		1.41, m		1.40, m
	7α		199.7	1.93, m	28.1	1.93, m	28.1	1.91, m	28.1
	7β			2.08, m		2.08, m		2.08, m
	8		140.3		133.7		133.7		133.6
	9		163.0		134.2		134.2		134.2
	10		40.5		37.6		37.6		37.4
	11α	4.70 t (6.0)	67.9	1.94, m	21.6	1.94, m	21.6	1.94, m	21.7
	11β			2.06, m		2.06, m		2.05, m
	12α	1.86, m	43.2	1.62 m/1.75, m	30.9	1.62, m/1.75, m	30.9	1.62, m/1.72, m	31.1
	12β	2.33, m		1.62 m/1.75, m		1.62, m/1.75, m		1.62, m/1.72, m
	13		46.9		44.3		44.3		44.3

Acknowledgment

The authors would like to thank Dr. Pham Van Ngot, Department of Botany, Faculty of Biology, Ho Chi Minh University of Education for the botanical authentication of the studied plant.

Appendix A. Supplementary data

Supplementary data related to this article can be found at