Valentin Emiya

Roland Badeau

come

Multipitch estimation of piano sounds using a new probabilistic spectral smoothness principle

Multipitch estimation of piano sounds using a new probabilistic spectral smoothness principle Valentin Emiya, Member, IEEE, Roland Badeau, Member, IEEE, Bertrand David, Member, IEEE Abstract-A new method for the estimation of multiple concurrent pitches in piano recordings is presented. It addresses the issue of overlapping overtones by modeling the spectral envelope of the overtones of each note with a smooth autoregressive model. For the background noise, a moving-average model is used and the combination of both tends to eliminate harmonic and sub-harmonic erroneous pitch estimations. This leads to a complete generative spectral model for simultaneous piano notes, which also explicitly includes the typical deviation from exact harmonicity in a piano overtone series. The pitch set which maximizes an approximate likelihood is selected from among a restricted number of possible pitch combinations as the one. Tests have been conducted on a large homemade database called MAPS, composed of piano recordings from a real upright piano and from high-quality samples.

Index Terms-Acoustic signal analysis, audio processing, multipitch estimation, piano, transcription, spectral smoothness.

I. INTRODUCTION

The issue of monopitch estimation has been addressed for decades by different approaches such as retrieving a periodic pattern in a waveform [1; 2] or matching a regularly spaced pattern to an observed spectrum [START_REF] Schroeder | Period histogram and product spectrum: New methods for fundamental-frequency measurement[END_REF][START_REF] Brown | Musical fundamental frequency tracking using a pattern recognition method[END_REF][START_REF] Doval | Fundamental frequency estimation and tracking using maximum likelihood harmonic matching and HMMs[END_REF], or even by combining both spectral and temporal cues [6; 7]. Conversely the multipitch estimation (MPE) problem has become a rather active research area in the last decade [START_REF] Klapuri | Multiple fundamental frequency estimation based on harmonicity and spectral smoothness[END_REF][START_REF] Yeh | Multiple fundamental frequency estimation of polyphonic music signals[END_REF][START_REF] Kameoka | A Multipitch Analyzer Based on Harmonic Temporal Structured Clustering[END_REF][START_REF] Christensen | Multi-Pitch Estimation[END_REF] and is mostly handled by processing spectral or time-frequency representations. This MPE task has also become a central tool in musical scene analysis [START_REF] Christensen | Multi-Pitch Estimation[END_REF], particularly when the targeted application is the automatic transcription of music (ATM) [START_REF] Raphael | Automatic transcription of piano music[END_REF][START_REF] Marolt | A connectionist approach to automatic transcription of polyphonic piano music[END_REF][START_REF] Bello | Automatic piano transcription using frequency and time-domain information[END_REF][START_REF] Klapuri | Signal Processing Methods for Music Transcription[END_REF][START_REF] Poliner | A discriminative model for polyphonic piano transcription[END_REF]. While recent works consider pitch and time dimensions jointly to perform this task, MPE on single frames has been historically used as a prior processing to pitch tracking over time and musical note detection. Indeed, in a signal processing perspective, a period or a harmonic series can be estimated from a short signal snapshot. In terms of perception, only a few cycles are needed to identify a pitched note [START_REF] Robinson | The duration required to identify the instrument, the octave, or the pitch chroma of a musical note[END_REF].

In this polyphonic context, two issues have proved difficult and interesting for computational MPE: the overlap between the overtones of different notes and the unknown number of such notes occurring simultaneously. As the superposition of two sounds in octave relationship leads to a spectral ambiguity V. Emiya is with the Metiss team at INRIA, Centre Inria Rennes -Bretagne Atlantique, Rennes, France, and, together with R. Badeau and B. David, with Institut Télécom; Télécom ParisTech; CNRS LTCI, Paris, France.

The research leading to this paper was supported by the French GIP ANR under contract ANR-06-JCJC-0027-01, Décomposition en Éléments Sonores et Applications Musicales -DESAM and by the European Commission under contract FP6-027026-K-SPACE. The authors would also like to thanks Peter Weyer-Brown from Telecom ParisTech and Nathalie Berthet for their useful comments to improve the English usage. and thus to an ill-posed problem, some knowledge is often used for the further spectral modeling of the underlying sources. For instance, when iterative spectral subtraction is employed, several authors have adopted a smoothness assumption for the spectral envelope of the notes [START_REF] Klapuri | Multiple fundamental frequency estimation based on harmonicity and spectral smoothness[END_REF][START_REF] Yeh | Multiple fundamental frequency estimation of polyphonic music signals[END_REF][START_REF] Kameoka | A Multipitch Analyzer Based on Harmonic Temporal Structured Clustering[END_REF].

Several preceding works [12-14; 16] specifically address the case of the piano. One of the interests in studying a single instrument is to incorporate in the algorithms some results established from physical considerations [18; 19], in the hope that a more specific model will lead to a better performance, with the obvious drawback of narrowing the scope of the application. Indeed, while a large number of musical pieces are composed for piano solo, the performance of ATM systems is relatively poor for this instrument in comparison to others [START_REF] Peeters | Music pitch representation by periodicity measures based on combined temporal and spectral representations[END_REF].

Two deviations from a simple harmonic spectral model are specific to free vibrating string instruments and are particularly salient for the piano: a small departure from exact harmonicity (the overtone series is slightly stretched) and the beatings between very close frequency components (for a single string two different vibrating polarizations occur and the different strings in a doublet or triplet are slightly detuned on purpose [START_REF] Fletcher | The Physics of Musical Instruments[END_REF]).

In this work, we propose a new spectral model in which the inharmonic distribution is taken into account and adjusted for each possible note. The spectral envelope of the overtones is modeled by a smooth autoregressive (AR) model, the smoothness resulting from a low model order. A smooth spectral model is similarly introduced for the residual noise by using a low-order moving-average (MA) process, which is particular efficient against residual sinusoids. The proposed method follows a preliminary work [START_REF] Emiya | Multipitch estimation of inharmonic sounds in colored noise[END_REF] in which the AR/MA approach was already used and MPE was addressed as an extension of a monopitch estimation approach. In addition to the opportunity to deal with higher polyphony levels, the current paper introduces a new signal model for simultaneous piano notes and a corresponding estimation scheme. The major advance from the previous study is thus to model and estimate the spectral overlap between note spectra. An iterative estimation framework is proposed which leads to a maximum likelihood estimation for each possible set of F 0 s. This paper is structured as follows. In section II, the overall MPE approach is described. The sound model is first detailed, followed by the principle of the algorithm: statistical background, adaptive choice of the search space and detection function. The estimation of the model parameters is then explained in section III. After specifying the implementation details, the algorithm is tested in section IV using a database of piano sounds and the results are analyzed and compared with those obtained with some state-of-the-art approaches.

Conclusions are finally drawn in section V.

Note that in the following, * denotes the complex conjugate, T the transpose operator, † the conjugate transpose, ⌊.⌋ the floor function and |.| the number of elements in a set, the absolute value of a real number or the modulus of a complex number. In addition, the term polyphony will be applied to any possible mixture of notes, including silence (polyphony 0) and single notes (polyphony 1).

II. MULTIPITCH ESTIMATION ALGORITHM

A. Generative sound model

At the frame level, a mixture of piano sounds is modeled as a sum of sinusoids and background noise. The amplitude of each sinusoid is considered as a random variable. The spectral envelope for the overtone series of a note is introduced as second order statistical properties of this random variable, making it possible to adjust its smoothness. The noise is considered as a moving-average (MA) process.

More precisely, a mixture of P ∈ N simultaneous piano notes, observed in a discrete-time N -length frame, is modeled as a sum x (t)

x p (t) Hp h=1 α hp e 2iπf hp t + α * hp e -2iπf hp t (1)
where α hp are the complex amplitudes and f hp the frequencies of the H p overtones (here, H p is set to the maximum number of overtones below the Nyquist frequency). Note p is parameterized by C p = (f 0p , β p ), f 0p being the fundamental frequency (F 0 ) and β p (f 0p ) being the so-called inharmonicity coefficient of the piano note [START_REF] Fletcher | The Physics of Musical Instruments[END_REF], such that

f hp hf 0p 1 + β p (f 0p ) h 2 (2)
We introduce a spectral envelope for note p as an autoregressive (AR) model of order Q p , parameterized by θ p σ2 p , A p (z) , where σ 2 p is the power and 1 Ap(z) is the transfer function of the related AR filter. Order Q p should be low and proportional to H p , in order to obtain a smooth envelope and to avoid overfitting issues for high pitches. The amplitude α hp of overtone h of note p is the outcome of a zero-mean complex Gaussian random variable 1 , with variance equal to the spectral envelope power density at the frequency f hp of the overtone:

α hp ∼ N 0, σ 2 p |A p (e 2iπf hp )| 2 (3)
In order to model a smooth spectral envelope without residual peaks, the noise x b is modeled as an MA process with a low order Q b , parameterized by θ b σ 2 b , B(z) , σ 2 b being the power and B(z) the finite impulse response (FIR) filter of the process. Furthermore, high note powers and low noise powers are favored by choosing an inverse gamma prior for σ 2 p :

1 Using these centered Gaussian variables, xp is thus a harmonic process, in the statistical sense. . A non-informative prior 2 is assumed for A p (z) and B(z).

With a user-defined weighting window w, we can equivalently consider the Discrete Time Fourier Transforms (DTFT) X p (f ) of x p (t) w (t), X b (f ) of x b (t) w (t) and X (f ) P p=1 X p (f ) + X b (f ) of x (t) w (t). W being the DTFT of w, we thus have

X p (f ) = Hp h=1 α hp W (f -f hp ) + α * hp W * (f + f hp ) (4)
In addition, the following synthetic notations will be used: a mixture of notes is denoted by C (C 1 , . . . , C P ); the set of parameters for spectral envelope models by θ (θ 1 , . . . , θ P ); the set of amplitudes of overtones of note p by α p α 1p , . . . , α Hpp ; and the set of amplitudes of overtones of all notes by α (α 1 , . . . , α P ).

B. Principle of the algorithm

The algorithm is illustrated in Fig. 1. The main principles are described in the current section, except for the model parameter estimation, which is detailed in Section III.

1) Statistical background: Let us consider the observed frame x and the set C of all the possible mixtures of piano notes. Ideally, the multipitch detection function can be expressed as the maximum a posteriori (MAP) estimator Ĉ, which is equivalent to the ML estimator if no a priori information on mixtures is specified:

Ĉ = arg max C∈C p(C|x) = arg max C∈C p(x|C) p(C) p(x) = arg max C∈C p(x|C) (5)
2) Search space: The number of combinations among Q possible notes being Q P for polyphony P , the size of the search set C is 26 for a typical piano with Q = 88 keys. Even when the polyphony is limited to P max = 6 and the number of possible notes to Q = 60 (e.g. by ignoring the lowest and highest-pitched keys), the number of combinations reaches Pmax P =0 Q P ≈ 56•10 6 , which remains a too huge search set for a realistic implementation. In order to reduce the size of this set, we propose to select a given number N c of note candidates. We use the normalized product spectrum function defined in dB as

Q P =0 Q P = 2 Q , i.e. around 3•10
Π X (f 0 , β) 1 H (f 0 , β) ν 10 log H(f0,β) h=1 |X (f h )| 2 (6)
where X is the observed spectrum, H (f 0 , β) is the number of overtones for the note with fundamental frequency f 0 and inharmonicity β, f h hf 0 1 + βh 2 , and ν is a parameter adjusted to balance the values of the function between bass and treble notes. As the true notes generate local peaks in Π X , selecting an oversized set of N c greatest peaks is an efficient way for adaptively reducing the number of note candidates. In addition, for candidate n c ∈ 1; N c , accurate values of its fundamental frequency f 0nc and inharmonicity β nc are found by a local two-dimensional maximization3 of Π X (f 0nc , β nc ). They are used in the subsequent estimation stages to locate the frequencies of the overtones. In the current implementation, the number of note candidates is set to N c = 9. This choice results from the balance between increasing the number of candidates and limiting the computational time. The size of the set C of possible mixtures thus equals Pmax P =0 Nc P = 466, for P max = 6.

3) Multipitch detection function: The multipitch detection function aims at finding the correct mixture among all the possible candidates. For each candidate C ∈ C, the parameters α, θ and θ b of the related model are estimated as explained in section III. The detection function is then computed, and the multipitch estimation is defined as the mixture with the greatest value.

Since equation ( 5) is intractable, we define an alternate detection function which involves the following terms:

• L p (θ p ) ln p(α p |θ p , C p ) is the log-likelihood of the amplitudes α p of overtones of note p, related to the spectral envelope models θ p ; 4 to the log-likelihood ln p x b related to the noise model θ b ; • the priors ln p(θ p ) on the spectral envelope of the note p and ln p(θ b ) on noise parameters. We empirically define the detection function as a weighted sum of these log-densities, computed with the estimated parameters (see Appendix A for a discussion):

• L b (θ b ) ln p(x|α, θ b , C) is equal
Lx (C) w 1 P p=1 Lp θ p /P + w 2 Lb θ b + w 3 P p=1 ln p σ 2 p /P + w 4 ln p σ 2 b -µ pol P (7)
where

                 Lp θ p 1 Hp L p σ 2 p , A p -µ env H p Lb θ b 1 |F b | L b σ 2 b , B -µ b |F b | w 1 , . . . , w 4 , µ pol , µ env , µ b are user-defined coefficients |F b |
is the number of noisy bins (see eq. ( 14)).

III. MODEL PARAMETER ESTIMATION

A. Iterative estimation of spectral envelope parameters and amplitudes of notes

We consider a possible mixture C = (C 1 , . . . , C P ). The estimation of the unknown spectral envelope parameters θ and of the unknown amplitudes of the overtones α is performed by iteratively estimating the former and the latter, as described in this section.

1) Spectral envelope parameter estimation: let us assume the amplitudes α are known in order to estimate the spectral envelope parameters θ in the maximum likelihood (ML) sense. Given that note models are independent, the likelihood of α is p(α|θ, C) = P p=1 p(α p |θ p , C p ). The optimization w.r.t. θ thus consists in maximizing the log-likelihood L p σ 2 p , A p ln p α p |σ 2 p , A p , C p w.r.t. θ p = σ 2 p , A p , independently for each note p. As proved in the Appendix B, the maximization w.r.t. σ 2 p leads to the expression

L p σ 2 p , A p = c + H p 2 ln ρ (A p ) (8)
with As c is a constant w.r.t. A p , the optimization consists in maximizing ρ (A p ), which measures the spectral flatness (i.e. the ratio between the geometrical and arithmetical means) of

c - H p 2 ln (2πe) - 1 2 Hp h=1 ln |α hp | 2 (9) ρ (A p ) Hp h=1 |α hp | 2 A p e 2iπf hp 2 1 Hp 1 Hp Hp h=1 |α hp | 2 |A p (e 2iπf hp )| 2 (10)
σ 2 p = 1 H p Hp h=1 |α hp | 2 A p e 2iπf hp 2 (11)
|α hp | 2 A p e 2iπf hp 2 1≤h≤Hp
. This quantity lies in

[0; 1]
and is maximum when the latter coefficients are constant, i.e. when the filter A p perfectly whitens the amplitudes α p . The estimation of A p from the discrete data α p thanks to the Digital All-Pole (DAP) method [START_REF] El-Jaroudi | Discrete all-pole modeling[END_REF] leads to a solution that actually maximizes ρ (A p ), as proved in [START_REF] Badeau | Weighted maximum likelihood autoregressive and moving average spectrum modeling[END_REF]. It is applied here to the amplitudes α p , for each note p.

The estimation of the spectral envelope of a note is illustrated in Fig. 2. A note is analyzed by considering two possible models: the model related to the true note (Fig. 2(a)) and the model related to its sub-octave (Fig. 2(b)). In the former case, the estimate of the spectral envelope is close to the amplitudes of the overtones, whereas in the latter case, the AR spectral envelope model is not adapted to amplitudes that are alternatively high and low: the low values obtained for the spectral flatness ρ (and, consequently, for the likelihood) are here a good criterion to reject wrong models like the suboctave (see Fig. 6(a) for the whole spectral flatness curve).

2) Estimation of the amplitudes of the overtones: let us now assume that spectral envelope parameters θ are known, that the frequencies of the overtones may overlap, and that the amplitudes α are unknown. In all that follows, we assume that at a given overtone frequency f hp , the power spectrum of the noise is not significant in comparison with the power spectrum of the amplitudes of the overtone.

When the overtone h of note p is not overlapping with any other overtone, the amplitude α hp is directly given by the spectrum value X (f hp ). In the alternative case of overlapping overtones, the observed spectrum results from the contribution of overtones with close frequencies. We propose an estimate of the hidden random variable α, given the observation X and the parameters θ that control the second-order statistics of α.

As defined by eq. ( 3), the amplitude α hp is a random vari-

able such that α hp ∼ N (0, v hp ) with v hp σ 2 p |Ap(e 2iπf hp )| 2 .
One can rewrite the sound model x as a sum of K sinusoids and noise

x(t) = K k=1 α k e 2iπf k t +x b (t) with α k ∼ N (0, v k ) and K = 2 P p=1 H p .
In this formula, the couples of indexes (h, p) related to overtones and notes have been replaced by a single index k. In the spectral domain, the DFT X of the N -length frame x using a weighting window w of DFT W is

X (f ) = K k=1 α k W (f -f k )
, the noise spectrum being removed since we are only interested in the values of X at frequencies f hp , where the noise term is insignificant.

In these conditions, for 1 ≤ k 0 ≤ K, the optimal linear estimator αk0 of α k0 as a function of X (f k0 ), obtained by minimizing the mean squared error

ǫ k0 = E |α k0 -αk0 | 2 is αk0 = W * (0) v k0 K k=1 |W (f k0 -f k )| 2 v k X (f k0 ) (12)
The proof of eq. ( 12) is given in the Appendix B. By ignoring non-overlapping overtones, the expression of the estimator of α hp can be simplified as

α hp W * (0) v 2 hp | f h ′ p ′ -f hp | <∆w |W (f h ′ p ′ -f hp )| 2 v 2 h ′ p ′ X (f hp ) (13)
where ∆ w is the width of the main lobe of W . The amplitude estimation is illustrated in Fig. 3 on a synthetic signal, composed of two octave-related notes, i.e. with overlapping spectra. As expected, the amplitudes are perfectly estimated when there is no overlap (see odd-order peaks of note 1). When the overtones overlap, predominant amplitudes are well estimated (see note 1 for f = 0.04 or note 2 for f = 0.4), as well as amplitudes with the same order of magnitude (see amplitudes at f = 0.2). The estimation may be less accurate when an amplitude is much weaker than the other (see note 1 at f = 0.36).

3) Iterative algorithm for the estimation of note parameters: in the last two parts, we have successively seen how to estimate the spectral envelope models from known amplitudes and the amplitudes from known spectral envelope models. None of these quantities are actually known, and both must be estimated. We propose to use the two methods above in the Algorithm 1 to iteratively estimate both the spectral envelope and the amplitudes of the overtones. It alternates the estimation of the former and of the latter, with an additional thresholding of the weak amplitudes in order to avoid the amplitude estimates becoming much lower than the observed Fig. 3. Estimation of amplitudes from overlapping spectra: example on a synthetic mixture of 2 notes. The F 0 s f 0,1 and f 0,2 of the two notes are in an octave relation and the estimation is performed from a N = 2048-length observation. For each note, the true amplitudes (squares) have been generated from a spectral envelope AR model (black line) using eq. ( 3). The amplitudes are estimated (crosses) from the observation of the mixture (grey line) using the AR envelope information (eq. ( 12)). after a number of iterations. Note that the ML estimates of the envelopes are directly related to the MAP estimation of the multipitch contents while amplitudes are estimated in the least mean square sense, which is a different objective function. Consequently, the convergence of the iterative algorithm is not proved or guaranteed but it is observed after about N it 20 iterations.

The estimation is illustrated in Fig. 4 with two typical cases. While the energy is split between the overlapping overtones, non-overlapping overtones help estimating the spectral envelopes, resulting in a good estimation in the case of a fifth (Fig. 4(a)), the octave being a more difficult -but successful -case (Fig. 4(b)).

Algorithm 1 Iterative estimation of note parameters

B (z) = Q b k=0 b k z -k , with b 0 = 1.
As we assumed that in a bin close to the frequency of an overtone, the spectral coefficients of noise are negligible w.r.t. the spectral coefficients of notes, the information related to noise is mainly observable in the remaining bins, i.e. on the frequency support defined by

F b k N fft ∀p ∈ 1; P , ∀h ∈ 1; H p , k N fft -f hp > ∆ w 2 (14)
where ∆ w denotes the width of the main lobe of w (∆ w = 4 N for a Hann window) and N fft is the size of the DFT. The noise parameter estimation is then performed using this subset of bins, which gives satisfying results asymptotically (i.e. when N → +∞, the number of removed bins being much smaller than the total number of bins). As proved in the Appendix B, it results in the maximization, w.r.t. B, of the expression

L b σ 2 b , B = c b + |F b | 2 ln ρ b (B) (15)
where

c b - |F b | 2 ln 2πe - 1 2 f ∈F b ln |X b (f )| 2 N ( 16
)
ρ b (B) f ∈F b X b (f ) B(e 2iπf ) 2 1 |F b | 1 |F b | f ∈F b X b (f ) B(e 2iπf ) 2 (17)
σ 2 b = 1 |F b | f ∈F b 1 N X b (f ) B (e 2iπf ) 2 (18)
As for the spectral envelope AR parameters (eq. ( 11) and ( 8)), the ML estimation of noise parameters consists in the maximization of a spectral flatness ρ b (B). It can be achieved thanks to the MA estimation approach proposed in [START_REF] Badeau | Weighted maximum likelihood autoregressive and moving average spectrum modeling[END_REF]. However, in order to speed up the computations, we use the Algorithm 3 described in the Appendix C, which is simpler and gives satisfying results for the current application.

The noise parameter estimation is illustrated in Fig. 5. When the true model is selected (Fig. 5(a)), most of primary lobes of the sinusoidal components are removed from F b and the resulting spectral coefficients are well-fitted by an MA envelope. In the case a wrong model is selected and a lot of F b bins are related to sinusoids (Fig. 5(b)), the MA model is not adapted to the observations which are not wellfitted. The resulting ρ b value and likelihood will be low so that the wrong model will be rejected. As shown in Fig. 6, the spectral flatness criterion for the spectral envelope and noise estimations are complementary cues for rejecting wrong models and selecting the right one. The criterion on spectral envelopes (Fig. 6(a)) shows many high values but also large minima for sub-harmonic errors (e.g. notes D♭ 3 , A♭ 3 and D♭ 3 in this example). Conversely, the criterion for the noise model (Fig. 6(b)) has a few high peaks located at the subharmonics F 0 s of the true notei.e. for every model all the sinusoids have been removed from the noise observation -, but is efficient for discriminating the other errors. Thus, if taken separately, these criteria are not good pitch estimators, but they efficiently combine into the detection function.

IV. EXPERIMENTAL RESULTS

A. Implementation and tuning

The whole method is summarized by Algorithm 2. The MPE algorithm is implemented in Matlab and C. It is designed to analyze a 93ms frame and to estimate its polyphonic content. A preprocessing stage aims at reducing the spectral dynamics and consists in flattening the global spectral decrease by means of a median filtering of the spectrum. The values of the parameters of the MPE algorithm are given in Table I. The order Q p of the spectral envelope filter A p (z) of a note p is set to Q p = H p /2 in order to be large enough to fit the data and small enough to obtain a smooth spectral envelope 7 . Parameters

k σ 2 p , E σ 2 p , k σ 2 b , E σ 2 b
, µ env , µ b , µ pol and (w 1 , . . . , w 4 ) have been estimated on a development database composed of about 380 mixtures from two different pianos, with polyphony levels from 1 to 6. They were jointly adjusted by optimizing the F-measure using a grid search, the bounds of the grid being set by hand. Derivation of the detection function related to the note combination (eq. ( 7)) end for Maximization of the detection function

B. Evaluation

The proposed MPE algorithm has been tested on a database called MAPS 8 and composed of around 10000 piano sounds either recorded by using an upright Disklavier piano or generated by several virtual piano software products based on sampled sounds. The development set and the test set are disjointed. Two pianos are used in the former while the latter comprises sounds from other five pianos. In total, two upright pianos and five grand pianos were used. Recording conditions and tunings vary from one instrument to the other. Polyphony levels lie between 1 and 6 and notes are uniformly distributed between C 2 (65Hz) and B 6 (1976Hz). One part of the polyphonic mixtures is composed of randomly related pitches whereas the other part comprises usual chords from western music (major, minor, etc.). For each sound, a single 93ms-frame located 10ms after the onset time is extracted and analyzed. Two additional algorithms have been tested on the same database for comparison purposes. The first one is Tolonen's multipitch estimator [START_REF] Tolonen | A computationally efficient multipitch analysis model[END_REF] for which the implementation from the MIR Toolbox [START_REF] Lartillot | A Matlab toolbox for musical feature extraction from audio[END_REF] was used. As the performance of the algorithm decreases when F 0 s are greater than 500Hz (C 5 ), the system was additionally tested in restricted conditionsdenoted Tolonen-500 -by selecting from the database the subset of sounds composed of notes between C 2 and B 4 only. The second one is Klapuri's system [START_REF] Klapuri | Multiple fundamental frequency estimation by summing harmonic amplitudes[END_REF]. The code of the latter was provided by its author.

Our algorithm was implemented in Matlab and C. The computational cost on a recent PC is about 150×real time. It thus requires more computations than other algorithms like [START_REF] Klapuri | Multiple fundamental frequency estimation by summing harmonic amplitudes[END_REF] but the proposed algorithm is computationally tractable, particularly when comparing it to the greedy and intractable joint-estimation approach where no note candidate selection is performed, as discussed in section II-B.

General results are presented in Fig. 7. Relevant items are defined as correct notes after rounding each F 0 to the nearest half-tone. Typical metrics are used: the recall is the ratio between the number of relevant items and of original items; the precision is the ratio between the number of relevant items and of detected items; and the F-measure is the harmonic mean between the precision and the recall. In this context, our system performs the best results for polyphony 1 and 2: 93% F-measure vs 85% (polyphony 1) and 91% (polyphony 2) for Klapuri's system. The trend then reverses between Klapuri's system and the proposed one, the F-measure being respectively 91% and 88% for polyphony 3, and 72% and 63% for polyphony 6. Moreover, the precision is high for all polyphony levels whereas the recall is decreasing when polyphony increases. Results from Tolonen's system are weaker for the overall tests, even with the restricted F 0 -range configuration.

The ability of Klapuri's system and ours to detect polyphony levels (independently of the pitches) is presented in Tab. II. For polyphony levels from 1 to 5, both systems succeed in detecting the correct polyphony level more often than any other level. It should also be noted that the proposed system was tested in more difficult conditions since polyphony 0 (i.e. silence) may be detected, which is the case for a few sounds 9 . The proposed system tends to underestimate the polyphony Proposed method Klapuri's method level since the parameter tuning consists in optimizing the F-measure on the development set. This objective function could have been changed to take the polyphony level balance into account. This would result in reducing the polyphony underestimation trend. However, the overall F-measure would decrease. From a perceptive point of view, it has been shown that a missing note is generally less annoying than an added note when listening to a resynthesized transcription [START_REF] Cemgil | A generative model for music transcription[END_REF]. Thus, underestimating the polyphony may be preferred to overestimating it. Still, this trend turns out to be the main shortcoming of the proposed method, and should be fixed in the future for efficiently addressing sounds with polyphony higher than 5 notes. The case of octave detection has been analyzed and results are presented in Fig. 8. Octave detection is one of the most difficult cases of multipitch estimation and the results are lower than the global results obtained for polyphony 2 (see Fig. 7). The proposed method reaches the highest results here, the Fmeasure being 81%, versus 77% for Klapuri's system and 77%/66% for Tolonen's (depending on the two F 0 ranges). This would suggest that the proposed models for spectral envelopes and overlapping spectra are significatively efficient. Finally, we report additional results which are not depicted. First, if polyphony is known, the performance of our system reaches the second rank after Klapuri's system, with correct detection rates from 95% (polyphony 1) down to 55% (polyphony 6). Second, F-measure values are between 5% and 10% better for usual chords than for random-pitch chords. This has been observed with all the tested methods for polyphony levels higher than two. While the algorithms face more harmonically-related notes in usual chordsi.e. more spectral overlap -, it seems that simultaneous notes with widely-spread F 0 s in random chords are a bigger difficulty. Third, the results obtained on the development set and the test set are comparable, with only a few % deviation. This shows that the parameter learning is not overfitting and that the system has good generalization abilities for other models of piano and different recording conditions. Fourth, the whole database includes sounds from seven different pianos. The results are comparable from one piano to the other, with about 3%-standard deviation. Results do not significantly depend on the upright/grand piano differences, on recording conditions or on whether a real piano or a software-based one is used, which suggests robustness for varying production conditions. Fifth, the proposed method uses a candidate selection stage which may fail, causing the subsequent multipitch estimation to fail. The performance of the candidate selection stage has thus been checked: satisfying results are obtained for low to medium polyphony levels, 99% of true notes being selected for polyphony 1 and 2, 94% for polyphony 3 and 86% for polyphony 4. Performance is slightly decreasing in polyphony 5 and 6, the scores being 78% and 71% respectively. Along the original-pitch dimension, these errors are mainly located below A 2 (110Hz), and above A 6 (1760Hz). Selecting a set of likely F 0 s is a challenging issue for future works since a lot of MPE algorithms would benefit from it. Indeed, they often consist in optimizing an objective criterion that presents a lot of local optima along the pitch dimension. Some basic solutions like exhaustive or grid search [START_REF] Cemgil | A generative model for music transcription[END_REF] or more elaborated ones like Markov chain Monte Carlo methods [START_REF] Walmsley | Polyphonic pitch tracking using joint Bayesian estimation of multiple frame parameters[END_REF] have already been proposed for searching the global optimum, and an efficient candidate selection stage would be very helpful to reach the result more quickly.

C. Integration in an automatic transcription system

The proposed MPE method has been introduced for a singleframe analysis. Beyond the multipitch issue, the automatic transcription task is addressed by integrating this method in a system that performs pitch tracking over time and outputs not only pitches but note events. In the current case, the MPE method can be used in the transcription framework proposed in [START_REF] Emiya | Automatic transcription of piano music based on HMM tracking of jointly-estimated pitches[END_REF]. The automatic transcription of piano music is thus obtained by: 1) using an onset detector to localize new events; 2) detecting a set of pitch candidates after each onset; 3) between two consecutive onsets, decoding the multipitch contents thanks to a frame-based Hidden Markov Model (HMM), the states being the possible combinations of simultaneous pitches, the likelihood being given by the proposed MPE method (eq. ( 7)); 4) postprocessing the decoded pitches to detect repetitions or continuations of pitches when an onset occurs.

This transcription system was presented at the Multiple Fundamental Frequency Estimation & Tracking task of the MIREX 10 contest in 2008 (system called EBD2). For the piano-only test set, the evaluation is performed in two different ways, depending on how a correct note is defined. In the first, more constraining evaluation, where a correct note implies a correct onset (up to a 50-ms deviation), a correct offset (up to a 20%-duration or 50-ms deviation) and a correct pitch (up to a quartertone deviation), the proposed system reaches the 3 rd rank with a 33.1% F-measure, out of 13 systems scoring from 6.1% to 36.8%. For that evaluation, the duration estimation is evaluated by the average overlap between correct estimations and reference notes: the proposed method reaches the 7 th position with 80%, the values being in a narrow interval ([77.4%; 84%]). In the second evaluation, where correctness only requires the onset and pitch criteria above, the proposed system reaches the 7 th rank with a 56.9% F-measure, out of 13 systems scoring from 24.5% to 75.7%. The best rank is obtained for average overlap with a 61% value, the lowest value being 40.1%. Thus, when the proposed MPE method is integrated in a full transcription system for piano music, state-of-the art results are reached in terms of global performance. In addition, good average overlap scores show that the proposed method is suitable for pitch tracking over time and note extraction.

Note that one can wonder whether the reported performance is significant when comparing MPE and ATM quantitative results (with roughly 20% F-measure deviation, no matter the method is). It actually depends not only on the database, but on the different testing protocols. While isolated frames composed of one chord are used in the proposed MPE evaluation, ATM evaluation implies other difficulties like having asynchronous notes overlaping in time; detecting onsets; estimating the end of damping notes; dealing with reverberation queues and so on. More, polyphony levels in musical recordings are often high and are not uniformly distributed at all, with a 4.5 average polyphony and a 3.1 standard deviation reported for a number of classical music pieces [29, p.114]. Hence, Fmeasure for MPE and ATM should be evaluated separately. 10 http://www.music-ir.org/mirex/2008/ V. CONCLUSIONS In this paper, a sound model and a method were proposed for the multipitch estimation problem in the case of piano sounds. The approach was based on an adaptive scheme, including the adaptive matching of the inharmonic distribution of the frequencies of the overtones and an autoregressive spectral envelope. We have shown the advantage of using a moving average model for the residual noise. The estimation of the parameters was performed by taking the possible overlap between the spectra of the notes into account. Finally, a weighted likelihood criterion was introduced to determine the estimated mixture of notes in the analyzed frame among a set of possible mixtures.

The performance of the method was measured on a large database of piano sounds and compared to the state-of-theart. The proposed method provides satisfying results when polyphony is unknown, and reaches particularly good scores for mixtures of harmonically-related notes.

This approach has been successively integrated in a full transcription system [START_REF] Emiya | Automatic transcription of piano music based on HMM tracking of jointly-estimated pitches[END_REF] and alternative investigations [START_REF] Badeau | Expectationmaximization algorithm for multi-pitch estimation and separation of overlapping harmonic spectra[END_REF] are ongoing. Future works may deal with the use of different spectral envelopes in a similar modeling and estimation framework. Indeed, while the proposed AR envelope model may be too generic to characterize the spectral envelope smoothness of musical instruments, this information can be easily replaced, as the variance of the amplitude Gaussian models, by any parametric envelope model. The method may also be extended to other instruments or to voice. Keeping the proposed sound model, it could be useful to investigate other estimation strategies in order to reduce the computational cost. This may be achieved by means of a hybrid approach with an iterative selection of the notes and a joint estimation criterion. Furthermore, the log-likelihood function related to the model for spectral envelopes is not very selective. Hence, some investigations on more appropriate functions could improve the performance of decision step. Finally, one could conduct others investigations about how to prune the set of all possible note combinations more efficiently. They may include iterative candidate selection or MCMC methods. APPENDIX A DISCUSSION ON THE DETECTION FUNCTION According to eq. ( 5), the multipitch estimation is theoretically obtained by maximizing, w.r.t. C, the likelihood p(x|C), which is expressed as a function of the parameters of the proposed model as:

p(x|C) = p(x, α, θ b |C) dαdθ b (19)
Since the derivation of eq. ( 21) is not achievable, a simpler detection function must be built. The proposed function can be interpreted as a weighted log-likelihood and is obtained from the integrand of eq. ( 21) by: The normalization operation aims at obtaining data that can be compared from one mixture C to another, since the dimension of the random variables depends on the mixture. The penalization is inspired by model selection approaches [START_REF] Stoica | Model-order selection: a review of information criterion rules[END_REF], in which an integral like ( 21) is replaced by a likelihood penalized by a linear function of the model order. The weighting by w 1 , . . . , w 4 is finally used to find an optimal balance between the various probability density functions. Note that in eq. ( 7), priors related to filters A p and B have been removed since they are non-informative, and thus can be considered as constant terms.

APPENDIX B PROOFS

Proof of eq. ( 8): Using eq. ( 3), the log-likelihood to be maximized is

L p σ 2 p , A p = -
The maximization w.r.t. σ 2 p leads to the estimate σ 2 p given by eq. ( 11), which is used in eq. ( 22) to obtain eq. ( 8).

Proof of eq. ( 12) and (13): The expected linear estimator is expressed as αk0 ηX (f k0 ) with η ∈ C. The mean squared error is then ǫ k0 (η) = E |α k0 -ηX (f k0 )|

2 . The optimal value η is such that dǫ k 0 dη (η) = 0, which is equivalent to the decorrelation between the error (α k0 -ηX (f k0 )) and the data X (f k0 ):

0 = E α * k0 -η * X * (f k0 ) X (f k0 ) = E α * k0 X (f k0 ) -η * E |X (f k0 )| 2 (23)
which leads to η = E[α k 0 X * (fk 0 )]

E h |X(fk 0 )| 2 i
, where

E [α k0 X * (f k0 )] = K k=1 W * (f k0 -f k ) E [α k0 α * k ] = W * (0) v k0 (24)
and

E |X (f k0 )| 2 = K k=1 K l=1 W (f k0 -f k ) × W * (f k0 -f l ) E [α k α * l ] = K k=1 |W (f k0 -f k )| 2 v k (25)
The related error is

ǫ k0 (η) = E |α k0 | 2 + |η| 2 E |X (f k0 )| 2 -ηE α * k0 X (f k0 ) -η * E [α k0 X * (f k0 )] = E |α k0 | 2 - |E [α k0 X * (f k0 )]| 2 E |X (f k0 )| 2 = 1 - |W (0)| 2 v k0 K k=1 |W (f k0 -f k )| 2 v k v k0 (26)
Note that this approach has some connections with the Wiener filtering technique [START_REF] Wiener | Extrapolation, Interpolation, and Smoothing of Stationary Time Series[END_REF] widely used in the field of audio source separation. In both cases, the aim is to estimate a hidden variable thanks to its second-order statistics and to the observations. In the considered short-term analysis context, the proposed approach explicitly models the overlap phenomenon and takes the resulting frequency leakage into account. As expected, the estimation error is all the larger as the estimated overtone is masked by another component, which justifies the approximation of eq. ( 12) in eq. ( 13).

In the spectral domain, the log-likelihood of the noise signal

P

  p=1 x p (t) + x b (t) of the note signals x p and of noise x b . The sinusoidal model for x p is

Fig. 1 .

 1 Fig. 1. Multipitch estimation block diagram.

σ 2 p∼ IG k σ 2 p , E σ 2 p and a gamma prior for σ 2 b : σ 2 b ∼ Γ k σ 2 b , E σ 2 b

 222222

4 1 =θ1 |α h1 | 2 (Fig. 2 .

 122 Fig. 2. Estimation of spectral envelopes: the AR estimation performs a better fitting of the amplitudes for the correct model (left) than for the sub-octave model (right).

  Periodogram of the mixture AR envelope model of note 1 |α h1 | 2 (true amplitudes) |α h1 | 2 (estimation) Periodogram of the mixture AR envelope model of note 2 |α h2 | 2 (true amplitudes) |α h2 | 2 (estimation) (b) Note 2.

Fig. 4 .

 4 Fig. 4. Iterative estimation of amplitudes c αp and spectral envelopes b θp: example of a fifth (Fig. 4(a)) and of an octave (Fig. 4(b)). spectral coefficients 5 . For p ∈ 1; P and h ∈ 1; H p , the estimate α hp of α hp and θ p of θ p are respectively the values of α (i) hp and θ (i) p

Fig. 5 .

 5 Fig. 5. Noise parameter estimation when selecting the true model (left) and the octave model (right). F b denotes the complement of F b .

  Fig. 6. ln ρ " c A 1 " (top) and ln ρ b " b B " (bottom) as a function of a singlenote model (true note: A♭ 4 ).

Algorithm 2 2 p

 22 Multipitch estimation. Preprocessing Computation of periodogram 1 N |X| 2 Selection of N c note candidates for each possible note combination C do Iterative estimation of the amplitudes of overtones and of spectral envelope of notes (algorithm 1) For each note p, derivation of L p (eq. (8)) and of prior p σ Noise parameter estimation (algorithm 3) Computation of L b (eq. (15)) and of prior p σ 2 b

Fig. 7 .

 7 Fig.7. Multipitch estimation results with unknown polyphony: for each algorithm, the F-measure, the precision and the recall are rendered as a function of the true polyphony. For the proposed method, the performance on the training set is plotted using a dashed line. P Pest 1 2 3 4 5 6 0 7 2 4 6 9 0 1 90 14 8 8 8 12 2 3 83 18 12 8 19 3 0 1 68 27 16 25 4 0 0 2 47 27 32 5 0 0 0 1 31 11 6 0 0 0 0 1 1

Fig. 8 .

 8 Fig.8. Octave detection: results for the 97 octave sounds extracted from the database (45 sounds for the Tolonen-500 system).

=

  p(x|α, θ b , C) p(α|C) p(θ b ) dαdθ b (20) = p(x|α, θ b , C) p(α|θ, C) p(θ) p(θ b ) dθdαdθ b

•

  considering the estimated parameters θ p , α p , θ b ; • taking the logarithm, thus turning the product into a sum; • normalizing the sums over the number of notes by P , and log-likelihoods L p and L b by the size H p and |F b | of their respective random variable; • introducing penalization terms using the C-dependent sizes P , H p , |F b | with coefficients µ pol , µ env , µ b ; • weighting each quantity by the coefficients w 1 , . . . , w 4 .

ln A p e 2iπf hp 2 - 2 A

 22 p e 2iπf hp 2

N - 1 k=0 B e 2iπ k N 2 . 1 2 x b † (BcircB † circ σ 2 b- 1 2 b 1 k=0 B e 2iπ k n 2

 12121212 Proof of eq.[START_REF] Klapuri | Signal Processing Methods for Music Transcription[END_REF]: In a matrix form, the filtering process is expressed asx b = B circ w b , where x b is an N -length frame of the noise process x b , w b ∼ N 0, I N σ 2 b and B circ is the N × N circulant matrix with first column (b 0 , . . . , b Q b , 0, . . . , 0). Thus, we have x b ∼ N 0, B circ (B circ ) † σ 2 b . B circ is circulant, so det B circ B † circ = The likelihood of x b is then p x b = e -) x b (2π) N det B circ B † circ σ

  Require: spectrum X, notes C 1 , . . . , C P . Initialize the amplitudes α estimation of α hp and θ p for p ∈ 1; P and h ∈ 1; H p .

	(0)
	(i) p from α (i-1) p	. {AR estimation}
	end for Jointly estimate all α (i) hp from X (f hp ) and θ	(i) p . {eq. (13)}
	Threshold α (i) hp at a minimum value.
	end for
	Ensure:

hp of overtones to spectral values X (f hp ) for p ∈ 1; P and h ∈ 1; H p . for each iteration i do for each note p do Estimate θ by a Q b -order FIR filter parameterized by its transfer function

TABLE II POLYPHONY

 II ESTIMATION: DETECTION RATE (%) W.R.T. TO THE NUMBER OF SOUNDS WITH TRUE POLYPHONY P , AS A FUNCTION OF THE TRUE POLYPHONY P AND OF THE ESTIMATED POLYPHONY PEST .

e.g. an improper, constant prior density, which will not affect the detection function.

The fminsearch Matlab function was used for this optimization.

In our implementation, this threshold was set to the minimum observed amplitude min f|X(f )| √ N.

The circularity assumption, which is commonly used and asymptotically valid, leads to a simplified ML solution.

Note that the number of degrees of freedom for the AR models is Hp/4 = Qp since half the poles are affected to the positive frequencies, the remaining poles being their complex conjugates.

MAPS stands for MIDI Aligned Piano Sounds and is available on request.

Note that silence detection could be improved by using an activity detector as a preprocessing stage, since silence is a very specific case of signal that can be detected using more specific methods than the proposed one.

is thus obtained using the Parseval identity:

When only considering the observations on the spectral bins F b , the log-likelihood [START_REF] Emiya | Transcription automatique de la musique de piano[END_REF] becomes

The maximization w.r.t. σ 2 b leads to the estimate given by eq. ( 18), which is used in eq. ( 30) to obtain eq. [START_REF] Klapuri | Signal Processing Methods for Music Transcription[END_REF].

APPENDIX C MA ESTIMATION

The algorithm is based on the decomposition r b = Bb of the first (Q b + 1) terms r b of the autocorrelation function of the process, as a product of the coefficient vector b

The estimate b of b is obtained using Algorithm 3. As B is upper triangular, the estimation of b in r b = B b is fast performed by back substitution, instead of inverting a full matrix. The algorithm convergence was observed after about 20 iterations.


Chris Kimble

Corinne Grenier

Karine Goglio-Primard

Innovation and Knowledge Sharing Across Professional Boundaries: Political Interplay between Boundary Objects and Brokers

The article examines the process of innovation and knowledge sharing from a perspective that focuses on the influence that local circumstances can have. In particular, it looks at the problems of knowledge sharing between groups of professionals. It presents a comparative analysis of two studies, one involving two groups of IT professionals; the other a network of healthcare professionals. The data was collected in two sets. The first set consisted of the results from two earlier, independent studies; the second was collected specifically for this article. We investigate the role played by boundary objects and brokers. Through an analysis of the interplay between boundary object and broker, we uncover the dynamics of the innovation process and show that the role played by the broker can be political. We identify two strategies that are used by brokers in the selection of a boundary object. The first is directed towards achieving a balance between the actors involved and the second is directed towards controlling their activities. We conclude by suggesting that other researchers should also consider the interplay between broker and boundary object when examining cross boundary knowledge sharing.

Introduction

It is now received wisdom that innovation stems from collaboration and knowledge sharing across professional or organizational boundaries. [START_REF] Conway | Informal Boundary-Spanning Communication In The Innovation Process -An Empirical-Study[END_REF] traces the idea back to the 1950s; [START_REF] Teigland | Integrating knowledge through information trading: Examining the relationship between boundary spanning communication and individual performance[END_REF] claim the idea originated in the 1960s; [START_REF] Henderson | Architectural Innovation: The Reconfiguration of Existing Product Technologies and the Failure of Established Firms[END_REF] draws on the literature from the 1970s. However, whatever its origin, the idea that innovation requires collaboration across boundaries is now well established [START_REF] Fagerberg | The Oxford handbook of innovation[END_REF].

The majority of the literature dealing with this area tends towards what [START_REF] Tsoukas | The firm as a distributed knowledge system: A constructionist approach[END_REF] describes as a taxonomic approach: seeking to discover global, or at least generic, solutions for effective knowledge sharing. These often attempt to formulate more or less complete descriptions of the different types of knowledge involved and to identify the specific conditions that facilitate their exchange. Such approaches are frequently based on macro level, multifirm surveys and tend to view knowledge sharing as a continuous process [START_REF] Holsapple | An investigation of factors that influence the management of knowledge in organizations[END_REF][START_REF] Hansen | Knowledge Networks: Explaining Effective Knowledge Sharing in Multiunit Companies[END_REF][START_REF] Bock | Behavioral intention formation in knowledge sharing: Examining the roles of extrinsic motivators, social-psychological forces, and organizational climate[END_REF][START_REF] Chen | How organizational climate and structure affect knowledge management -The social interaction perspective[END_REF]. The spread of electronic communication [START_REF] Coakes | Co-operative work practices and knowledge sharing issues: A comparison of viewpoints[END_REF] and notions such as the resource-based view of the firm [START_REF] Wernerfelt | A resource-based view of the firm[END_REF][START_REF] Grant | Toward a Knowledge-Based Theory of the Firm[END_REF] have also contributed to the popularity of this view. [START_REF] Tsoukas | The firm as a distributed knowledge system: A constructionist approach[END_REF]2002) however claims that this approach is fundamentally flawed; quoting [START_REF] Boden | The Business of Talk[END_REF] he argues that the structures that shape how knowledge is shared are always and inevitably influenced by "immediate circumstances and local agendas" (Boden, 1994, p. 18). He argues instead for a view of knowledge that is dispersed with no single actor in a position to formulate rules or principles to determine what knowledge should be shared. This approach tends to view knowledge sharing as an episodic rather than a continuous process. Where categories and taxonomies exist, "The stability of their meanings is precariously maintained" (Tsoukas & Chia, 2002, p. Studies that examine collaboration and knowledge sharing from this perspective have received less attention in the literature and tend to be long-term ethnographic studies that place more emphasis on group dynamics and organizational politics. Blacker and McDonald (2000) provide one such example. Taking an action research approach, they describe the problems of building and maintaining an understanding between a team of researchers and the company they are investigating in the face of the changing objectives and boundaries of both. Engeström's work on activity theory also provides some examples of this type of approach, for example when he describes the problems faced by teams of doctors in Finnish hospitals [START_REF] Engeström | When the center does not hold: The importance of knotworking[END_REF][START_REF] Engeström | Expansive Learning at Work: toward an activity theoretical reconceptualization[END_REF].

The goal of this article is to make a further contribution to this literature through an analysis of the issues that arise when groups of professionals from different organizations work together to achieve a collective goal; it does this through examining the findings from two independent case studies. Our approach uses boundary objects [START_REF] Star | Institutional Ecology, `Translations' and Boundary Objects: Amateurs and Professionals in Berkeley's Museum of Vertebrate Zoology[END_REF]) and brokers [START_REF] Wenger | Communities of Practice: Learning, Meaning, and Identity[END_REF] to track the ways in which groups manage the exchange of knowledge across their respective professional boundaries. In a departure from most other studies using boundary objects and brokers, we also examine the political interplay between boundary object and broker to reveal the influence of what Boden terms "immediate circumstances and local agendas" on this process.

Innovation and knowledge sharing across boundaries

Perhaps paradoxically, the root of the problem of effective cross boundary knowledge sharing is also what makes it of value. The knowledge within a group tends to reflect its own norms and preoccupations; this makes it unlikely that the group will generate novel ideas on its own. To do this a group needs the stimulus of fresh ideas and new information from outside. However, this exchange of knowledge is not without its difficulties.

In general terms, if one group does not share the other's world view, how can communication between the two ever, in [START_REF] Clark | Grounding in Communication[END_REF] terms, be grounded? If these groups exist in an environment that is itself changing, how much more difficult will the problem be? Finally, the more radical the innovation, the greater will be the potential problems of the redistribution of power across boundaries [START_REF] Christensen | Will disruptive innovations cure health care?[END_REF]. Cohesive groups, such as professional networks, pose a further set of problems.

Groups of professionals readily share knowledge related to their profession within the network but, for political and professional reasons, do not share this knowledge with outsiders [START_REF] Teigland | Integrating knowledge through information trading: Examining the relationship between boundary spanning communication and individual performance[END_REF]. Within such networks, informal meetings and working groups may be established to learn and share knowledge and provide actors with a space to compare professional practice. Even if they are not named as such, these often exhibit many of the features of Communities of Practice [START_REF] Wenger | Communities of Practice: Learning, Meaning, and Identity[END_REF]: groups that [START_REF] Swan | The construction of 'communities of practice' in the management of innovation[END_REF] and [START_REF] Hislop | The Complex Relations Between Communities of Practice and the Implementation of Technological Innovations[END_REF] observe can also inhibit the sharing of knowledge across boundaries.

Clearly, the sharing of knowledge across professional boundaries is both important and problematical. The notions of brokers [START_REF] Wenger | Communities of Practice: Learning, Meaning, and Identity[END_REF] and boundary objects [START_REF] Star | Institutional Ecology, `Translations' and Boundary Objects: Amateurs and Professionals in Berkeley's Museum of Vertebrate Zoology[END_REF] are widely cited as providing two possible channels through which such epistemically and politically distinct groups can communicate.

Brokers

Brokers are members of multiple communities and are able to make effective connections between them; they make co-ordination possible by opening up new possibilities for learning C. Kimble, C. Grenier and K. Goglio-Primard Innovation and knowledge sharing across professional boundaries: Political interplay between boundary objects and brokers. International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00 and exchange [START_REF] Brown | Organizing Knowledge[END_REF]. The broker's role is essentially that of an interlocutor: to help other actors transfer, translate or transform the meanings encountered during joint activities [START_REF] Carlile | Transferring, translating, and transforming: An integrative framework for managing knowledge across boundaries[END_REF]. Wenger describes it in the following way:

"The job of brokering is complex. It involves processes of translation, coordination and alignment between perspectives. It requires enough legitimacy to influence the development of a practice ... it also requires the ability to link practices by facilitating transactions between them and to cause learning by introducing into a practice, elements of another." (Wenger, 1998, p 109) A broker translates knowledge created in one group into the language of another so that the new group can integrate it into its cognitive portfolio. To do this, brokers must be able to manage the relations between individuals as well as act as translators.

The broker's role is a delicate balancing act. To be effective brokers need to have authority within all of the groups to which they belong. They need to be able to evaluate the knowledge produced by the different groups and to earn the trust and respect of the various parties involved. Over time, the broker's activities may lead to the development of a repertoire of shared resources such as rules, procedures and the boundary objects used by the group.

Boundary Objects

Like brokers, boundary objects are also concerned with communication between communities, although their role is more indirect. The term originates with [START_REF] Star | Institutional Ecology, `Translations' and Boundary Objects: Amateurs and Professionals in Berkeley's Museum of Vertebrate Zoology[END_REF] study of Berkeley's Museum of Vertebrate Zoology where they describe a boundary object as "an object that lives in multiple social worlds and which has different identities in each" (Star & Griesemer, 1989, p 409).

Boundary objects are artefacts that link different sets of diverse interests; they are the physical or virtual entities that allow groups to coalesce and form stable, if transitory, working relationships. They allow coordination without consensus or shared goals, as boundary objects permit an actor's local understanding to be reframed in the context of a wider collective activity [START_REF] Bechky | Sharing meaning across occupational communities: The transformation of understanding on a production floor[END_REF]. When different groups collaborate on a common task, some form of local agreement is necessary for the work to proceed. As the work progresses, these temporary local agreements are subject to negotiation and re-negotiation; new understandings are forged, new ideas generated and new accommodations made as the groups interact with each other.

Boundary objects are often technologies, although they can be drawings, sets of rules, research projects or documents. [START_REF] Kimble | Dualities, Distributed Communities of Practice and Knowledge Management[END_REF], for example, describe how a planning document that was originally designed for internal use within the UK core of a transnational community of practice became, initially, a boundary object between the UK and American cores and later between the community of practice and the functional groups that surrounded it. They describe how: "During discussions around the document, other new and innovative ideas would often be triggered; as well as identifying projects already listed on the document, new ideas emerged that could form the basis for further participation." (Kimble & Hildreth, 2005, p 108) [START_REF] Carlile | A Pragmatic View of Knowledge and Boundaries: Boundary Objects in New Product Development[END_REF] argues that boundary objects have a particular role to play in supporting the different forms of coordination found in collaborative working. When a situation is familiar and routine, a simple boundary object, perhaps only a single word, is all that is needed for a group C. Kimble, C. Grenier and K. Goglio-Primard Innovation and knowledge sharing across professional boundaries: Political interplay between boundary objects and brokers. International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00 to coordinate its activities. He terms this syntactic coordination, effectively a simple process of information transfer. As complexity increases, actors need to establish common meanings that are shared by everybody in the group. Here the boundary object needs greater informational richness in order to support what Carlile terms semantic coordination, a process involving some degree of translation. Finally, in novel situations that involve a degree of negotiation and compromise, a boundary object needs to be flexible enough to allow what he terms pragmatic coordination, a process involving change or transformation. This form of coordination is the most difficult to achieve as change can be costly if the actors have a stake in the established way of doing things. [START_REF] Carlile | Transferring, translating, and transforming: An integrative framework for managing knowledge across boundaries[END_REF] also recognizes the political nature of these processes, as the positions held by actors can be divergent and contradictory.

A comparative analysis of two cases

As we have seen, although the link between knowledge sharing and innovation is widely recognized, the sharing of knowledge can be problematical. The goal of this article is to contribute to the literature on knowledge sharing through an analysis of the issues that arise when groups of professionals work together. In particular, we wish to examine the dynamics and politics of knowledge sharing in such groups. In order to further our understanding of this process, our study will depart from others in this area and set out to examine the interplay between boundary object and broker to expose the effect of political and contextual factors on this process.

Methodology

The data for our studies came from two separate cases. The first was a group of IT professionals from different companies in a French science park who collaborated to build a Content Management System; the second was a series of innovations produced by a pluridisciplinary network of heath care professionals in a medium-sized French city. In both cases, the data was collected in two sets that covered a similar period.

The first set of data consisted of two independent studies that had been carried out by two of the authors in pursuit of their own individual research interests. The second set of data was collected by the same two authors who, in order to complete the comparative analysis presented in this article, returned to the field and re-interviewed key actors to gain a better understanding of their role (e.g. as broker) and the role of certain artefacts (e.g. boundary objects).

In particular, we were interested in the mechanisms by which the boundary objects were chosen, the different types of boundary objects that were deployed and the role of the broker in terms of their legitimacy and autonomy within the groups. All of the actors involved were interviewed several times at different points in the process; the interviews lasted from 30 to 90 minutes. The two data sets are summarized in Table 1 below.

The analysis followed what [START_REF] Denzin | The Discipline and Practice of Qualitative Research[END_REF] describe as a moderate inductive approach. The set of data from the first independent studies was re-used and, together with the set of data from second targeted study, was re-analyzed using a single set of questions that related to the process of innovation and the role of boundary object and broker [START_REF] Thome | Qualitative secondary analysis[END_REF]. Throughout the analysis, we followed the general principles outlined in [START_REF] Miles | Qualitative data analysis: An expanded sourcebook[END_REF] The system administrator that acted as a broker, 5 design engineers, 4 sales engineers, 2 e-business managers, the President of the Sophia Antipolis association and the person in charge of supervising the cluster dealing with innovation.

Two brokers, three physicians who had been involved since 2002 and one newly recruited neuropsychologist.

Table 1 Summary of the two data sets

The first study is based on a single technological innovation where, in order to succeed, a number of boundary objects, and later a broker, needed to be deployed. This study shows clearly how boundary objects and brokers change according to immediate circumstances and the demands of the particular task in hand. The second study concerns three separate, less technologically demanding, innovations each of which use only one boundary object and broker. Here we are able to see more clearly, how boundary objects, brokers and objectives change over time.

The results of this analysis are presented below in terms of the innovations that were produced by the groups, the boundary objects they used and the role of the broker in the process. Readers should note that although both studies illustrate the demands of "immediate circumstances and local agendas" (Boden, 1994, p. 18), they differ in character and emphasis.

Study one: the content management system

The first study was based in the Sophia-Antipolis Science Park near Nice in the south of France. Sophia-Antipolis is sometimes described as France's 'Silicon Valley'; it brings together more than 1,300 companies in the life sciences, multimedia, computer and telecommunications sectors and several educational institutions. In 1991, a group of scientists and engineers created an association so that people working in the park could exchange ideas and knowledge more freely. Over time, the association grew into a more formalized multidisciplinary community of professionals, whose members meet to discuss their work in expert seminars. Customers want straightforward, turnkey technical solutions to their problems.

Table 2 Actors and motivations in study one

The software engineers in companies A and B recognized the existence of various boundaries that would inhibit the achievement of their shared goal. The mechanism they used to overcome these was to attempt to develop a new system by co-building a web site for a customer from Company A. The success of this venture would rest on the ability of the two software companies and, to a lesser extent, the two companies and the customer, to share knowledge and expertise across boundaries.

"We would not have been able to meet the customer's expectations alone. Our cooperation with Company B, clearly made a difference for the customer and certainly influenced its final selection" (Manager, Company A)

The software engineers in Company A wished to use the CMS built by Company B in their own company's products. This would mean that they could provide web sites that had more functionality and were more efficient. Similarly, the engineers from Company B wanted to find new applications for their software, but lacked knowledge of other domains where it might be used.

Working together on the code for the CMS enabled both firms to begin to develop the new system and to consolidate their links with the customer. They were able to start to combine their technical and commercial expertise and to mobilize a project team to develop a solution.

The code for the CMS acted as the first boundary object and provided a degree of syntactic coordination, however, the problems of semantic coordination needed to be resolved using a different approach. In Company B, the software engineers knew each other well, worked C. The Sophia Antipolis Association exists primarily to facilitate professional links between organizations in the Sophia Antipolis Science Park. The software engineers from companies A and B were able to discuss the objectives and the technical problems of the CMS with their peers from other companies, their customers and members of the research institutions through seminars and forums organized by the association. Effectively, the events organized at the science park became the second boundary object and the mechanism by which the gap between the two groups was bridged.

"... our geographic and technological proximity helped us understand each other and be committed to the project" (Manager, Company B)

The association had also developed a professional code of conduct to facilitate the inter-firm cooperation that also helped to minimize any commercial concerns that might otherwise have hindered the process.

Finally, to deal with the problems of pragmatic coordination, the two companies appointed a systems administrator from Company B, the company that developed the original CMS, to act as an intermediary. This systems administrator effectively took on the broker's role and was required to give the final formal approval to the software created by the two groups of engineers.

"We appointed an engineer from firm B to this position. His specific role consisted in validating the functionalities created by our engineers and to inform us of existing functionalities" (Software Engineer, Company A)

However, to fulfil this role he needed to be able to coordinate the activities of other actors, to translate requirements between them and, crucially, to create a space where the actors could work free from the conflicts inherent in this type of venture [START_REF] Kaulback | Holding the Virtual Space: The Roles and Responsibilities of Community Stewardship[END_REF].

Through a series of informal meetings, he created a sense of commitment between the two sets of engineers that allowed them to share their knowledge and develop a mutual understanding. In terms of his wider role, he also helped to differentiate the contribution of the two firms, which in turn made them more attractive to their respective customers. Finally, he also helped the actors to use, understand and accept the rules of the association. Through this, the actors were able to recognize other firms' complementary skills and to learn to trust each other.

Thus, in this case, the role of the two boundary objects was to enable the coordination of the activities of the groups at the syntactic and semantic level. The role of the broker focused mainly on providing legitimacy for the proposed technical solutions, and on building trust and maintaining a fair and balanced exchange between the two firms. Thus, in this case, the broker's role was to manage the relationships between the actors at the pragmatic level. professional boundaries: Political interplay between boundary objects and brokers.

International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00

Study two: the healthcare network

For many decades, different professional groups in the French health sector have set up various collective arrangements to help improve their knowledge of, and response to, sociomedical issues such as AIDS, Alzheimer's disease and drug or alcohol addiction. These collective arrangements are normally set up when a response based on a single agency proves unsatisfactory. These arrangements are often termed 'cure and care' networks. In 1996, regulations began to be introduced that created a framework for such networks and set out the conditions under which they could receive public funding.

The network in this study is dedicated to the diagnosis, cure and care of the cognitive diseases. The network started in 2001 as an informal ad-hoc group, developed and grew over time, and finally became a publicly funded network at the end of 2004. The group brought together several disparate specialist communities that represented different, and occasionally conflicting, interests. The principal actors and their motivations are shown in Table 3 below.

Actors Areas of expertise / knowledge

Motivations

Physicians (General Practitioners)

Have a general knowledge of the patient and their medical history but work in isolated practices with no specialist knowledge of cognitive diseases.

Interested in any cognitive disorder.

Interested in facilitating diagnosis and the followup of the patient.

To enrich practice through maintaining a role in the long-term follow-up of a patient.

The Neurologist

Has specialized knowledge in Alzheimer's disease.

Interested in tools to help a neurologist make a more rapid diagnosis.

To maintain the core role of neurologists in diagnosis.

The Gerontologist

Knowledge of cognitive disorders and other pathologies in elderly people.

Interested in taking part in the diagnosis, including having the right to make a diagnosis instead of the neurologist.

The Coordinator (Neuropsychologist)

No practice before the emergence of the network (new role and new knowledge).

To maintain a pluridisciplinary-based approach to work and to coordinate practices.

Interested in any social intervention with patients and their families.

The Speech Therapists

Mostly involved with elderly and disabled people.

To be more involved and to be legitimized as an actor that participates in the care and cure of people with cognitive disorders.

Table 3 Actors and motivations in study two

Initially, a neurologist, some physicians, a gerontologist and a speech therapist started to meet on a monthly basis to hold 'case conferences' -collective discussions that allow different points of view to be heard and common themes to be identified. In the early stages of the network, the physicians used their own patient files for these discussions. The case conferences, which were organized by the neurologist, highlighted the need to have one tool to help physicians to quickly and simply differentiate cognitive disorders from other disorders with similar symptoms. The rapid memory test was developed in response to this need.

The neurologist, who effectively acted as a broker, arranged the network in such a way that it would focus on patients with the problems that he was skilled in diagnosing and interested in, mainly those with Alzheimer's disease.

C. The selection of patient files by physicians as boundary objects strengthened this position. The network preserved an informal but strongly institutionalized hierarchy that meant neurologists were the only ones allowed to make a diagnosis of the disease. The neurologist regulated the links between the different professional communities in such a way that he limited the opportunities for different communities to mix. In effect, he reinforced his own authority and his community's professional boundaries.

The rapid memory test was developed based on information gained from the crossing of boundaries; however, it represented little more than a means of improving the links between the work of physicians, who were able to use the test to identify possible cognitive disorders, and the neurologists, who were able to see the patient more quickly. Once the rapid memory test had been developed and training sessions in its use had begun, some physicians and speech therapists began to discuss the development of a more comprehensive tool for the assessment of Alzheimer's disease. This tool, which would allow neurologists to make a more detailed diagnosis of the disease, became the cross-disciplinary neuropsychological assessment.

Once again, the neurologist controlled the links between the professional communities, although he now had to open the discussion to speech therapists and neuropsychologists. He acted as a broker, directing the discussion and validating any proposed solution. For example, he turned down the proposal by a gerontologist, skilled in diagnosing diseases of the elderly, that gerontologists should play a role in the diagnosis process arguing, "... dementia is not Alzheimer disease; dementia is a cognitive process of cognitive degradation. It is very different from the Alzheimer disease; the latter is much more complex. You cannot make a diagnosis of Alzheimer disease with a gerontologist diploma" (neurologist)

The gerontologist did not attend any further meetings of the network.

The development of the cross-disciplinary neuropsychological assessment was supported by the same boundary object and the same boundary hardening strategy as the previous example and achieved the same outcome for the neurologist.

"Thanks to the network, I can now concentrate on the diagnosis of the more complex cognitive cases … the other less complex cases are examined and diagnosed by other actors" (neurologist)

However, this innovation was only made possible by an additional crossing of a professional boundary when the physicians and the speech therapists began to discuss their respective professional practices together. The actors, involved all agreed that the process was slower and more difficult than the first, as the physician's patient file did not really contain adequate information to build a more interdisciplinary form of coordination.

The coordinated patient trajectory was the third innovation produced by this network. This consisted of a comprehensive assessment that identified all the actors concerned with the care and cure of cognitive disorders, from the initial diagnosis to the follow-up social and medical care. This required the use of a different boundary object, the case files of patients C. Kimble, C. Grenier and K. Goglio-Primard Innovation and knowledge sharing across professional boundaries: Political interplay between boundary objects and brokers.

International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00 who had already been followed-up by the network. These files contained information collected during other aspects of the network's activities. For example, "Sometimes patients deliver to the speech-therapist or other actors, information that they would not give to their family physicians" (speech therapist)

It also required the opening of discussions to new actors with expertise in the social and medical follow-up of the patients and of their families. This innovation was made possible by a change of broker, which was dictated primarily by a change in local circumstances. The network was seeking public funding and, in order to meet the criteria to receive public funds, it had to show that the goal of the network was to coordinate the activities of all of the actors involved in the care and cure of the patient. The neurologist stepped down and a neuropsychologist took on a new and more formal role as network coordinator.

The neuropsychologist was interested in care and cure activities after the initial diagnosis had been made, and so was open to involvement of groups other than physicians and neurologists. After the coordinated patient trajectory had been developed, it was accepted that the initial diagnosis of Alzheimer's disease could be made either by a neurologist or by a gerontologist, reversing the group's previous decision.

"Thanks to the network, all various actors are now involved and each one has found his place [in the coordinated patient trajectory]" (coordinator)

This case, which covers a longer period and wider range of activities, presents a rather more complex picture than the first as here brokers, boundary objects and high-level objectives all changed over the period of the study. Consequently, this case more clearly illustrates the use of the boundary object either to control the direction of the collective action or to open a broader discussion of topics around the object.

Discussion: the interplay between boundary objects and brokers

We saw earlier that the literature on innovation and knowledge sharing describes brokers and boundary objects as channels through which epistemically distinct groups can communicate and collaborate. We adopted this general approach to examine the process by which knowledge is shared and innovations are produced at a local level.

At first sight, the boundary objects in our study simply acted as a means for transforming and transferring knowledge between groups. It appeared that it was mainly the complexity of the innovation that determined which boundary object was chosen [START_REF] Carlile | A Pragmatic View of Knowledge and Boundaries: Boundary Objects in New Product Development[END_REF][START_REF] Carlile | Transferring, translating, and transforming: An integrative framework for managing knowledge across boundaries[END_REF]. The selection of the boundary object appears to be a 'technical' choice based on the level of information needed to sustain the innovation process; the broker merely acts as tertius iungens by connecting the interested parties [START_REF] Obstfeld | Social Networks, the Tertius Iungens Orientation, and Involvement in Innovation[END_REF].

In the first study, the code for CMS (the first boundary object) allowed the actors to develop the concrete technical solutions that allowed them to make some initial progress with their work. Similarly, the framework and rules provided by the association (the second boundary object) allowed the actors to continue to work together in ways that would not have been possible without them. The association fostered the development of trust and commitment between the two firms, firstly because the association was itself composed of expertscompetence based trust -and secondly because membership of the association bound its members to a code of behaviour allowing the development of trust based on reciprocity and goodwill. professional boundaries: Political interplay between boundary objects and brokers.

International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00

In the second study, the patient file created by physicians (the first boundary object) allowed actors to create the first two innovations, the rapid memory test and the cross-disciplinary neuropsychological assessment, but the patient file created by the network as a whole (the second boundary object), was required to support the third innovation, the coordinated patient trajectory. Changes in the boundary object occurred when the former boundary object was no longer able to sustain the innovation process because of its inability to support a discussion that included a wider range of competences. Thus, the second boundary object was chosen specifically in order to embrace these competencies.

However, by further examining the interplay between broker and boundary object, we are able to highlight an additional dimension to the selection of the boundary object: the boundary object as a resource for actors who wish to further their own interests. [START_REF] Grenier | Apprentissage de la coordination entre acteurs professionnelsle cas d'un réseau de santé[END_REF] suggests that the boundary objects are often chosen by the leaders of groups in accordance with the degree of diversity they are prepared to tolerate. Applying this perspective to our study reveals an additional dimension and a more complex story. We propose a 'political' interplay between boundary object and broker.

In the first case study, the two software companies were potential competitors in the same market. Using the CMS code alone laid one company open to the 'extortion' of its knowledge by the other. Consequently, the broker need to introduce a second boundary object to maintain fair and balanced cooperation. In doing so, the broker acquired a legitimacy that was beyond a simple recognition of his technical skill which allowed him to set the conditions for cooperation between companies, avoid an unbalanced appropriation of knowledge by one company from the other, and maintain a stable environment in which the work that they were all engaged in could proceed smoothly. In this example, the selection of the boundary object was a political act taken to maintain the stability of the collective that effectively allowed a new inter-firm Community of Practice to emerge based around the common goal of commercial success and the sharing of ideas on the building of a CMS.

The second study presents a slightly different picture from the first. The first broker, the neurologist, selected a boundary object that favoured the interests of his own and the physician's professional body. This strengthened his position and that of his professional community. The second broker, the neuropsychologist, also made a political choice, but for different reasons. She chose a boundary object that would reorient the network towards the social care of the patients rather than the diagnosis of diseases. She selected an object that allowed more diversity and acknowledged the value of the other actors' expertise, thus weakening the position previously established by the neurologist. Thus, in this example, the choice of boundary object was also a political act directed towards (re)defining or steering the direction of the evolution joint enterprise, by either restricting the flow of information or by giving a greater acknowledgement to the importance of other actors' expertise.

Boundary objects are particularly appropriate for this task as they have not only symbolic value but also a political message [START_REF] Swan | The construction of 'communities of practice' in the management of innovation[END_REF]. Viewed in this way, our work complements that of Gal et al [START_REF] Gal | The Dynamics of Boundary Objects, Social Infrastructures and Social Identities[END_REF] who consider boundary objects to be a resource that can be used to transform social identities. By looking more closely at the interplay between broker and boundary object we can reveal how the selection of the boundary object can be a political act directed towards maintaining or redefining the direction of the group's activities. Using Obstfeld's terminology [START_REF] Obstfeld | Social Networks, the Tertius Iungens Orientation, and Involvement in Innovation[END_REF], in these circumstances, the broker acts as tertius gaudens ("the third who benefits") rather than tertius iungens ("the third who joins").

Comparing the two cases, we see two forms of political interplay emerge: one is more collectively oriented and comes into play where a broker selects a boundary object to further C. Kimble, C. Grenier and K. Goglio-Primard Innovation and knowledge sharing across professional boundaries: Political interplay between boundary objects and brokers. International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00 collective goals; the other is more individually oriented, and comes into play when a broker chooses a boundary object principally to defend their own position. These two political orientations for the interplay between boundary object and broker are summarized in table 5 below

Collectively-oriented strategy

Individually-oriented strategy The role of the boundary object

The boundary object functions at different levels: it contains both technical information and offers ways to work collectively.

The boundary object is an intermediary object, offering mainly technical information related to the innovation.

The interplay between broker and boundary object

The boundary object is mobilized by the broker to aid the exchange of information and to facilitate coordination between the actors in the collective.

The boundary object is mobilized by the broker to limit the amount of information available and to define the direction of the joint enterprise.

Table 4 Political interplay between boundary object and broker 5 Conclusions

Innovation in groups depends on information and knowledge gained by crossing boundaries between communities of actors. This is a difficult and complex process because, for it to be successful, the actors from the different communities must first reach a shared understanding about what they are trying to do and how it might be achieved. These problems can be exacerbated when the communities of actors concerned are groups of professionals where their respective professional knowledge is what helps to define their status and is the key to their authority.

Much of the work in this area suggests that the selection of a boundary object is more or less technical in nature: a matter of choosing the right boundary object for a particular set of circumstances [START_REF] Harvey | Boundary objects and the social construction of GIS technology[END_REF][START_REF] Smeds | Global business process development in a virtual community of practice[END_REF]. Our studies suggest that this process is more complex, dynamic and can be explicitly political in nature. We believe that this observation constitutes our first contribution to the work in this area. We therefore suggest that, in addition to simply looking at the role of the boundary object, researchers should also examine the role of a broker in its selection.

Our second contribution is to qualify this political interplay between boundary object and broker further and identify two distinct strategies by which a broker might use a boundary object. The first is directed towards achieving some form of political balance between the actors in a community and focuses on making information more available. The second is directed towards the definition or control of the overall direction of the community and is more concerned with controlling the flow of information.

We believe that by adopting this approach of examining the interplay between boundary object and broker, researchers will be able achieve a more rounded view of the dynamics of innovation and knowledge sharing, particularly in situations such as those we describe here. We believe that, in turn, this could lead to the consideration of other political dimensions in this process, such as who should be in charge of the system of brokerage, what that system should be and other issues related to what might be termed the governance of innovation.

  573): they are stable enough to be consistently deployed, but are always transient, local and open to negotiation. C. Kimble, C. Grenier and K. Goglio-Primard Innovation and knowledge sharing across professional boundaries: Political interplay between boundary objects and brokers. International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00

  methodological framework: data reduction, coding and analysis based on codes created from a review of the literature and emergent codes created during analysis.

		Content Management System	Emerging Healthcare Network
	Period of collection for the first data set	From 2003 to 2006	From 2002 to 2007
		20 software engineers (8 from firm	The number varied from 6 (the
		A and 12 from Firm B), 2 e-	initiator of the network, some
		business managers and 8 sales	physicians, a speech therapist, a
		engineers (3 from Firm A and 5	neurologist and a
	Number and categories of	from Firm B), the system	neuropsychologist, including the
	actors interviewed	administrator who acted as a	two actors acting as brokers) to
		broker, the President of the Sophia	more than 15 actors (additional
		Antipolis association and the	physicians, speech therapists,
		person in charge of supervising the	together with the two actors acting
		cluster dealing with innovation.	as brokers)
	Period of collection for the second data set	November 2008	November 2008
	Number and categories of
	actors interviewed

C. Kimble, C. Grenier and K. Goglio-Primard Innovation and knowledge sharing across professional boundaries: Political interplay between boundary objects and brokers. International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00

  However, to do this, they needed to work with a second group of engineers in Company B. Company B had already designed and built a CMS but wanted to improve its functionality by using it in different application areas. Both companies were independent Business Units that sold and marketed software solutions, and both had a network of local offices in France. Similarly, both groups of engineers had professional skills and expertise in their own right, both had specific knowledge that the other needed, but neither had knowledge of the other's practices or working methods. The principal actors and their motivations for the first study are shown in Table2 below.

	Principal Actors	Areas of expertise /	Motivations
		knowledge
	Eight software engineers belonging to a computer services company (Company A)	All the actors share the same practices and have similar technical expertise.	Company A wish to appropriate the functionality of the CMS built by Company B to add value to the bids they make to customers.
		All the actors share the same
	Twelve software	practices and have similar	Company B wants to find new
	engineers belonging to a	technical expertise. The actors	applications for their existing
	software development	have already succeeded in	CMS and promote its use in the
	company (Company B)	creating a CMS that is currently	Sophia Antipolis and beyond.
		in use.
		Domain knowledge of
	Business Customers	semiconductors, telecom
		services, infrastructure services.

The study focused on two groups of software engineers, one belonged to a computer services company (Company A); the other to a software development company (Company B). The engineers from Company A wanted to build a particular type of Content Management System (CMS) that would increase the value of the bids made by the commercial services division of C. Kimble, C. Grenier and K. Goglio-Primard Innovation and knowledge sharing across professional boundaries: Political interplay between boundary objects and brokers. International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00 that company.

  and observed each other's practices. This enabled them to share their experience and knowledge when developing new versions of the CMS within the company. However, when working with engineers from Company A, "... it's very difficult to develop trust between two competing firms because we have strategic skills that we use for the same customers"(Engineer, Company B)

Kimble, C. Grenier and K. Goglio-Primard Innovation and knowledge sharing across professional boundaries: Political interplay between boundary objects and brokers. International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00 closely together

  "... thanks to [the network] I can receive in my office one patient with a richly documented file, so as to ease the making of the diagnosis" (neurologist)

Kimble, C. Grenier and K. Goglio-Primard Innovation and knowledge sharing across professional boundaries: Political interplay between boundary objects and brokers. International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00

professional boundaries: Political interplay between boundary objects and brokers. International Journal of Information Management, 30(5), 2010, pp. 437 -444. DOI: 10.1016/j.ijinfomgt.2010.02.00