Abdeldjalil Aissa

El Bey
email: elbey@tsi.enst.fr

Karim Abed-Meraim

Yves Grenier
email: grenier@tsi.enst.fr

A Aïssa-El-Bey

BLIND SEPARATION OF AUDIO SOURCES USING MODAL DECOMPOSITION

published or not. The documents may come

Blind separation of audio sources using modal decomposition

INTRODUCTION

The problem of blind source separation consists of finding independent source signals from their observed mixtures without a priori knowledge on the actual mixing matrix. The source separation problem is of interest in various applications [START_REF]Blind estimation using higherorder statistics[END_REF] such as the localization and tracking of targets using radars and sonars, separation of speakers (problem known as "cocktail party"), detection and separation in multiple access communication systems, independent components analysis of biomedical signals (EEG or ECG), multispectral astronomical images etc. This problem has been intensively studied in the literature and many effective solutions have been proposed so far [START_REF]Blind estimation using higherorder statistics[END_REF]. Nevertheless, the underdetermined case where the number of sources is greater than the number of sensors (observations) remains relatively poorly treated, and its resolution is one of the open problems of blind source separation. In the case of non-stationary signals (including the audio signals), certain solutions using time-frequency analysis of the observations exist for the underdetermined case [START_REF] Nguyen | Separating more sources than sensors using time-frequency distributions[END_REF][START_REF] Jourjine | Blind separation of disjoint orthogonal signals: demixing n sources from 2 mixtures[END_REF]. In this paper, we propose an alternative approach using modal decomposition of the received signals [START_REF] Huang | The em-pirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary times series analysis[END_REF][START_REF] Flandrin | Empirical mode decomposition as a filter bank[END_REF]. More precisely we propose to decompose a supposed locally periodic signal which is not necessarily harmonic in the Fourier sense into its various modes. The audio signals and more particularly the musical signals can be modeled by a sum of damped sinusoids [START_REF] Boyer | Audio modeling based on delayed sinusoids[END_REF] and hence are well suited for our separation approach. We propose here to exploit this last property for the separation of audio sources by means of modal decomposition.

DATA MODEL

The blind source separation model assumes the existence of N independent signals s 1 (t), . . . , s N (t) and M observations x 1 (t), . . . , x M (t) that represent the mixtures. These mixtures are supposed linear and instantaneous, i.e.

x i (t) = N j=1 a ij s j (t) i = 1, . . . , M (1)
This can be represented compactly by the mixing equation

x(t) = As(t) (2)
where s(t

) def = [s 1 (t), . . . , s N (t)]
T is a N × 1 column vector collecting the source signals, vector x(t) similarly collects the M observed signals, and the M × N mixing matrix A def = [a 1 , . . . , a N ] with a i = [a 1i , . . . , a M i ] T contains the mixture coefficients. We will suppose that for any pair (i, j) with i = j, the vectors a i and a j are linearly independent. The source signals are supposed to be decomposable in a sum of modal components c j i (t), i.e:

s i (t) = l i j=1 c j i (t) t = 0, . . . , T -1 (3)
The usual source independence assumption is replaced here by a quasi-orthogonality assumption of the modal components, i.e.

c j i |c j i c j i c j i ≈ 0 for (i, j) = (i , j ) (4)
where

c j i |c j i def = T -1 t=0 c j i (t)c j i (t) * (5)
and

c j i 2 = c j i |c j i ( 6
)
Remark: Assumption (4) may be restrictive in certain applications. However, it can be relaxed in such a way to allow common modal components to different sources as shown in [START_REF] Aissa-El-Bey | Séparation aveugle sous-déterminée de sources audio par la méthode EMD (Empirical Mode Decomposition)[END_REF].

SEPARATION USING MODAL DECOMPOSITION

Based on the previous model, we propose an approach in two steps consisting of:

• An analysis step: in this step, one applies an algorithm of modal decomposition to each sensor output in order to extract all the harmonic components from them. We compare, for this modal components extraction two decomposition algorithms that are the EMD (Empirical Mode Decomposition) algorithm introduced in [2, 3] and a parametric algorithm which estimates the parameters of the modal components modeled as damped sinusoids.

• A synthesis step: in this step we group together the modal components corresponding to the same source in order to reconstitute the original signal. This is done by observing that all modal components of a given source signal 'live' in the same spatial direction. Therefore, the proposed clustering method is based on the component's direction evaluated by correlation of the extracted (component) signal with the observed antenna signal.

Signal analysis using EMD

A new nonlinear technique, referred to as Empirical Mode Decomposition (EMD), has recently been introduced by N.E. Huang et al. for representing non-stationary signals as sum of zero-mean AM-FM components [START_REF] Huang | The em-pirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary times series analysis[END_REF]. The starting point of the EMD is to consider oscillations in signals at a very local level. Given a signal z(t), the EMD algorithm can be summarized as follows [START_REF] Flandrin | Empirical mode decomposition as a filter bank[END_REF]:

1. Identify all extrema of z(t).

2. Interpolate between minima (resp. maxima), ending up with some envelope e min (t) (resp. e max (t)).

3. Compute the mean m(t) = (e min (t) + e max (t))/2.

Extract the detail d(t) = z(t) -m(t).

Iterate on the residual m(t).

By applying EMD algorithm to the i th mixture signal x i which is written as

x i (t) = N j=1 a ij s j (t) = N j=1 lj k=1 a ij c k j (t)
one obtains estimates c k j (t) of components c k j (t).

Parametric signal analysis

In this section we present an alternative solution for signal analysis. For that, we represent the source signal and hence the observations as sum of damped sinusoids:

x k (t) = L l=1 α l,k z t l ( 7
)
where α l,k represents the complex amplitude and z l = e d l +iω l is the l th pole where d l is the negative damping factor and ω l is the angular-frequency.

[H(x k )] n 1 n 2 def = x k (n 1 + n 2 )
, D being a window parameter chosen in the range T /3 ≤ D ≤ 2T /3. We use of Kung's algorithm given in [START_REF] Kung | Spacetime and singular-value decomposition based approximation methods for the harmonic retrieval problem[END_REF] that can be summarized in the following steps:

1. Form the data Hankel matrix H(x k ).

Estimate the

2L-dimensional signal subspace U (L) = [u 1 . . . u 2L ] of H(x k
) by means of the SVD (u 1 . . . u 2L are the principal left singular vectors of H(x k )).

3. Solve (in the least squares sense) the shift invariance equation

U (L) ↓ Ψ = U (L) ↑ ⇔ Ψ = U (L)# ↓ U (L) ↑ ( 8
)
where Ψ = Φ∆Φ -1 , Φ being a non-singular 2L × 2L matrix and ∆ = diag(z 1 , z * 1 , . . . , z L , z * L ). () # denotes the pseudo-inversion operation and arrows ↓ and ↑ denote respectively the last and the first rowdeleting operator.

4. Estimate the poles as the eigenvalues of matrix Ψ.

Estimate the complex amplitudes by solving the least squares fitting criterion

min α x k -Zα 2 ⇔ α = Z # x k ( 9
)
where

x k = [x k (0) . . . x k (T -1)
] T is the observation vector, Z is a Vandermonde matrix constructed from the estimated poles and α is the vector of complex amplitudes.

Signal synthesis using vector clustering

For the synthesis of the source signals one observes that thanks to the quasi-orthogonality assumption, one has:

x|c j i c j i 2 def = 1 c j i 2    x 1 |c j i . . . x M |c j i    ≈ a i
where a i represents the i th column vector of A. We can then associate each component c k j to a space direction (vector column of A) that is estimated by

a k j = x| c k j c k j 2
Two components of a same source signal are associated to the same column vector of A, Therefore, we propose to gather these components by clustering the vectors a k j into N classes. One will be able to rebuild the initial sources up to a constant by adding the various components within a same class.

Source pairing and selection

Let us notice, that by applying the approach described previously (analysis plus synthesis) to all the antenna outputs x 1 (t), • • • , x M (t), we obtain M estimates of each source signal. The estimation quality of a given source signal varies significantly from one sensor to another. Indeed, it depends strongly on the matrix coefficients and, in particular, on the signal to interference ratio (SIR) of the desired source. Consequently, we propose a blind selection method to choose a 'good' estimate among the M we have for each source signal. For that, we need first to pair the source estimates together. This is done by associating each source signal extracted from the first sensor to the (M -1) signals extracted from the (M -1) other sensors that are maximally correlated with it. The correlation factor of two signals s 1 and s 2 is evaluated by s 1 |s 2 s 1 s 2 . Once, the source pairing achieved, we propose to select the source estimate of maximal energy, i.e.

s i (t) = max j {E j i = T -1 t=0 | s j i (t)| 2 , j = 1, • • • , M } (10)
where E j i represents the energy of the i th source extracted from the j th sensor. One can consider other methods of selection based on the dispersion around the centroid of each class, the number of components of each source estimate, etc.

Discussion

We provide here some comments to get more insight onto the proposed separation method:

• Over-determined case: In that case, one is able to separate the sources by left inversion of matrix A. The latter can be estimated from the centroids of the N clustering classes (i.e., the centroid of the i th class represent the estimate of the i th column of A).

• Estimation of the number of sources: This is a difficult and challenging task in the underdetermined case. Few approaches exist based on multi-dimensional tensor decomposition [START_REF] Lathauwer | ICA techniques for more sources than sensors[END_REF] or based on the clustering with joint estimation of the number of classes [START_REF] Frank | The data analysis handbook[END_REF]. However, these methods are very sensitive to noise, to the source amplitude dynamic and to the conditioning of matrix A. In this paper, we assume the number of sources known (or correctly estimated).

• Number of modal components: In the parametric approach, we have to choose the number of modal components L needed to well approximate the audio signal. Indeed, small values of L lead to poor signal representation while large value of L increases the computational cost. In fact, L depends on the 'signal complexity' and in general musical signals require less components (for a good modeling) than speech signals. In section 4 we illustrate the effect of the value of L on the separation quality.

• Hybrid separation approach: It is most probably that the separation quality can be improved using signal analysis in conjonction with spatial filtering. Indeed, it has been observed that the separation quality depends strongly on the mixture coefficients. Spatial filtering can be used to improve the SIR for a desired source signal and consequently its extraction quality. This will be the focus of a future work.

SIMULATION

We present here some simulation results to illustrate the performance of our blind separation algorithms. For that, we consider a uniform linear array with M = 3 sensors receiving the signals from N = 4 audio sources (except for the third experiment where N varies in the range [START_REF] Huang | The em-pirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary times series analysis[END_REF][START_REF] Nguyen | Separating more sources than sensors using time-frequency distributions[END_REF]).

The angles of arrival of the sources are chosen randomly. formance obtained by our algorithm using EMD and the parametric technique with L = 30. As a reference, we plot also the NMSE obtained by pseudo-inversion of matrix A [10] (assumed exactly known). It is observed that both EMD and parametric based separation provide better results than those obtained by pseudo-inversion of the exact mixing matrix. The plots in figure 2 illustrate the effect of the number of components L chosen to model the audio-signal. Too small or too large values of L degrade the performance of the method. In other words, it existe an optimal choice of L that depend on the signal type. In figure 3, we present the separation performance loss that we have when the number of sources increases from 2 to 6 in the noiseless case. For N = 2 and N = 3 (overdetermined case) we estimate the sources by left inversion of the estimate of matrix A. In the underdetermined case,

CONCLUSION

This paper introduces a new blind separation method audio-type sources using modal decomposition. The proposed method can separate more sources than sensors and provides, in that case, a better separation quality than the one obtained by pseudo-inversion of the mixture matrix (even if it is known exactly). For the signal analysis step of the proposed method, two algorithms are used and compared using respectively the EMD and the ESPRIT-like technique for the estimation of the poles of the modal components modeled as damped sinusoids.

Fig. 1 .

 1 Fig. 1. NMSE versus SNR

Fig. 2 .

 2 Fig. 2. NMSE versus L: SNR=10 and 30

Fig. 3 .

 3 Fig. 3. NMSE versus N (noiseless case)

  (•) represents the real part of a complex entity. For the extraction of the modal components, we propose to use the ESPRIT-like (Estimation of Signal Parameters via Rotation Invariance Technique) technique that estimates the poles of the signals by exploiting the row-shifting invariance property of the D×(T -D) data Hankel matrix


Abdeldjalil Aissa

El Bey

Karim Abed-Meraim

Yves Grenier

A Aïssa-El-Bey

UNDERDETERMINED BLIND SEPARATION OF AUDIO SOURCES IN TIME-FREQUENCY DOMAIN

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

INTRODUCTION

Blind source separation (BSS) considers the recovery of unobserved original sources from several mixtures observed at the output of a set of sensors. Each mixture contains a combination of the sources that results from the mixing medium between the sources and the sensors. The term "blind" indicates that no a priori knowledge of the sources and the medium structure is available. To compensate for this lack of information, the sources are usually assumed to be statistically independent. Blind source separation has application in different areas, such as communications, speech processing, image processing and biomedical engineering [START_REF]Blind estimation using higher-order statistics[END_REF]. A challenging problem of BSS occurs when there are more sources than sensors, and this is referred to as underdetermined blind source separation (UBSS). A time-frequency based UBSS algorithm has been recently proposed in [START_REF] Yilmaz | Blind separation of speech mixtures via time-frequancy masking[END_REF][START_REF] Linh-Trung | Separating more sources than sensors using time-frequency distributions[END_REF] to successfully separate speech sources using time-frequency distributions (TFDs). This algorithm provides good separation performance when the sources are disjoint in the TF plane. It also provides the separation of TF quasi-disjoint sources, that is the sources are allowed to have a small degree of overlapping in the TF plane. However, the intersection points in the TF plane are not directly treated. More precisely, a point at the intersection of two sources is clustered "randomly" to belong to one of the sources. As a result, the source that picks up this point now contains some information from the other source while the later source loses some information of its own. However, for the other source, there is an interference at this point, hence the separation performance may degrade if no treatment is provided for this. An increasing in the number of intersection points degrades the separation quality. In this paper, we propose another algorithm, combining the TF-UBSS with subspace projection, that allows an explicit treatment of the intersection points. The main assumption used in this algorithm is that the number of sources simultaneously present at an intersection point in the TF plane cannot exceed the number of sensors.

PROBLEM FORMULATION

Data model

Let s(t) = [s 1 (t), . . . , s N (t)]
T represent the N nonstationary source signals. The source signals are transmitted through a medium so that an array of M linear sensors picks up a set of mixed signals represented by an M -dimensional vector

x(t) = [x 1 (t), . . . , x M (t)]
T . We consider the instantaneous mixing medium that is modeled as follows

x(t) = As(t) + w(t), (1)
where A = [a 1 , . . . , a N ] is the mixing matrix and w(t) = [w 1 (t), . . . , w M (t)] T is the observation noise vector. We assume that any M columns of A are linearly independent. The goal of BSS is to recover s(t) from x(t). When M < N , the problem becomes UBSS. Let Ω 1 and Ω 2 be the TF supports (i.e. the points of TF plane where the local energy of the considered sources is non-zero) of two sources s 1 (t) and s 2 (t).

If Ω 1 ∩ Ω 2 = ∅, the sources are said to be non-disjoint in the TF plane. The second assumption is that the sources are not necessarily disjoint, and in particular, there exist, at most, simultaneously (M -1) sources at the same TF point. However, we still assume that there exists for each source signal a region R i in the TF plane where it exists alone, i.e. the energy of the other sources are negligible at the TF points within the considered region. For this reason, a TF representation is commonly referred to as a time-frequency distribution (TFD). TFDs have been applied to a wide variety of engineering problems. Specifically, they have been successfully used for signal recovery at low signal-to-noise ratio (SNR), accurate estimation of the instantaneous frequency (IF), signal detection in communication, radar processing and for the design of time-varying filter. For more details on TFDs and related methods, see for example the recent comprehensive reference [START_REF] Boashash | Time Frequency Signal Analysis and Processing: Method and Applications[END_REF]. The method presented in this paper, uses the Short-Time Fourier Transform (STFT) that is defined as:

Time-frequency representation

S x (t, f ) = m=+∞ m=-∞ h(t -m)x(m)e -j2πf m (2)
where h(t) is the Hamming window.

CLUSTER-BASED TF-UBSS APPROACH FOR DISJOINT SOURCES

In this section, we briefly review the STFT method in [START_REF] Yilmaz | Blind separation of speech mixtures via time-frequancy masking[END_REF], and propose a cluster-based linear TF-UBSS algorithm using STFT to avoid some of the drawbacks in [START_REF] Yilmaz | Blind separation of speech mixtures via time-frequancy masking[END_REF]. First, under the transformation into the TF domain using the STFT, the model in (1) leads to:

S x (t, f ) = AS s (t, f ), (3)
where

S xi (t, f ) = m=+∞ m=-∞ h(t -m)x i (m)e -j2πf m (4a) S x (t, f ) = [S x1 (t, f ), . . . , S xM (t, f )] T . ( 4b
)
and S s (t, f ) is the N × 1 source STFT vector. To avoid processing all TF points (and hence to reduce computational cost), we apply first a noise thresholding as that for each timeslice (t, f ):

If S x (t, f 0 ) max f { S x (t, f ) } > ǫ, then keep (t, f 0 ), ( 5
)
where ǫ is a small threshold (typically, ǫ = 0.05). Then, the set of all selected points, Ω, is expressed by Ω = N i=1 Ω i , where Ω i is the TF support of the source s i (t). Under the assumption that all sources are disjoint in the TF domain, (3) is reduced to

S x (t, f ) = a i S si (t, f ), ∀(t, f ) ∈ Ω i , ∀i = 1, • • • , N. (6)
where the source STFT vector has been reduced to only the STFT of the source s i (t). Now, in [START_REF] Yilmaz | Blind separation of speech mixtures via time-frequancy masking[END_REF], the structure of the mixing matrix is particular as such it has only 2 rows (i.e. the method uses only 2 sensors) and the first row of the mixing matrix contains all 1. Then, ( 3) is expanded to

S x1 (t, f ) S x2 (t, f ) = 1 . . . 1 a 2,1 . . . a 2,N    S s1 (t, f ) . . . S sN (t, f )    , (7)
and ( 6) to

S x1 (t, f ) S x2 (t, f ) = 1 a 2,i S si (t, f ),
which results in

a 2,i = S x2 (t, f ) S x1 (t, f ) . (8)
Therefore, all the points for which the ratios on the right-hand side of ( 8) have the same value form the TF support Ω i of a single source, say s i (t). Then, the STFT estimate of s i (t) is computed by:

Ŝsi (t, f ) = S x1 (t, f ), ∀(t, f ) ∈ Ω i , 0, otherwise.
Finally, the source estimate ŝi (t) is obtained by converting Ŝsi (t, f ) to the time domain using inverse STFT [START_REF] Griffin | Signal estimation from modified short-time Fourier transform[END_REF]. For more details, refer to this paper. It is observed that the structure of the mixing matrix, as expressed in (7) has some limiting factors. First, the extension of the UBSS method in [START_REF] Yilmaz | Blind separation of speech mixtures via time-frequancy masking[END_REF] to more than two sensors is not obvious. Second, the division on the right-hand side of ( 8) is prone to error if the denominator is close to zero. To avoid the above mentioned problems, we propose here a modified version of the method valid for any number of sensors. This method is now referred to as the cluster-based linear TF-UBSS algorithm. The clustering method proceeds as follows: first compute the spatial direction vectors by:

v(t, f ) = S x (t, f ) S x (t, f ) , (t, f ) ∈ Ω, (9)
and force them, without loss of generality, to have the first entry real and positive. Next, we cluster these vectors into N classes {C i | i = 1, • • • , N }, using the k-mean clustering algorithm [START_REF] Frank | The data analysis handbook[END_REF]. The collection of all points, whose vectors belong to the class C i , now forms 2. Vector clustering by (9) and [START_REF] Frank | The data analysis handbook[END_REF].

3. Mixing matrix and source STFT estimation by ( 10) and (11).

4. Source TF synthesis by [START_REF] Griffin | Signal estimation from modified short-time Fourier transform[END_REF].

the TF support Ω i of the source s i (t). Then, the column vector a i of A is estimated as the centroid of this set of vectors:

âi = 1 |C i | (t,f )∈Ωi v(t, f ), ( 10
)
where |C i | is the number of vectors in this class. Therefore, we can estimate the STFT of each source s i (t) (up to scalar constant) by:

Ŝsi (t, f ) = âH i S x (t, f ), ∀ (t, f ) ∈ Ω i , (11)
since, from (6), we have

âH i S x (t, f ) = âH i a i S si (t, f ) ∝ S si (t, f ), ∀ (t, f ) ∈ Ω i .
This algorithm is summarized in Table 1.

SUBSPACE-BASED TF-UBSS APPROACH FOR NON-DISJOINT SOURCES

We propose here to use an appropriate subspace projection to estimate the TFDs of the individual sources, under the previously stated data assumptions. Under the TF non-disjoint condition, consider a source point (t, f ) ∈ Ω at which there are K contributing sources s α1 (t), . . . , s αK (t), with K < M . Then, (3) is reduced to the following

S x (t, f ) = ÃS s(t, f ), ∀(t, f ) ∈ Ω (12)
where à and s are defined by:

s = [s α1 (t), . . . , s αK (t)] T , (13a) Ã = [a α1 , . . . , a αK ]. ( 13b
)
Let Q Ã be the orthogonal projection matrix onto the noise subspace of Ã. Then, Q Ã can be computed by:

Q Ã = I -Ã ÃH Ã -1 ÃH . (14)
We have the following observation:

Q Ãa i = 0, i ∈ {α 1 , . . . , α K } Q Ãa i = 0, otherwise . (15)
Table 2. Subspace-based TF-UBSS algorithm 1. STFT computation.

2. Single-source point selection; mixing matrix estimation by, k-mean algorithm.

3. For all source points, perform subspace-based TFD estimation of sources by ( 14), ( 16) and (17).

4. Source TF synthesis by [START_REF] Griffin | Signal estimation from modified short-time Fourier transform[END_REF].

If A is known or a priori estimated, then this observation gives us the criterion to detect the indices α 1 , . . . , α K ; and hence, the contributing sources at the considered TF point (t, f ). In practice, to take into account noise, one detects the column vectors of à minimizing:

{α 1 , . . . , α K } = arg min β1,...,βK Q ÃS x (t, f ) | Ãβ (16)
where Ãβ = [a β1 , . . . , a βK ].

Next, TFD values of the K sources at TF point (t, f ) are estimated by:

Ŝs (t, f ) ≈ Ã# S x (t, f ). (17)
where Ã# represents the pseudo-inverse of Ã. Now, to apply the above procedure, we need to estimate A first. This is performed here by clustering all the spatial direction vectors in (9) as for the preview TF-UBSS algorithm. Then within each class C i we estimate the far-located vectors from the centroid (in the simulation we estimate vectors v(t, f ) such that: v(t, f )-âi > 0.8 max

v(t,f )∈Ωi v(t, f )-âi
leading to a reduced size class Ci . This is to essentially keep the vectors corresponding to the TF region R i (which are ideally equal to the spatial direction a i of the considered source signal). Finally, the i th column vector of A is estimated as the centroid of Ci . Table 2 provides a summary of the subspace projection based TF-UBSS algorithm.

SIMULATIONS AND RESULTS

Simulation results are illustrated in the figures below. In this simulation, we have used uniform linear array of M = 3 sensors. It receives signals from N = 4 independent speech sources, lasting 8192 samples. In figure 2, the upper line represents the original source signals, the second line represents the M mixtures and the bottom one represents the sources estimates by our algorithm. In figure 3, we compare the performance of our method with the TF-UBSS method of

CONCLUSION

This paper introduces a new approach for blind separation of non-disjoint and nonstationary sources using TFDs. The proposed method can separate more sources than sensors and provides, in the case of non-disjoint sources, a better separation quality than the method proposed in [START_REF] Yilmaz | Blind separation of speech mixtures via time-frequancy masking[END_REF]. This method is based on a vector clustering procedure that estimates the mixing matrix A, and subspace projection to separate the sources at the intersection points in the TF plane.

Fig. 1 .

 1 Fig. 1. (a)-TF disjoint, (b) TF non-disjoint

Fig. 2 .

 2 Fig. 2. Blind source separation example for 4 speech sources and 3 sensors in instantaneous mixture case: the upper line represents the original source signals, the second line represents the M mixtures and the bottom one represents estimates of sources by our algorithm.

Fig. 3 .

 3 Fig. 3. NMSE versus SNR for 4 speech sources and 3 sensors: comparison of the performance of our algorithm with the modified TF-UBSS

Table 1 .

 1 Cluster-based TF-UBSS algorithm 1. Mixture STFT computation by (4).

Table 1

 1 (i.e. modified method of[START_REF] Yilmaz | Blind separation of speech mixtures via time-frequancy masking[END_REF]). The plots represents the average normalized MSE (NMSE) of the estimated sources versus the SNR in dB. For the subspace-based method we have used K = 2 for all TF points. As can be observed, a significatif gain is obtained, thanks to our subspace projection.

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Karl J Wittmann
email: karl.wittmann@meduniwien.ac.at

Pierre Chevaldonné
email: pierre.chevaldonne@imbe.fr

Description of Heteromysis (Olivemysis) ekamako sp. nov. (Mysida, Mysidae, Heteromysinae) from a marine cave at Nuku Hiva Island (Marquesas, French Polynesia, Pacific Ocean)

Keywords:

Combined faunistic and genetic studies in the marine Ekamako Cave at the southern coast of Nuku Hiva, Marquesas, in the central Pacific yielded Heteromysis (Olivemysis) ekamako as a new species. This taxon differs from its congeners by a specific combination of morphological characters: flagellate, modified spines dorsally on each of the three segments of the antennular peduncle, a large smooth spine at the tip of only the second male pleopod, series of small flagellate spines along the oblique -1 -terminal margin of only the third and fourth male pleopods, and by 2-3 simple spines medially near the statocyst on the endopods of uropods. Although abundant at the entrance of Ekamako Cave, it has not been observed in nine additional submersed marine caves investigated at the Marquesas.

Introduction

It has been about three decades since the detection of Aberomysis muranoi and Palaumysis simonae at islands of Palau (Micronesia) and their description by [START_REF] Băcescu | Contribution to the knowledge of Mysidacea from western Pacific: Aberomysis muranoi n.gen., n.sp. and Palaumysis simonae n.gen., n.sp. from marine caves on Palau, Micronesia[END_REF]. Now, the further inspection of marine caves in remote, geographically isolated, oceanic archipelagos -this time in Marquesas Islands, French Polynesia in the Central Pacific -again yielded an endemic species of Mysidae with comparatively large eyes. This mysid is described here as a new species of the genus Heteromysis S.I. Smith, 1873. Most of the so-far described 83 species of this genus are known from cryptic habitats in a broader sense. Nonetheless, only five species were previously reported from marine caves: the Caribbean H. guitarti [START_REF] Băcescu | Heteromysini nouveaux des eaux cubaines: trois espèces nouvelles de Heteromysis et Heteromysoides spongicola n.g. n.sp[END_REF], H. bermudensis Sars, 1885, H. cyanogoleus Bamber, 2000, and the Indian Ocean species H. dentata Hanamura &Kase, 2001, andH. longiloba Hanamura &Kase, 2001. The species described below is the first Heteromysis from a marine cave in the Pacific.

Material and methods

Samples were collected during the French Agency of Marine Protected Areas (AAMP) biodiversity survey 'Pakaihi i te Moana' aboard the R/V Braveheart [START_REF] Poupin | Deep-water decapod crustaceans studied with a remotely operated vehicle (ROV) in the Marquesas Islands, French Polynesia (Crustacea: Decapoda)[END_REF]. Leg 3 (10-30 January 2012) was devoted to the deep sea and to the shallowwater caves. Three dives recovered mysid samples (leg. P. Chevaldonné), all from Ekamako Cave (Pérez et al. in press) at 8-10 m depth, 10-30 m from the entrance: 9 specimens upon dive #445, 7 Jan. 2012 (sample #MQ1-GR-PC1), 39 upon dive #451, 12 Jan. 2012 (sample #MQ1-GR-PC5), and 131 upon dive #468, 28 Jan. 2012 (sample #MQ1-GR-PC13). Collection took place with a suction bottle operated by SCUBA diver [START_REF] Chevaldonné | Improvements to the "Sket bottle": a simple manual device for sampling small crustaceans from marine caves and other cryptic habitats[END_REF]. Collected mysids were then stored in 95% ethanol.

Body size was measured from the tip of the rostrum to the posterior margin of the telson, excluding the spines. Further details on preparation, measurements, and examination of materials follow [START_REF] Wittmann | Two new species of Heteromysini (Mysida, Mysidae) from the Island of Madeira (N.E. Atlantic), with notes on sea anemone and hermit crab commensalisms in the genus Heteromysis S. I. Smith[END_REF] and citations therein; morphological terminology as in [START_REF] Wittmann | Orders Lophogastrida Boas, 1883, Stygiomysida Tchindonova, 1981, and Mysida Boas, 1883 (also known collectively as Mysidacea)[END_REF].

In order to obtain DNA barcodes of the new species, total genomic DNA was extracted as in [START_REF] Chevaldonné | Molecular and distribution data on the poorly known, elusive, cave mysid Harmelinella mariannae (Crustacea: Mysida)[END_REF] from two specimens from dive #445 (Heka445-1 and Heka445-2). A fragment of the nuclear gene of the small subunit ribosomal RNA (18S) has already been published by [START_REF] Chevaldonné | Molecular and distribution data on the poorly known, elusive, cave mysid Harmelinella mariannae (Crustacea: Mysida)[END_REF]. The present study also amplified a 658 bp fragment of the mitochondrial gene coding for cytochrome c oxidase subunit I (COI) using classical PCR protocols [START_REF] Chevaldonné | Molecular and distribution data on the poorly known, elusive, cave mysid Harmelinella mariannae (Crustacea: Mysida)[END_REF].

Results

Family

Etymology

The species name is used in apposition, adopted from the name of the type locality, the Ekamako Cave.

Definition

Carapace shows a well-formed subtriangular rostrum ending in a rounded apex. Large eyes with cornea occupying distal 30-40% eye surface. Medial margin of eyestalks produced in an obliquely anterior facing, acute spiniform extension. Each of the three articles of the antennular peduncle dorsally with a disto-medial flagellate spine (spinelike seta). Stout antennal scale extends beyond the (more basally inserting) trunk of the antennal flagellum but not beyond the antennular peduncle. Third thoracic endopod with 6-7 subapically flagellate, serrated, strongly modified spines on medial margin of carpus. Tip of each penis with two finger-like lobes and a rounded, flattened, posteriorly directed lobe. Second male pleopod apically ending in a large, non-flagellate spine; third male pleopod with series of 5-9 flagellate spines along distal margin; fourth male pleopod with series of 13-26 smaller flagellate spines in this position. Uropodal endopod armed with only 2-3 spines. Each lateral margin of telson armed with 5-6 spines along distal half, not counting the pair of apical spines; outer apical spine 3-4 times longer than inner; proximally rounded 'V'-shaped terminal cleft occupies 25-28% length of telson, anterior 78-83% of its margins armed with 18-21 acute laminae.

Description

Small, robust, light-red mysids with cephalothorax occupying 37-41% body length, pleon (without telson) 48-51%, and carapace 29-34%. Abdominal somites 1-5 are 0.8-0.9, 0.9-1.0, 0.8-1.0, 0.7-0.9, and 0.7-0.9 times the length of the sixth somite, respectively.

Carapace (Fig. 1A-C) normal, without apparent sexual dimorphism. Its anterolateral edges appear roughly evenly rounded. Cervical sulcus strongly developed, cardial sulcus less apparent but always evident. Posterior margin of carapace evenly rounded, weakly emarginated, leaving only the ultimate thoracic somite dorsally exposed. Arrangement of pores on carapace closely resembles that in H. dardani [START_REF] Wittmann | Two new species of Heteromysini (Mysida, Mysidae) from the Island of Madeira (N.E. Atlantic), with notes on sea anemone and hermit crab commensalisms in the genus Heteromysis S. I. Smith[END_REF]: a group of 10-12 pores with about 1 µm diameter are in median position behind the cardial sulcus. These pores surround a larger, less distinctly porelike structure in a roughly butterfly-shaped manner (Fig. 1C). In front of the cervical sulcus there is an additional group of 19-22 pores in roughly 'V'-shaped arrangement (Fig. 1B). Except for sulci and pores, the outer surface of the carapace is smooth in both sexes.

Eyes (Fig. 1A,D). Eyes well developed, stalk and cornea thick. Eyestalks and cornea dorsoventrally somewhat compressed. Cornea calotte-shaped in dorsal, oval in lateral, and calotte-shaped to sub-reniform in ventral view. Eyestalks with small group of scales on the inner basal corner.

Antennulae (Fig. 1A,D,). Peduncle three-segmented, whereby 42-44% of its length is occupied by the basal segment, 17-20% by the middle, and 35-41% by the terminal one. Basal segment terminally with a small dorsal and a larger outer setose apophysis. The dorsal apophysis anteriorly with 3-4 plumose setae, a slender smooth seta, and a modified spine (spine-like seta) with a subapical flagellum (Fig. 1E,J,K).

Median segment anteriorly obliquely truncate, its anterior margin with a flagellate spine (Fig. 1G,H) accompanied by a large plumose seta near inner distal corner. Flagellate spine from this segment (Fig. 1G,H) more seta-like and bearing its flagellum in more apical position compared to those from the basal (Fig. 1J,K) and the terminal (Fig. 1F, L, M) segment. Terminal segment also bearing a specialized setation at its inner distal corner: 1-2 large, medially directed, plumose setae on ventral face versus an obliquely laterally directed thicker, smooth seta, plus an obliquely medially-anteriorly directed, flagellate spine on dorsal face (Fig. 1F,L,M). Males with short, rounded appendix masculina in submedian, almost terminal position on the ventral surface of the terminal segment (Fig. 1L). This appendix shows a tuft of rather few, comparatively short setae extending obliquely downwards. In both sexes, the outer antennular flagellum is thicker than the inner one, by a factor of 1.4-2.2 when measured near the basis of the flagella.

Antennae (Fig. 1A,D). Antennal scale without spines, setose all around; its length 2.9-3.8 times maximum width. A small apical segment of 6-9% scale length is marked by a transverse suture; this segment broader than long, with five plumose setae.

Antennal sympod shows a forward projecting, tongue-like, terminally rounded process.

Posteriorly it bears a roughly ovoid lobe containing the end sac of the antennal gland.

Three-segmented antennal trunk slightly longer than the antennal scale, nonetheless not reaching up to the tip of the scale due to its more basal position. Basal segment amounts to 16-19% of trunk length, second to 48-50% and third to 32-35%.

Mouthparts. Labrum, mandibles, labium and maxillae as normal in this genus.

Mandibular palp normal, three-segmented. Basal segment is 11-14% palp length, median segment 60-65%, terminal segment 21-26%. Basal segment smooth all around.

Median segment is 2.4-2.9 times its maximum width. Only normal setae along the inner and outer margins of the median segment, with the reservation that the distal half of the outer margin is largely smooth, bearing only 1-2 setae. Pars molaris showing a strong grinding surface in both mandibles. Pars incisivus with 1-2 large teeth, digitus mobilis with two large plus 2-4 small teeth, and pars centralis ('spine row' in the terminology of [START_REF] Tattersall | The British Mysidacea[END_REF] with three very spiny teeth. Only smooth spines terminally at the distal segment of the maxillula, where there is a transverse row of three plumose setae in subterminal position. Closely in front of the basis of these setae there is a total of only 2-4 pores in variable arrangement. Endite of the maxillula with three large, spine-like setae at tip, and with additional 12-14 smaller setae in more proximal position, these latter setae with diverse small modifications. Thoracopods (general; Fig. 2). Basal plate of exopods 1-7 shows a distinct lateral expansion (Fig. 2A,B), so that plate length is only 1.4-2.3 times maximum width. By contrast, this relation is 2.0-3.0 in the basally less expanded exopod 8 (Fig. 2H). Outer margin of the plate ends in a rounded edge (Fig. 2A,B,H). However, in both sexes any exopod may bear a minute, rounded to acute knob at this edge, as shown in Fig. 2B, in contrast to the absence of knobs in Fig. 2A,H. Flagellum 8-segmented in first exopod, 9-segmented in exopods 2-7, whereas 8-or 9-segmented in eighth exopod (Fig. 2H), not counting the large intersegmental joint between basis and flagellum. The first thoracopods bear a comparatively large, leaf-like, smooth epipod. Length of endopods increases in order of thoracopods 1, 2, 4, 3, 8, 6, 7, and 5 (Fig. 2A,B,H). Length of ischium increases from first to last endopod. Merus longer than ischium in endopods 1-4 (Fig. 2A,B), whereas shorter than ischium in endopods 5-8 (Fig. 2H). Carpopropodus of endopods 1-8 with 2, 2, 2, 3, 3-5, 4-5, 4-5, and 4-5 segments, respectively (Fig. 2A,B,D,H). Carpus and dactylus always entire. Endopod 3 (Fig. 2A,B) with powerful carpus 0.5-0.7 times the length of the merus, or 0.8-1.0 times ischium. Thoracic endopods 1-2 each with large dactylus, endopod 3 with a relatively smaller one (Fig. 2A,B), and finally endopods 4-8 with again smaller but always distinct dactylus (Fig. 2D,E,H,J). Length of claws increasing in order of endopods 5, 6, 7, 8, 1, 3, and 4 (Fig. 2A,B,E,J). Claw of thoracic endopod 2 missing, claw of endopod 3 being the most powerful one (Fig. 2A,B), whereas claw of endopod 4 is the longest but also the thinnest one (Fig. 2E).

Endopod of first and second thoracopods modified as maxilliped. Coxa of first maxilliped with broadly and continuously rounded endite bearing one plumose seta; its basis with large prominent endite, whereas ischium and merus with merely a feebly projecting endite. The endites of basis, ischium, and merus are hairy and densely setose on inner margin. Dactylus characterized by a strong, subapically serrated claw. Basis of second maxilliped shows a distinctly projecting endite which is slightly larger in males than in females. In both sexes, the merus is slender, longer than combined praeischium and ischium, but somewhat shorter than combined carpopropodus and dactylus.

Dactylus with a dense brush of setae only. 10-14 among these setae are spine-like modified, bearing series of teeth in their median portions on either side. A true claw is missing on the dactylus of only the second maxilliped.

Endopod of third thoracopod modified as gnathopod (Fig. 2A-C). Basis with much shorter endite compared to that of the second endopod. Ischium and merus strong as is normal in gnathopods. Along the outer margin of the merus there are 4-5 setae that are unilaterally barbed along their median to subterminal portions. Third thoracic endopod moderately dimorphic: maximum length of the carpopropodus is 2.1-2.3 times its maximum width in males, compared to 3.0-3.3 in females. Maximum length of the carpopropodus, expressed in the same order (males versus females), is 0.7-0.8 versus 0.6-0.7 times that of the merus and 1.1-1.2 versus 0.9-1.1 that of the ischium. Both sexes with carpus showing 6-7 subapically flagellate spines (Fig. 2C) along terminal 35-55% of its medial margin. These spines with their inner margin serrate between subbasal portions and the flagellum; outer margin with a rugged subbasal portion (Fig. 2C). These spines arranged in three pairs plus one optional, unpaired, weaker spine in most basal position. The paired partners are located side by side at about the same position along the carpus (therefore only one of each shown in Fig. 2A). Claw smooth, strong, with apically increasing curvature (Fig. 2A,B).

Endopod of fourth to eighth thoracopods (Fig. 2D-J). These legs are moderately long and slender. Fifth endopod, when stretched, extending shortly beyond the rostrum, the eighth endopod up to the labrum. Basis of endopods 4-8 with lappet-to tongue-like apophysis in both sexes; this apophysis extends beyond the inner margin of the basis only in endopods 6-8 of females (Fig. 2G), but not in males (Fig. 2F,H). Fourth endopod with small dactylus bearing a long, almost straight, very thin and seta-like claw (Fig. 2D,E). Dactylus of endopods 5-8 equipped with stronger, short claw armed with acute, spine-like cilia (Fig. 2J) along its median portions and showing a distally increasing curvature. These cilia become continuously larger towards the tip of the claw (Fig. 2J). Endopods 5-8 each with three large, almost smooth and strongly curved paradactylary setae (Fig. 2H). Corresponding setae on endopod 4 much more weakly curved (Fig. 2D).

Marsupium. Females with large oostegites on thoracopods 7, 8. Thoracopod 6 with rudimentary oostegite represented merely by a small lobe with three plumose setae (Fig. 2G).

Penes (Fig. 2H). Penes slender, only slightly shorter than the merus of the ultimate thoracic endopod. Their shape roughly that of tubes, weakly bent forwards, even more weakly also outwards. Each penis stiff, with smooth cuticle all around, except for one small, plumose seta at about one third of its length on the exterior face; tip with lobes.

Thoracic sternal processes (Fig. 1N,O). Both sexes with a subtriangular, anteriorly directed, terminally rounded process from first thoracic sternite. No additional processes in females. Males with additional small, smooth, median bulge from first thoracic sternite and with median processes from thoracic sternites 2-8. These latter are small simple processes from sternites 2, 7, 8, but larger and terminally finger-like from sternites 3-6, each flanked by two shorter medio-lateral processes (Fig. 1N). Only females with fields of hairs on sternites 2-5 (Fig. 1O).

Pleopods (Fig. 3A-G). Pleopods reduced to small setose, bilobate, or obscurely bilobate plates in both sexes. Length without setae or spines increases from first to fifth pleopods in both sexes. However, more discontinuously in males, with a stronger increase between pleopods one and three versus a weak, inconspicuous increase in numbers three to five. All pleopods of females (Fig. 3A) and pleopods 1, 5 of males (Fig. 3B,F) lacking spines. For spines on second (Fig. 3C), third (Fig. 3D), and fourth (Fig. 3E) male pleopods, see 'Definition' above. A small flagellum (Fig. 3G) inserts shortly below the tip of each flagellate spine (= spine-like seta) on male pleopods 3, 4.

Not considering spine-like setae, all setae of females and most setae of males are plumose, at least in their apical portions. A smooth seta found only on the tip of pleopod 4 in males (Fig. 3E). Uropods (Fig. 3H). The exopods reach with 12-20% of their length beyond the endopods and 40-53% beyond the telson, nonetheless the endopods 31-44% of their length beyond the telson. Exopods 3.7-3.8 times longer than their maximum width.

Their medial margin much more strongly convex than the outer one. Endopods with 2-3 spines on medial margin, in subbasal position near statocyst. This statocyst large, containing a comparatively small statolith with a diameter of 55-60 µm. The statoliths are discoidal showing an indistinct fundus and a distinct tegmen; statolith formula is 2 + 3 + (6-10) + (4-6) = 16-20 (N = 5 statoliths from 3 dissected specimens). Mineral composition is fluorite (as also in eight Heteromysis species examined by [START_REF] Ariani | A comparative study of static bodies in mysid crustaceans: evolutionary implications of crystallographic characteristics[END_REF][START_REF] Wittmann | Heteromysis arianii sp.n., a new benthic mysid (Crustacea, Mysidacea) from coralloid habitats in the Gulf of Naples (Mediterranean Sea)[END_REF][START_REF] Wittmann | Centennial changes in the near-shore mysid fauna of the Gulf of Naples (Mediterranean Sea), with description of Heteromysis riedli sp. n. (Crustacea, Mysidacea)[END_REF][START_REF] Wittmann | Two new species of Heteromysini (Mysida, Mysidae) from the Island of Madeira (N.E. Atlantic), with notes on sea anemone and hermit crab commensalisms in the genus Heteromysis S. I. Smith[END_REF].

-12 -Telson (Fig. 3J) length 1.10-1.15 times that of the sixth pleonite and 0.65-0.76 times the uropodal exopod. Telson subtriangular with length 1.3-1.4 times its maximum width. Lateral margins straight to slightly concave. Apical cleft distinctly deeper than wide. Margins of cleft lined by acute laminae that are slightly shorter up to equally sized compared with average-sized spines on the lateral margins of the telson. For further details of the telson, see 'Definition' above.

Eggs and larvae (Fig. 3K-M)

The female with 4.8 mm body length carried five eggs with 0.35-0.38 mm diameter.

Two females with 3.8 and 4.3 mm, respectively, each carried a total of four late stage 2 nauplioid larvae. These larvae bear short setae at the tip of antennula and antenna (Fig. 3L), and of the tail (Fig. 3M). Their setae much smaller than, for example, in the nauplioids of Heteromysis (Olivemysis) wirtzi [START_REF] Wittmann | Two new species of Heteromysini (Mysida, Mysidae) from the Island of Madeira (N.E. Atlantic), with notes on sea anemone and hermit crab commensalisms in the genus Heteromysis S. I. Smith[END_REF], from the N.E. Atlantic (Wittmann 2008: Fig. 4m, n).

DNA sequences

The two specimens extracted yielded the same 818 bp 18S sequence (accession # HG315710; [START_REF] Chevaldonné | Molecular and distribution data on the poorly known, elusive, cave mysid Harmelinella mariannae (Crustacea: Mysida)[END_REF]. The COI amplifications, however, revealed one different haplotype for each specimen (2 synonymous substitutions). These two COI haplotypes have been deposited at the ENA-EMBL database (accession # LT555314-LT555315).

Discussion

The new species, Heteromysis ekamako, from a marine cave at an island in the central Pacific Ocean, shows very close morphological similarities with two species from the West Atlantic, H. mayana [START_REF] Brattegard | Mysidacea from shallow water in the Caribbean Sea[END_REF], from diverse shallow-water habitats, occasionally associated with sea anemones, along the Caribbean coast of Mexico, and with H. gomezi [START_REF] Băcescu | New spongicolous Heteromysis of the Caribbean Sea (H. gomezi n.sp. and H. mariani n.sp.)[END_REF], associated with sponges in Cuba. Besides the 'normal' features shared by members of the subgenus Olivemysis Băcescu, 1968, these three species share a single, large spine on the tip of the second male pleopod. They also share most of the other details of eyes, pleopods 2-5, uropods, and telson, given by [START_REF] Băcescu | Heteromysini nouveaux des eaux cubaines: trois espèces nouvelles de Heteromysis et Heteromysoides spongicola n.g. n.sp[END_REF][START_REF] Băcescu | New spongicolous Heteromysis of the Caribbean Sea (H. gomezi n.sp. and H. mariani n.sp.)[END_REF] and [START_REF] Brattegard | Mysidacea from shallow water in the Caribbean Sea[END_REF]. No other known species, particularly no Pacific species, shows such great similarities with the new species, especially regarding the second male pleopod. Nonetheless, the new Pacific species differs from the two Caribbean ones, among other features, by modified, flagellate spines (Fig. 1G-K) on basal and median segments of the antennular peduncle in both sexes, by a normal first male pleopod (Fig. 3B) without terminal spine, and by fewer flagellate spines on the third male pleopod (Fig. 3D).

The DNA sequences obtained provide little further information on the systematic relationships of H. ekamako with other Heteromysinae because of the scarcity of such sequences in DNA databases. This is particularly true for the COI sequences which only poorly match (ca. 80% identity) general Mysida sequences, due to the saturation of this marker. They will, however, be useful for future reference in the taxonomy of cave and/or Polynesian Heteromysinae. In contrast, the 18S sequences were compared to several other Heteromysis entries in GenBank, confirming their position in a Heteromysis clade as shown in [START_REF] Chevaldonné | Molecular and distribution data on the poorly known, elusive, cave mysid Harmelinella mariannae (Crustacea: Mysida)[END_REF].

There is surprisingly very little literature that refers to mysids in the shallow waters of Polynesia (but see [START_REF] Murano | New and already known species of the genus Anisomysis (Mysidacea) from Hawaii and the Society Islands[END_REF]. H. ekamako is, however, rather conspicuous at the entrance of Ekamako Cave, south of Nuku Hiva, where it forms dense aggregations just above the very fine sandy bottom. It is most abundant immediately after the entrance, between 10 and 30 m inside the cave, where large ripple-marks testify to the prominent influence of the powerful oceanic swell at this shallow depth (Pérez et al. in press).

Importantly, although similar exploration was conducted in ten caves throughout the whole Marquesas archipelago (from Fatu Hiva in the south to Hatutaa in the north), H. ekamako was found only at its type locality in Nuku Hiva (Pérez et al. in press). The reason for such a restricted distribution is yet unknown but apparently frequent in cave Heteromysinae [START_REF] Wittmann | Retromysis nura new genus and species (Mysidacea, Mysidae, Heteromysini) from a superficial marine cave in Minorca (Balearic Islands, Mediterranean Sea)[END_REF][START_REF] Chevaldonné | Molecular and distribution data on the poorly known, elusive, cave mysid Harmelinella mariannae (Crustacea: Mysida)[END_REF]. One singularity of Ekamako cave, however, is that it is the largest explored so far in the Marquesas. It is at least 100 m long and several metres wide, with a large entrance, but also more or less isolated chambers (Pérez et al. in press) that may provide a unique diversity of microhabitats favourable to the permanent residence of a large population of H. ekamako.

Conflict of Interest:

The authors declare that they have no conflict of interest.

Zoologie, Vol. 4 Part B (54), Brill, Leiden, pp 189-396, colour plates pp 404-406

Figure captions

Fig. 1 Heteromysis (Olivemysis) ekamako sp. nov., paratypes; A-C, male 3.8 mm; D, H, K, M, O, female 4.8 mm; E-G, J, L, N, male 3.7 mm. A, anterior body region of male, dorsal; B, cervical pore group on carapace; C, cardial pore group on carapace; D, cephalic region of female, dorsal; E, male antennula, dorsal; F-K, modified, flagellate spines of the antennula in male (F, G, J) and female (H, K); L, terminal segment of male antennular peduncle, ventral; M, the same for female, dorsal; N, thoracic sternites of male; O, first and second thoracic sternites of female [print in B/W; adjust printed width for fit with printed page width]

  Heteromysis sp.,Chevaldonné et al. (2015: Fig. 5) Heteromysis,Pérez et al. (in press) Type material From dive #451: holotype, adult male (body size 3.7 mm), paratypes: five adult females (3.8-5.0 mm), one subadult female (3.6 mm), and four immatures of both sexes (2.6-2.8 mm); three paratypes were completely dissected: two adult males (3.7, 3.8 mm) and one adult female (4.8 mm). From dive #468: paratypes, 4 adult males (3.6-4.0 mm). The types are deposited in the Naturhistorisches Museum Wien (Vienna), crustacean collection: holotype, adult male (reg. no. NHMW 25722) and paratypes, 2 adult females from dive #451 (NHMW 25723), 2 adult males from dive #468 (NHMW 25724); and in the Muséum National d'Histoire Naturelle in Paris: 9 paratypes (1 adult male, 3 adult females, 1 subadult female, 4 immatures) from dive #451 (MNHN-IU-2014-17470), 2 paratypes (adult males) from dive #468 (MNHN-IU-2014-17471). The dissected specimens were retained by one of us (KJW) as the slides will degrade within a few decades. Type locality Ekamako Cave at the southern coast of Nuku Hiva Island, Marquesas, French Polynesia, Pacific Ocean, 08°56.215'S 140°05.450'W. Notes on microdistribution are given by Pérez et al. (in press): see also Discussion.

Fig. 2

 2 Fig. 2 Heteromysis (Olivemysis) ekamako sp. nov., paratypes; A, G, female 4.8 mm; B-

Fig. 3

 3 Fig. 3 Heteromysis (Olivemysis) ekamako sp. nov., paratypes; A, female 4.8 mm; B-J,

Acknowledgements

We first of all wish to thank Thierry Pérez for leading Leg 3 of the "Pakaihi I Te Moana" expedition and for the Ekamako cave dives with one of us (PC). We are also indebted to Xavier "Pipapo" Curvat for showing us the cave, to Laurent Albenga and John Starmer for their hard work underwater and to the captain and crew of R/V Braveheart. The French Agence des Aires Marines Protégées (AAMP) was the main sponsor and coordinator of this expedition. The Marquesan people are warmly thanked for their spirit and hospitality.


Chhavarath Dary

Sok-Siya Bun
email: sok-siya.bun@univ-amu.fr.

Gaëtan Herbette

Hot Bun Fathi Mabrouki

Hot Bun e Sothea Kim

Florian Jabbour

Sovanmoly Hul

Béatrice Baghdikian

Evelyne Ollivier

Chemical profiling of the tuber of Stephania cambodica Gagnep. (Menispermaceae) and analytical control by UHPLC-DAD

Keywords: Accuracy profile, alkaloid, method validation, palmatine, quantification, roemerine, tetrahydropalmatine

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

Introduction

Stephania cambodica Gagnep. (Menispermaceae) is a woody climber found in mountainous regions in Cambodia and Vietnam. The main characteristic of this species is the absence of leaves during the blooming period. Mature individuals of S. cambodica often have multiple tubers lying on rocks and are interconnected with a woody stem (Figure S1). Known by its Cambodian vernacular name "Komar Pich", the plant tuber has been traditionally used by local people in forms of decoction or hydroethanolic macerate to treat various diseases and symptoms such as anxiety, malaria, fever, wounds, joint pains, fatigue and male sexual dysfunction (Center of Traditional Medicine 2013). In Vietnam, the tuber of S. cambodica is used in combination with other plants for treatment of various diseases such as depression, asthma, hypertension… [START_REF] Do | Selected Medicinal Plants in Vietnam[END_REF]. Despite its well-established use, few phytochemical studies have been undertaken on S.cambodica [START_REF] Thanh | Two protoberberine alkaloids isolated from tuber of Stephania cambodica Gagnep. (Menispermaceae)[END_REF][START_REF] Dinh | Interaction of Vietnamese Medicinal Plant Extracts with Recombinantly Expressed Human Neurokinin-1 Receptor[END_REF].

Rotundine (l-tetrahydropalmatine) the main alkaloid isolated from S. cambodica tuber has been shown to be responsible for the inhibition of neurokinine-1 receptor gene expression [START_REF] Dinh | Interaction of Vietnamese Medicinal Plant Extracts with Recombinantly Expressed Human Neurokinin-1 Receptor[END_REF]. The presence of rotundine in S. cambodica tuber could justify its traditional use as an anxiolytic remedy in Cambodia since in Vietnam and China, rotundine is used as an anxiolytic and hypnotic drug [START_REF] Wang | Treatment of Cocaine Addiction[END_REF]. This neuro-sedative activity was also shown in rats and mice [START_REF] Semwal | Efficacy and safety of Stephania glabra: An alkaloid-rich traditional medicinal plant[END_REF].

Liquid chromatography is widely used for quality control of alkaloids from Stephania species [START_REF] Bory | Simultaneous HPLC determination of three bioactive alkaloids in the Asian medicinal plant Stephania rotunda[END_REF][START_REF] Xie | Microwave-assisted extraction of bioactive alkaloids from Stephania sinica[END_REF][START_REF] Liu | Microwave-Assisted Extraction Followed by Solid-Phase Extraction for the Chromatographic Analysis of Alkaloids in Stephania cepharantha[END_REF]. Ultra-high performance liquid chromatography (UHPLC) method has recently been employed to characterise the alkaloids of Stephania tetrandra S.Moore [START_REF] Sim | Simultaneous determination of structurally diverse compounds in different fangchi species by UHPLC-DAD and UHPLC-ESI-MS/MS[END_REF]. However, the analytical control of the tuber of S. cambodica using these techniques has not yet been documented.

The aims of this study are firstly to characterise chemical constituents of the tuber of S. cambodica, which is the main plant part used in traditional medicine. Secondly, a thorough development and validation of the UHPLC method for the determination of the main metabolites of this plant was performed.

Results and discussion

A new aporphine glycoside (1, 0.5 mg) named "angkorwatine" (Figure 1), and eight known alkaloids namely oblongine (2, 0.2 mg) [START_REF] Kato | Examination of Alkaloidal Constituents of Zanthoxylum usambarense by a Combination of Ion-pair Extraction and Ion-pair Chromatography Using Sodium Perchlorate[END_REF], stepharine (3, 0.6 mg) [START_REF] Thuy | Aporphine and protoaporphine alkaloids from Stephania rotunda[END_REF]), asimilobine-β-D-glucopyranoside (4, 3.8 mg) [START_REF] Likhitwitayawuid | Cytotoxic and antimalarial alkaloids from the tubers of Stephania pierrei[END_REF], isocorydine (5, 0.5 mg) [START_REF] Ferreira | Aporphine and bisaporphine alkaloids from Aristolochia lagesiana var. intermedia[END_REF], tetrahydropalmatine (THP) (6, 1.0 mg) [START_REF] Mastranzo | Asymmetric synthesis of (S)-(-)-tetrahydropalmatine and (S)-(-)-canadine via a sulfinyl-directed Pictet-Spengler cyclization[END_REF], jatrorrhizine (7, 0.1 mg) [START_REF] Shi | Chemical Constituents and Biological Activities of Stephania yunnanensis H.S. Lo[END_REF], palmatine (PAL) (8, 0.4 mg) [START_REF] Shi | Chemical Constituents and Biological Activities of Stephania yunnanensis H.S. Lo[END_REF] and roemerine (ROE) (9, 1.0 mg) [START_REF] Thuy | Aporphine and protoaporphine alkaloids from Stephania rotunda[END_REF] were simultaneously isolated from the hydroethanolic extract of S. cambodica by preparative HPLC (Figure S2). The isolation of alkaloids from this species tuber in previous reports involved conventional chromatography [START_REF] Thanh | Two protoberberine alkaloids isolated from tuber of Stephania cambodica Gagnep. (Menispermaceae)[END_REF].

The alkaloid-type structure of the nine compounds isolated was revealed by the NMR spectra. The NMR data of compounds (2-9) were all in accordance with the literature values.

Angkorwatine (1) was isolated as amorphous powder, and the molecular formula was assigned as C 23 H 27 NO 8 by high-resolution mass spectrum (HR-ESI-MS) (m/z 446.1811

[M+H] + , calcd for C 23 H 27 NO 8 , 446.1809) (Figure S3) and NMR data implying 11 degrees of unsaturation. The 13 C NMR data gave a total of 23 separate resonances, including six signals assignable to sugar. The 1 H NMR spectrum exhibited one methoxy group (  3.79), five aromatic protons (  7.12; 7.36; 7.43; 7.47; 8.48), four ethylene protons (  3.03; 3.27; 3.49; 3.69), one signal of oxymethine proton (  4.74), one signal of methine proton (  4.47and signals assigned to the sugar moiety with an anomeric proton (  4.98, d, J=7.8Hz). The 1 H and 13 C resonances of 1 were typical of 7-oxygenated aporphine glycoside alkaloid. The HMBC crosspeak between H-1' (  4.98) and C-2 ( C 153.1) and NOESY crosspeak between H-1' (  4.98) and H-3 (  7.12) placed the sugar moiety at C-2 of the 7-oxygenated aporphine. The sugar moiety was identified as -D-glucopyranose from the proton signals at 3.56 (dd, J=9.1, 7.8 Hz, H-2'), 3.48 (brt, J=9.0 Hz, H-3'), 3.40 (dd,J=9.4,9.0 Hz,3.50 (ddd,J=9.4,6.2,2.0 Hz,3.94 (dd,J=12.1,2.0 Hz,3.71 (dd,J=12.1,6.2 Hz, and from the carbon resonances at  C 102.5 (C-1'), 74.9 (C-2'), 78.4 (C-3' and C-5'), 71.5 (C-4'), and 62.3 (C-6') in the 13 C NMR spectrum. The HMBC crosspeak between methoxy group H-12 (  3.79) and C-1 ( C 147.5) and NOESY crosspeak between H-12 (  3.79) and H-11 (  8.48) placed the methoxy group at C-1 of the 7-oxygenated aporphine. The other proton signals were at   3.27 (m), 3.03 (brd, 15.8) and 3.69 (m), 3.49 (m) for the four aliphatic protons, which were assigned to H-4 and H-5. The two last signals at   4.77 (brs) and 4.74 (brs) were assigned to H-6a and H-7. In this particular case, the 1 H NMR analysis between 300 and 340K did not allow for a coupling constant to be observed between these signals: the two protons H-6a and H-7 appeared as a broad singlet (W½ ~ 8 Hz) which seemed to correspond to a coalescence of a cis H-7 and H-6a (J = 0 -> 3 Hz) [START_REF] Hocquemiller | Anaxagoreine, a new aporphine alkaloid, isolated from two species of the genus Anaxagorea[END_REF]. S1.

  4.98 (d, J=7.8Hz, H-1'),
Compounds 1-5 and 9 were identified for the first time in the tuber of this species while compounds 4, 6, 8 and 9 were the major alkaloids. The nine compounds isolated belong to five classes of alkaloids, namely aporphine (1, 3, 4, and 9), quinoline (5), benzyltetrahydroisoquinoline (2), protoberberine (7), and tetrahydroprotoberberine (6, 8). As asimilobine-β-Dglucopyranoside (4) is commercially unavailable, palmatine (8), roemerine (9) and tetrahydropalmatine (6) were selected as analytical markers of S. cambodica (Figure 1).

During the development process, the system suitability test (Table S2) and selectivity of UHPLC method were verified. Concerning the UHPLC conditions, acetonitrile and methanol are frequently preferred to ethanol as the mobile phase in analysis of alkaloids. However, our study shows that ethanol gives a better resolution of the three analytes than methanol and acetonitrile. According to our knowledge, the developed UHPLC method is the first simultaneous determination of palmatine, roemerine and tetrahydropalmatine in the tuber of S. cambodica (Figure S2).

This UHPLC method was then validated in terms of analysis of response functions, trueness, precision, accuracy, limits of quantification (LOQ) and detection (LOD) and linearity. The validation parameters are summarised in Table S3. The calibration curves were based on the through-origin linear regression model which was fitted with concentration levels ranging from 1.67-33.20 µg/mL, 1.54-30.80 µg/mL and 4.24-84.70 µg/mL for PAL, ROE and THP, respectively. Each calibration point was analysed over the course of three consecutive days. Independent validation standards were also prepared by following the same process: five concentration levels ranging from 0.31-4.18 µg/mL, 2.01-30.72 µg/mL and 4.29-64.42 µg/mL for PAL, ROE and THP, respectively. Each point was analysed in triplicate over three consecutive days. The coefficients of determination of each-day equation of the regression line were all greater than R 2 >0.999 for reference solutions and test samples.

The data have been presented in Table S3. From the results obtained, the concentration of the validation standards were back-calculated to determine the mean relative bias, the relative standard deviation (repeatability and intermediate precision) and the upper and lower βexpectation tolerance limits at 95% level. The accuracy profile was built using trueness and intermediate fidelity variance. The acceptance thresholds were set at ±10% for ROE, THP and at ±20% for PAL. As indicated in Table S3, trueness expressed in terms of relative bias (%) was assessed by means of validation standards. RSD values smaller than 5% illustrated the good trueness of the method. The precision of the method was determined by computing the Relative Standard Deviation (RSDs) for repeatability and time-differentiated intermediate precision at each concentration level of the validation standards. The precision at each concentration level of the validation standards did not exceed 10% for PAL and 5% for ROE and THP, as shown in Table S3. The comparable RSDs between repeatability and intermediate fidelity were mainly due to non-significant intergroup variances, validating the precision of the developed method. The accuracy of the method was also evaluated taking into account the total error (sum of the systematic and random errors) of the test results. βexpectation tolerance intervals were determined to investigate the accuracy profile of the method. If β=0.95, this means that on average, 95% of the future results are included in the interval. As illustrated in Figure S10 and Table S3, the relative upper and lower β-expectation tolerance limits (%) did not exceed the adopted acceptance limits (±10% for ROE, THP and ±20% for PAL). Consequently, the method is able to provide accurate results over the investigated concentration range: 1.39-4.18 µg/mL, 2.01-30.72 µg/mL and 4.29-64.42 µg/mL for PAL, ROE and THP, respectively. As the smallest and highest quantity of the target substance in the sample could be assayed under experimental conditions with welldefined accuracy, the lower and upper LOQ were evaluated by calculating the smallest and highest concentrations. Beyond these points the accuracy limits or β-expectation tolerance limits would fall outside the acceptance limits. As the accuracy profile was included within the acceptance limits (Figure S10), the first concentration level was considered as the lower LOQ for all molecules studied (1.39 µg/mL for PAL, 2.01 µg/mL for ROE, and 4.29 µg/mL for THP) and the highest concentration level as the upper LOQ for three alkaloids (4.18 µg/mL for PAL, 30.72 µg/mL for ROE, and 64.42 µg/mL for THP). As for the limit of detection (LOD), it was estimated using mean intercept of calibration model and the residual variance of the regression. The LODs were evaluated at 0.19 µg/mL for PAL, 0.38 µg/mL for ROE and 2.36 µg/mL for THP. To demonstrate the linearity of the method, a linear regression line through origin was fitted to the estimated or back-calculated concentrations of all the series of validation standards (N = 45) as a function of the introduced concentrations. This was done by applying a linear regression model based on the least squares method. The following regression equations were determined: y=0.9721x (r 2 =0.9975), y=0.9939x (r 2 =0.9993) and y=0.9623x (r 2 =0.9996) for PAL, ROE and THP, respectively (Table S3).

The developed and validated method was applied to quantify alkaloid content in different samples of S. cambodica (Table S4). Subsequently, no difference in alkaloid content in tubers collected in the two successive years was observed. The results suggested that the collection time may not have influenced the alkaloid content in this species. The content of PAL, ROE and THP in stem was comparative to those of tubers. As the stem is a renewable part, it could potentially be a good alternative to tubers in traditional use. Also, the use of the stem assists in reducing over-exploitation of S. cambodica and hence preserving this species.

Experimental

Plant material

The plant collection for research was approved by the Ministry of Health in Cambodia.

Vegetal material was collected in two successive years from the same individual plant in Preah Vihear in Cambodia (14.223143 N-104.980178 E) (Figure S1). It was authenticated by Dr. Sovanmoly Hul. Vouchers were then deposited at Paris Herbarium (France).

Reagents and materials

Ethanol, methanol and formic acid of HPLC Ultra-Gradient grade were purchased from Carlo Erba (Val de Reuil, France). Ultrapure water (18.2 MΩ) for HPLC analysis was obtained from a Milli-Q Reference A+ system (Millipore, CO., Bedford, MA, USA). Palmatine, roemerine and tetrahydropalmatine were purchased from Sigma-Aldrich (Saint Quentin Fallavier, France), Ambinter (Orléans, France) and Phytolab (Vestenbergsgreuth, Germany), respectively.

Phytochemical study

Preparative HPLC isolation

Dried powder of S. cambodica tuber (0.5 g) was extracted with 10 mL of ethanol 50% (v/v) for 15 min in a microwave (CEM Corporation Matthews, NC, USA). This extractive protocol was developed in a previous study [START_REF] Desgrouas | Rapid and green extraction, assisted by microwave and ultrasound of cepharanthine from Stephania rotunda Lour[END_REF]. The dried extract (50 mg) was dissolved in a 2.5 mL mixture of formic acid 0.1% (v/v) methanol (70:30, v/v). The isolation of the compounds was carried out using a Gilson PLC 2020® preparative chromatograph with a DAD detector (LT350026, Gilson inc., USA). The separation and purification of the constituents were performed on the Luna C18 column (10 µm, 150 × 4.6 mm -Phenomenex).

A solvent system consisting of formic acid 0.1% (v/v) (A) and methanol (B) was used as the mobile phase in gradient mode. The eluting program was optimised as follows: linear gradient from 10% to 80% B (0-60 min). The flow rate was 12 mL/min with monitoring at 272 nm.

Identification of the isolated compounds

Structural elucidation of isolated compounds was based on spectroscopic experiments: 1D and 2D NMR, ESIMS/HRESIMS and by comparison of the spectral and chemical data with literature. 1 H and 13 C NMR spectra were measured with a 600 MHz Avance III spectrometer (Bruker) ( 1 H, 600 MHz; 13 C, 150 MHz), equipped with a 5 mm BBFO + probe. Spectra were recorded with a 2-mm NMR capillary tube in 80 µL of 99.96% CD 3 OD solvent ( 1 H 3.31 ppm- 13 C 49:00 ppm) at 300K. The 1 H (600 MHz) and 13 C NMR (150 MHz) data were reported in ppm downfield from tetramethylsilane. Coupling constants were expressed in Hz where s stands for singlet, d for doublet, t for triplet, q for quartet, m for multiplet and br for broad. Hydrogen connectivity (C, CH, CH 2 , CH 3 ) information was obtained from edited HSQC and/or DEPTQ-135 experiments. Proton and carbon peak assignments were based on 2D NMR analyses. ESIMS / HRESIMS analyses were measured with a SYNAPT G2 HDMS mass spectrometer (Waters). Accurate mass measurements were performed in triplicate with two internal calibrations. The direct sample introduction was performed at a 5 µL/min flow rate. Optical rotations were recorded on a Anton Paar MCP200 589 nm Polarimeter equipped with a sodium lamp (CH 3 OH, c in g/mL).

UHPLC analysis

The UHPLC apparatus used for the analysis of PAL, ROE, and THP were an Agilent Infinity 1290 liquid chromatography system equipped with a binary pump solvent delivery system and photodiode array detector (Agilent technologies Inc., Germany). Chromatographic separation was achieved on a Zorbax Eclipse Plus RRHD-C18 column (50 × 2.1 mm, 1.8 µm, Agilent, Germany), operated at 30 °C. The mobile phase consisted of a gradient elution of formic acid 0.1% (v/v) (solvent A) and ethanol (solvent B). The gradient program was: 0-1 min at 5% of B, 1-7 min from 5 to 42% of B with 3 min of post-time at a flow rate of 0.35 mL/min. The injected volume was 2 µL. UV detection wavelengths were 280 nm for THP and 272 nm for PAL and ROE. The system suitability test and selectivity of the method were carried out following FDA (1994) and ICH guidelines (2005).

Method validation

The validation strategy was based on the recommendations of the "Société Française des Sciences et Techniques Pharmaceutiques" (SFSTP) [START_REF] Bellenot | Issues of an analytical procedure development for the assay of constituents in herbal medicinal products IV. Recommendation for development and validation[END_REF]. In order to validate the analytical method, two kinds of samples were prepared independently. The concentrations of calibration standards (THP, PAL and ROE) are presented in Table S3. The desired concentrations of the validation standard was obtained by ultrasonication of different weight of powdered tuber for 10 min in 10 mL of ethanol 50% (v/v). One mL of the filtrate was diluted in 20 mL of ethanol 50% prior to analysis (Table S3).

Conclusions

Nine alkaloids were simultaneously isolated from the hydroethanolic extract of the tuber of Stephania cambodica. A new isolated glycoalkaloid was named angkorwatine. This particular study suggests that the validated method for the quantification of palmatine, roemerine and tetrahydropalmatine is a rapid, innovative and effective analytical approach to control the quality of the tuber of S. cambodica and regulate its use in traditional medicine.

Supplementary material

The underlying research materials for this article is available online, alongside Figure S1-S10.

Disclosure statement

Authors declare no conflict of interest in this work.

C

  23 H 27 NO 8 . [α] 25 D = -72.5° (CH 3 OH, c 0.0008). UV (CH 3 OH) λ max 210, 272 nm. The NMR spectra and data of angkorwatine are provided in Figure S4-9 and Table

Figure caption Figure 1 .

 caption1 Figure caption

Funding

The research was supported by French government scholarships.