Marcelo D Vinces

Matthieu Legendre

Marina Caldara

Masaki Hagihara

Kevin J Verstrepen

Unstable Tandem Repeats in Promoters Confer Transcriptional Evolvability

come

The genomes of most organisms are not uniformly prone to change because they contain hotspots for mutating events. An abundant class of sequences that mutate at higher frequencies than the surrounding genome is composed of tandem repeats (TRs, also known as satellite DNA), DNA sequences repeated adjacent to one another in a head-to-tail manner (1). Errors during replication make TRs unstable, generating changes in the number of repeat units that are 100 to 10,000 times more frequent than point mutations (2). Variable TRs are often dismissed as nonfunctional "junk" DNA. However, some TRs located within coding regions (exons) have demonstrable functional roles. For example, TR copy numbers in genes such as FLO1 in Saccharomyces cerevisiae generate plasticity in adherence to substrates (3). In canines, variable repeats located in Alx-4 and Runx-2 confer variability to skeletal morphology, which may have facilitated the diversification of domestic dogs bred by humans (4). Thus, repeats located in coding regions may increase the evolvability of proteins.

There is also evidence that repeats influence expression of certain genes (5)(6)(7). To investigate the involvement of TRs in gene expression variation, we first mapped and classified all repeats in the S288C yeast genome (8) (data set S1). TRs are enriched in yeast promoters (table S1). Of the ~5700 promoters in the genome, 25% (1455) contain at least one TR. Many TRs in promoters consist of short, A/T-rich sequences (table S2, fig. S1, and data set S2). Comparison of orthologous regions in genomes of different S. cerevisiae strains showed that many of the TRs are variable (data set S1). For example, 24.1% of orthologous TR loci in promoters differ in the number of repeat units between the two fully sequenced strains, S288C and RM11 [START_REF]Material and methods are available as supporting material on Science Online[END_REF]. To confirm this, we sequenced 33 randomly chosen promoter repeats in seven S. cerevisiae genomes (Fig. 1A, figs. S2 and S3, and data set S3). Twentyfive of the 33 TRs differed in repeat units in at least one of the seven strains. The repeat variation frequency is 40-fold higher than the frequency of insertions and deletions (indels) and of point mutations in the surrounding nonrepetitive sequence (P < 10 -15 ) (figs. S2 and S3).

To determine whether promoter TR variation affects gene expression, we compared repeat variablity to expression divergence (ED), which represents how fast the transcriptional activity of each gene evolves [START_REF] Choi | [END_REF](10)(11). Promoters containing TRs showed significantly (P < 1.75 × 10 -4 ) higher amounts of ED than did promoters lacking TRs when comparing yeast species (S. cerevisiae, S. paradoxus, S. mikatae, and S. kudriavzevii) (Fig. 1, B to D, and fig. S4A) and S. cerevisiae strains (S288C and RM11) (Fig. 1, E to G, and fig. S4, B andC). This difference was independent of factors known to affect transcriptional divergence, for example, the presence of TATA boxes (fig. S5). Only promoters containing variable numbers of repeat units between strains or species showed the elevated ED (Fig. 1, D andG). Furthermore, when variable TRs were binned into variable and highly variable (10% most variable) groups, highly variable repeats displayed even higher ED. Hence, ED correlates not merely with TRs in promoters but more specifically with repeat number variation.

To directly test whether changes in promoter TRs affect transcriptional activity, we varied the TR repeat number in the promoters of yeast genes YHB1, MET3, and SDT1 (Fig. 2 and fig. S6A). For each construct, expression increased as the length of the TR increased from zero, until a certain size was reached, after which expression dropped off. To determine whether natural variation between strains corresponded to similar changes in gene expression, we cloned promoters of several strains into the respective promoters of strain S288C. These transformants indeed mirrored the expression-level patterns that we observed with the engineered TR strains (fig. S6,B to D). Moreover, TR-mediated changes in expression have functional consequences. SDT1 encodes a pyrimidine nucleotidase that confers resistance to the nucleotide analog 6-azauracil (6AU) (12), and we observed that strains with various SDT1 promoter TR constructs show differences in growth that match the SDT1 expression changes (fig. S7).

Because promoter TR length variation affects transcription, we speculated that it should be possible to exploit promoter TR instability to quickly select for changes in gene expression. We used strains with a relatively long SDT1 TR tract, because repeat mutation rates increase with increasing tract length (13), and selected for variants having higher gene expression. The SDT1 open reading frame was replaced with selectable markers, either URA3 or yellow fluorescent protein (YFP), for selection in SC-ura (medium requiring yeast to express URA3 to grow in) or selection by sorting with flow cytometry, respectively. After a few rounds of selection, both regimes yielded mutants that showed increased growth on medium lacking uracil or increased YFP fluorescence. These mutants showed significant (P < 1 × 10 -15 ) changes in the length of the TR tract in the SDT1 promoter. The most common tract lengths yielded by both selections was 13 repeats (26 nucleotides), corresponding to a size close to that of the engineered TR constructs with the highest expression (Fig. 2B). Construction of a 13-unit TR revealed that it had the highest expression of all the engineered strains (Fig. 3A). When strains containing the long TR tract were grown without any selective pressure, most strains remained at the initial 48 units, and the few mutants that arose show a broader TR size distribution. We were unable to obtain strains with higher expression or TR size changes when the repeat sequence in the promoter was replaced by a randomized (no repeat) sequence of equal length as the 48-unit repeat tract (Fig. 3B).

TRs can contain transcription factor (TF) binding sites, so variation in the tract length may result in the removal or addition of binding sites. Of the 1455 TR-containing promoters, 113 contain known TF binding sites located within the repeats. Many of these TRs overlap stress-response TF binding sites (table S3). Investigation of one of these TRs, located in the promoter of YKL107w, indicated that, in this case, changes in the TR number may affect transcription through variation in the number of binding sites of the oxidative-stressresponsive TF, Yap1 (fig. S8).

Most promoter TRs, however, do not overlap known TF sites, indicating that another mechanism underlies repeat-related expression differences. To investigate whether distance between promoter elements affects transcription, we replaced the SDT1 TR with different DNA sequences of the same length. These changes mostly led to severely reduced transcription, indicating that altered spacing alone is not sufficient to explain the effect of repeat variation on transcription (Fig. 4, A to C). Many promoter TRs are extremely A/Trich, suggesting they may facilitate DNA melting. However, some of the constructs with the same high A/T content as the original repeat tract still show reduced transcription.

Most promoter TRs are located ~200 base pairs upstream from the translational start codon (Fig. 4D and fig. S9), corresponding to the nucleosome-free region of yeast promoters (14), suggesting a link between chromatin structure and TRs. We compared available genomewide nucleosome positioning data with the positioning of TRs. Nucleosome density across promoter regions showed an inverse correlation with the presence of TRs (Fig. 4D and fig. S9A). Nucleosome depletion is especially pronounced around AT-rich repeats, which compose 80% of all repeats (fig. S9B). These results suggest either that TRs preferentially form in nucleosome-free regions or that nucleosomes cannot easily bind TRs. We also found that nucleosomes containing the histone variant H2AZ (15) tended to border the TRs (Fig. 4D and fig. S9). Although no simple rule governs nucleosome positioning, nucleosome positioning in the yeast genome is largely directed by DNA sequence (15)(16)(17)(18), and a computational algorithm exists that uses DNA sequence information to predict where nucleosomes bind (16,19). This algorithm predicts that TR regions in promoters are nucleosome-free (fig. S10), suggesting that promoter TR sequences intrinsically bind poorly to nucleosomes, presumably because the repeats affect biophysical properties of DNA (e.g., bendability) (20). In line with these predictions, an analysis of a transcriptome data set for a large group of chromatin remodeling mutants (21) showed that the expression of repeatcontaining promoters is strongly influenced by regulators of chromatin structure and activity (fig. S11).

If repeats control nucleosome positioning, changing the repeat sequence should influence the local nucleosome structure. Deletion of the TR of SDT1 resulted in binding of nucleosomes to this region and also disturbed the positioning of downstream nucleosomes (Fig. 4E). Intermediate deletions of the TRs resulted in gradual changes in nucleosome occupancy (fig. S12), indicating that repeat variation directly affects the local chromatin structure. Replacing the repeat with a sequence predicted to have a high affinity for nucleosomes (19) resulted in a well-positioned nucleosome in the previously nucleosomefree region and in greatly reduced SDT1 expression (Fig. 4, F andG).

Although several molecular mechanisms may underlie the effect promoter TRs have on gene expression, our data indicate that repeat-dependent changes in DNA sequence and chromatin structure play a role. Local chromatin structure is known to affect transcriptional activity (22). Most repeats in promoters do not contain the hallmark dinucleotide periodicities that are associated with nucleosome-binding DNA (19). As a result, these repeat tracts may help to establish variable nucleosome-free DNA structures and influence nucleosome positioning in nearby regions. Moreover, because of the high A/T content of most promoter TRs, it remains to be tested whether these nucleosome-free TRs may allow DNA melting for loading of the RNA polymerase.

Changes within coding regions and in protein sequence underlie much biological adaptation and innovation. However, changes in the regulation of genes may be equally important (23,24). Our results presented here are consistent with a role for TRs as ubiquitous and adjustable "evolutionary tuning knobs" (25) for transcription that mediate rapid evolution of gene expression. Genes that respond to changing environmental conditions would be particularly suited for such variable genetic elements. Indeed, genes driven by repeatcontaining promoters show elevated responsiveness to changing environmental conditions (fig. S13).

A preliminary analysis of Homo sapiens promoters reveals a TR distribution comparable to that of yeast, suggesting that similar mechanisms are also at play in higher organisms (fig. S14).

Promoters containing variable TR tracts show elevated expression divergence. (A)

Nucleotide alignments of two gene promoters from seven yeast strains (indicated on left side and in table S4) showing variable TRs (boxed). More examples in fig. S2 and data sets S1 and S3. (B) ED is associated with presence of TRs. Promoters were divided into those containing TRs and those lacking TRs. The average ED calculated from expression data from four Saccharomyces sensu strictu yeast species (S. cerevisiae, S. paradoxus, S. mikatae, and S. kudriavzevii) (11) is greater for promoters that contain TRs than for those that do not (P < 1.75 × 10 -4 ; error bars represent SE). (C) Promoters analyzed in (B) were sorted by their EDs and split in bins of 100 promoters (fig. S4A). The number of repeatcontaining promoters in each bin and ED were significantly correlated. Shown is the correlation coefficient of the data set (blue dot; Z score = 2.70, empirical P value = 6.75 × 10 -3 ) and of randomly shuffled data (gray histogram). (D) Only repeats that vary between the four yeast species show elevated ED. ED was calculated for promoters divided into four categories as shown (error bars represent SE). (E to G) Similar analyses as in (B) to (D), except that ED values were calculated by using data from two S. cerevisiae strains (S288c and RM11) [START_REF] Choi | [END_REF]. The results show a similar correlation of variable repeats and ED (all P values are < 10 -3 ). The data set for (F) is in fig. S4B. (15); and location of greatest TR enrichment, dashed vertical line. All repeat-containing promoters were aligned relative to the translational start site (ATG) or to the transcriptional start site (fig. S9A). (E) Deletion of TRs in the SDT1 promoter interferes with maintenance of the nucleosome-free region. SDT1 coordinates on the x axis are relative to the ATG. The y axis represents the signal from a PCR-based nucleosome positioning assay (26). The yellow box represents TR location. Inferred nucleosome positions based on our experimental data in the graph are depicted above (WT, blue ovals; -TR mutant, red ovals). Above these are the predicted nucleosome profiles (16). (F) Nucleosome positioning when SDT1 promoter TRs are replaced with a sequence predicted to position nucleosomes (Nuc+). (G) SDT1 expression in the Nuc+ strain compared with those of WT and TRstrains.

Fig. 1 .

 1 Fig. 1.

Fig. 2 .

 2 Fig. 2. Mutation of TRs in promoters alters gene expression. Sets of strains with varying numbers of repeat units were constructed for two yeast gene promoters: (A) MET3 and (B) SDT1. Expression was determined by quantitative polymerase chain reaction (PCR). All values are normalized to transcript levels of housekeeping gene ACT1 and to wild-type (WT) expression levels; error bars indicate SE, n = 3. Data for YHB1 are in fig. S6A.

Fig. 3 .

 3 Fig. 3.Experimental evolution of gene expression mediated by TRs. (A) Selection for higher expression of the SDT1 promoter results in changes in the number of TR units in the promoter. The starting strain (48 repeat units, indicated by arrow) has relatively low expression (blue line, left axis). The green (URA3) and red (YFP) lines represent the final size distributions of TRs after selection for higher expression by using URA3 or YFP reporters. TR size distribution without selection (black line) remains mostly at the initial 48 units. See (8) for details. (B) Growth on SC-ura medium of strains with native URA3 (positive control); with ura3 deleted (negative control); and with URA3 fused to the SDT1 promoter containing a long nonrepetitive (scrambled, random) sequence, a 48-AT repeat, or a 13-AT repeat.

Fig. 4 .

 4 Fig. 4. TRs act as nucleosome positioning elements in promoters. Replacement of TRs with various sequences of the same size does not restore normal gene expression of (A) MET3, (B) YHB1, or (C) SDT1. TRs were replaced with other sequences of the same length: random (nonrepetitive) sequences (% A/T content indicated) and dinucleotide repeats (TG and TT repeats). The TR-strain lacks the entire TR. Error bars represent standard errors. (D) Genome-wide nucleosome position is largely anticorrelated with positions of TRs. Positions of the TR tracts are marked in blue; nucleosome positions, red (18); H2AZ nucleosome positions, green (15); and location of greatest TR enrichment, dashed vertical line. All repeat-containing promoters were aligned relative to the translational start site (ATG) or to

Science.Author manuscript; available in PMC 2011 July 11.

Acknowledgments

We thank B. Calderon, B. (Sze Ham) Chan, and B. Breaux for their contributions; B. Stern, E. O'Shea, A. Murray, A. Rowat, and A. New for critique of the manuscript; and the anonymous reviewers for their useful suggestions. Research in the lab of K.J.V. is supported by NIH National Institute for General Medical Studies grant P50GM068763, Human Frontier Science Program (HFSP) award RGY79/2007, the Flemish Institute for Biotechnology (VIB), and the Fonds Wetenschappelijk Onderzoek Vlaanderen-Odysseus program. M.D.V. acknowledges the Ford Foundation and the Belgian American Education Foundation.

Supplementary Material

Refer to Web version on PubMed Central for supplementary material.


domain: spi phys math info

text:
A Practical Method to Speed-up the Experimental Procedure of Iterative Learning Controllers

Oktay Koc ¸an1 , Augustin Manecy 1 , Charles Poussot-Vassal 1

Abstract-This paper proposes a practical approach for fastening the lengthy experimentational processes that may occur with iterative learning control (ILC) upto a certain level using simple low order identified models. The traditional practice in ILC experiments is to update the ILC signal by directly using the experimental data after each run of the process which corresponds to one ILC update per one run. When considered from the point of experimental time, even conducting a moderate number of ILC updates can take quite long with this procedure. Since an accurate linear model can adequately represent the actual system upto a certain amplitude and/or frequency of the desired reference, we propose that the experiment length can be reduced by updating the ILC signal via predicted system data until the limits of the linear model. This approach allows one to carry out large number of ILC updates while not needing to carry out the same amount of real experiments. Consequently, a significant number of experiments that would be needed for achieving the same results can be skipped with a simulation approach. The efficiency of the proposed method was tested through experimentation with three different UAV reference trajectories and the results demonstrated that it is possible to attain significant amount of tracking precision in several flight experiments.

I. INTRODUCTION

One can think of iterative learning control (ILC) as to simply learn from the previous trial errors of a process (e.g. trajectory or movement). The repetitiveness of the process under same initial conditions is a must for ILC since it improves the output tracking by filtering the repeated error. This filtered error is used to change the system input in the following trial in order to reach a better tracking.

An ILC can significantly improve a system's behaviour when it is used in conjunction with traditional control techniques such as feedback control. This is a result of the efficiency of ILC in completing the deficiencies of traditional controllers when it comes to repeating errors and lags in the output. Although a well designed feedback controller can successfully deal with non-repeating disturbances and noise, its control signal does not depend on the repetitiveness of the process and stays the same for each system run which gives the same amount of repeating non-zero tracking error [START_REF] Owens | Iterative learning control -an optimization paradigm[END_REF]. In such a case, ILC provides with an advantage of detecting the repeating errors between process iterations and eliminating them gradually as iterations continue.

Another reason that makes ILC an appealing method is that it can easily be integrated to an existing system. Unlike adaptive controllers and neural network controllers which modify the control parameters in the system, ILC only modifies the input signal [START_REF] Bristow | A survey of iterative learning control: A learning-based method for high-performance tracking control[END_REF]. Therefore, one can simply add the ILC to an already designed closed-loop system by way of an open loop connection.

One can notice that the majority of the recent ILC publications is related to an optimization-based ILC update method even though there exist many other ILC update methods such as Ptype, D-type, PD-type, fractional-order, inversion-based ILCs. This preference can be seen as a result of the efficiency and the promisive nature of the optimization based approaches. In general, the optimization based ILC methods are grounded on solving a convex optimization problem that is defined by an objective function to be minimized under some constraint equations. The main goal here can be seen as making the tracking error of the system as small as possible by varying the system input. A sufficient understanding on the application of optimization based ILC methods can be gained through [START_REF] Gunnarsson | On the design of ilc algorithms using optimization[END_REF]- [START_REF] Togai | Analysis and design of an optimal learning control scheme for industrial robots: A discrete system approach[END_REF]. Moreover, the P.h.D theses [START_REF] Norrlof | Iterative learning control: Analysis, design, and experiments[END_REF] and [START_REF] Hatonen | Issues of algebra and optimality in iterative learning control[END_REF] are quite useful for having a deeper insight on the mathematical theory as well as for reviewing derivations of convergence conditions in general.

The outline of this paper hereafter is as follows: Section II explains the idea behind our method; Section III gives insight to the details of the control architectures we used and designed; Section IV shows the experimental setup including the data flow and initialitation processes; Section V represents our experiment results and analyses; and finally Section VI is dedicated for the conclusions.

II. UAV ORIENTED PROBLEM STATEMENT

A general practice when conducting ILC experiments with UAVs is to perform one ILC signal update per flight of a given trajectory. In other words, each update is done utilizing the experimental data of the previous flight. Although it is straightforward to follow such an update procedure, one can argue about the efficiency of this approach when the number of experiments that are needed to be done to get the stabilizing ILC signal increases. Moreover, the procedure of experimentation with UAVs can become tedious considering the factors such as the time spent for the experimental setup, the length of the chosen flight trajectory, the requirement of battery change and any unexpected problem that may occur along the flight and cause a need of rerun. Under these conditions, even conducting 20 experiments may take long, not to mention the cases in which the number of experiments reaches more than 100 as in [START_REF] Lupashin | A simple learning strategy for high-speed quadrocopter multi-flips[END_REF]. On the other hand, it is usually easy to obtain a linear dynamic model of a UAV for a given trajectory. If the task is to reach a certain tracking performance, using this linear model with ILC can make it much faster to approach the desired performance when ILC is applied in a non-traditional way by using predicted iteration data. The linear model can be utilized to predict the future flight data and to carry out large number of ILC iterations which would then allow one to largely improve the ILC signal without needing to actually perform real flight experiments. What makes this practical approach interesting is that one can highly improve the tracking accuracy by using simple linear models such as UAV models identified with a few number of poles and zeros.

To our best knowledge, the practical approach presented in this work was not introduced by other authors in the ILC literature.

III. PHILOSOPHY AND CONTROL DESIGN

In this section, we present the design of our cascade control architecture with an aim of motivating its usage. We assume that operator can give an arbitrary repetitive sequence of position setpoints. As this sequence can be discontinuous and not achievable by the UAV, we first systematically filter this raw sequence by means of a 3rd order filter (see Section III-A). The resulting filtered sequence thus suits our dynamic objectives by becoming continuous and twice differentiable. Following that, a position feedback controller is used to compute the attitude and total thrust references. Thrust of each rotor is then adjusted in order to track the references thanks to an attitude controller and mixer matrix.

The position controllers (one per axis) were designed to achieve robustness objectives rather than to achieve high tracking performances. Consequently, they lead to lags and poor tracking when dynamical position sequences are given by an operator. Considering that the operator's position sequences are repetitive, an ILC algorithm was added to achieve the best possible tracking performances for a given trajectory by compensating for the weak performance of the position feedback controller.

A. Reference trajectory & Pre-filter

As mentioned previously, a pre-filter is used to smooth the raw repetitive trajectories in order to make them continuous along attitude references. This operation allows some time for the UAV to reach the desired position at the beginning of the reference trajectory which is initialized according to the UAV's initial state. Moreover, we implement one pre-filter per axis which allows us to adjust the DC-gains differently and to produce only a small phase delay without having any change in amplitude w.r.t the initial trajectory given by the operator. The pre-filter's transfer function can be described as:

(.

) ref (s) (.) raw ref (s) = G (.) (τ 1(.) s + 1)(τ 2(.) s + 1)(τ 3(.) s + 1) (1)
where (.) can be X, Y or Z, the 'ref 'and 'raw ref ' signify the filtered and unfiltered references, respectively and τ 1(.) ,τ 2(.) and τ 3(.) define the time responses which were chosen to be less than 2s. Thus, the first reference trajectory for the UAV is selected as an eight-shaped path at 1 meter altitude with a period of T =7.5s. The eight-shape is obtained by combining two sinusoidal signals on X and Y -axes with same amplitudes (A X,Y =1m) but different frequencies; i.e f X = 0.5f Y .

B. The feedback control

The horizontal and vertical positions of the UAV are each controlled by a position and a speed feedback loops. The controller design was done utilizing an LQ method with a linearized model of the UAV with an aim of achieving an overshoot of < 5% for the position tracking (X, Y, Z), a limited command noise and good robustness properties. The main drawback of this feedback controller is, as illustrated later, its "slow" time response (see Fig. 4 and5). It takes approximately 5.5s to reach a reference position, which introduces delay when tracking fast varying trajectories.

In Fig. 1, one can observe the architecture of the position closed-loop system. The LQ horizontal controllers deliver the attitude references α x and α y in the OptiTrack frame which are then converted in Euler angles references φ and θ . The vertical LQ controller generates thrust reference δT to which a nominal thrust u T 0 is added to compensate for the weight of the UAV. Furthermore, Euler angle references and thrust references are tracked by the PX4 controllers which generate setpoints for the motors (ω ri ). The position and speed of the UAV are then measured by the optitrack system and used by the LQ controllers. Hence, the closed-loop system considered by ILC consists of the transfer functions between the position references X , Y and Z that are assigned to position controllers and the measured position outputs X, Ȳ and Z:

G X (s) = X(s) X (s) , G Y (s) = Ȳ (s) Y (s) , G Z (s) = Z(s) Z (s) . (2)

C. Structure of the used ILC algorithm

A norm-optimal ILC (NO-ILC) was chosen as the ILC update method for the UAV experiments. The method is based on the minimization of a quadratic cost function (J ) which may vary with different requirements. In our case, the J is defined in the following form:

J(u i+1 ) = e T i+1 W e e i+1 + u T i+1 W u u i+1 + λ[(u i+1 -u i ) T (u i+1 -u i ) -δ], (3)
where i is the iteration index of ILC; e i+1 ∈ R N is the system's current tracking error; u i+1 ∈ R N is the system's current input; u i ∈ R N is the system's previous input; γ ∈ R 1 is the constraint on the input increment; λ ∈ R 1 is the Lagrange multiplier and W e ∈ R N ×N ; and W u ∈ R N ×N are the respective weighting matrices (Here, one should assume that N is the length of the vectors e i+1 , u i+1 and u i which is determined by the selected simulation and step times).

The NO-ILC that is applied in this paper was designed according to the procedure provided in [START_REF] Norrlof | Iterative learning control: Analysis, design, and experiments[END_REF]. In broad strokes, the procedure is based on the analytical solution of a cost function that yields an ILC update equation from which one can extract the stuctures of the ILC filters Q ∈ R N ×N and L ∈ R N ×N having the forms given in ( 5) and [START_REF] Chen | An optimal design of pd-type iterative learning control with monotonic convergence[END_REF]. The cost function is written by considering the system's curent output tracking error (e i+1 ), current input (u i+1 ) and current input difference (u i+1 -u i ). Then the optimization is done via the method of Lagrange multipliers. Furthermore, the convergence of the ILC algorithm is determined by the tuning of two scalar parameters: ρ > 0 and λ > 0 which are the weight on the input and the Lagrange multiplier, respectively. They have to be selected in a way that ||Q|| 2 < 1 and ||QL|| 2 ≤ 0.5/ √ ρ + λ. The NO-ILC performance can be seen as a matter of trade-off between these two parameters.

The NO-ILC update equation ( 4) and filters ( 5)-( 6) are written as given below:

u i+1 = Qu i + QLe i , (4)
Q = ((λ + ρ)I + G T G) -1 (λI + G T G), (5)
L = (λI + G T G) -1 G T , ( 6
)
where G is the lifted-matrix (see in [START_REF] Bristow | A survey of iterative learning control: A learning-based method for high-performance tracking control[END_REF]) of the closed-loop system's impulse response.

IV. EXPERIMENTAL SETUP The flight experiments were carried out in a flight arena equipped with OptiTrack motion capture system. The UAV that was used during the experiments is a Parrot AR. Drone 2.0. As it was previously mentioned, a cascade control scheme was chosen. The fast and robust attitude regulation loop is implemented in the Pixhawk PX4 autopilot which computes motors' references to track attitude set-points. The guidance and navigation loops are implemented in a more powerful calculator, the Gumstix, yielding attitude references to the textitpixhawk to track desired position trajectories. The Fig. 1 shows the experimental environment in a schematic way. The specific role of each component can be detailed as below:

1) Ground station: a Simulink model can both sends high level position reference to the Gumstix or execute its own guidance law (position feedback and ILC) and directly send attitude references to the Gumstix. 2) Wi-Fi Link: Wi-Fi has been chosen for the data transfer between the drone, the ILC computer and OptiTrack system. 3) Gumstix Board: It is the bridge between the data received via Wi-Fi and the PX4 autopilot. The Gusmtix can run its own guidance law or directly receive attitude commands coming from the ground station. 4) Pixhawk PX4: joined to the Gumstix by a serial link, the PX4 is the actual autopilot of the drone, where attitude control takes place.

A. Data flow of ILC

The ILC experiments were carried out following a procedure that is different than the traditional way. Normally, one uses the experimental data from the previous flight in order to obtain the input signal in the next flight and this leads to one ILC update per one experiment. This becomes a problematic issue when one needs to do large number of iterations to reach a desired reference. We propose that it is possible to overcome this problem by using a closed-loop system identification process together with an ILC algorithm. The data flow procedure applied during the experiment is given in Fig. 2. It can be seen that the first flight includes no ILC signal, i.e. the UAV flies with its own internal closed-loop controllers that are adjusted to have low performance. The data from the first flight is used to identify the UAV dynamics in X, Y and Z-axes. Then, ILC makes 300 iterations by predicting the positions for next flight. The signal from the last iteration is then used to modify the reference signal of the system. After applying the same steps for 3 times, this approach reaches its limit and the identification does not improve the trajectory further. At this point, the update process is switched back to the traditional way where the ILC begins directly using the error from the real flights and this process yields one update per flight.

The reason why the proposed procedure can provide a rapid correction of closed-loop lags and errors from model imperfections by means of only simulated ILC iterations in several flights at the beginnig is because the reidentification process of the linear UAV model after each flight allows us to obtain a close behaviour to the desired tracking. Basically, what ILC does is to refine the UAV linear model as of the first flight. One can think of each newly performed flight with the current ILC signal as a new operating point which is closer to the desired reference trajectory. Thus, the forthcoming ILC signal needs to include the information of the last operating point to better the tracking and this is the point where the reidentification is made use of. In this way, the simulation based ILC approach improves the tracking until the limits of the linear UAV model. Accordingly, it can be said that when ILC is switched back to the traditional update, the remaining errors are due to the disturbaces which cannot be approximated by our linear model.

B. Initialization of the ILC

The initialization of the ILC was done according to the data provided in Table I. The values of ρ and λ were selected with respect to the two convergence conditions given in Section III-C. The low value set for ρ indicates that a high convergence rate is aimed. Besides, identification algorihtm is asked for continuous transfer functions of low complexity (3 poles and no zeros) and it can be noticed that the initial UAV state is 'hovering' at 1m altitude.

n poles = 3; nzeros = 0 Initial states [0 0 -1] T ∈ R 3×1 Initial system input [x ref y ref z ref ] ∈ R N ×3 Initial ILC input [0 0 0] ∈ R N ×3 Number of ILC iterations 300 Weight on the error, We ρI ∈ R N ×3 Weight on the system input, We I ∈ R N ×3 ρ 0.001 λ 0.1

V. EXPERIMENTAL RESULTS AND ANALYSES

In this section, the tracking results for an eight-shaped reference trajectory are presented first and then the same procedure is extended to two more references to further test the efficiency of the designed ILC procedure. These references consist of a square-shaped trajectory and an inclined elliptical trajectory. All the flight experiments were conducted with respect to the data flow and the initialization procedures given in Section IV-B except the readjustments applied in the simulations time and the initial UAV altitude.

A. Eight-shaped trajectory tracking results

For the eight-shaped trajectory, the experimentation was done until the ninth flight considering the fact that the tracking precision was not improving further. The tracking results obtained with the NO-ILC algorithm are depicted in Fig. 3. The ILC update for the first 4 flights are based on the predicted data obtained through the identified models of the system. On the other hand, the ILC used directly the real flight data for the remaining 5 flights. It can be observed that the reference tracking almost does not improve as of the fifth flight. This is due to the fact that it was possible to reach the maximum tracking performance with ILC using the identified system models by the end of the fourth flight. Moreover, one can also see in Fig. 3 how the mean position error in each axis changed along the flight experiments. It is straightforward to conclude that a sufficiently accurate tracking performance can be obtained in only 4 flight experiments.

On the identified transfer functions: After each flight, we identify the UAV transfer functions on each axis. Since the translational speeds, and the attitude angles become more aggresive as the ILC improves the tracking, the identified linear transfer functions are slightly different after each flight. This simply highlights the utility of identifying a new transfer function after each flight. As shown in Fig. 4, the identified transfer function of the X-axis evolves only for a small amount along the flights whereas the differences are relatively larger on the Y -axis (Fig. 5). This can be found reasonable since it is harder to follow the trajectory on the Y -axis that is of a frequency twice as the one on X-axis.

B. Amplitude analysis for eight-shaped trajectory tracking

After obtaining a satisfactory tracking performance for an eight-shaped trajectory with the characteristics given in Section III-A an amplidute analysis was performed in order to find the limitation of the used ILC algorithm. In different words, the same procedure was applied using the reference trajectories with higher amplitudes but the same frequency as before. In this process, a simulator of the UAV was used instead of carrying II in terms of the absolute values of the mean and maximum position errors in each axis. Looking at the error values in general, one may observe that increments in reference amplitude cause larger mean and maximum errors. Until A 4 =1.75m, the errors in Z-axis show a different fashion along the runs; i.e. they increase whereas the errors in X and Y -axes decrease as aimed. Then, at A 5 =2.00m, the mean errors in X and Y -axes first decrease and then slightly increase while the errors in Z-axis keep the same trend. The issue observed in Z-axis can be seen as an outcome of higher pitch and roll angles that were taken by the UAV for improving the accuracy of the lateral trajectory which accordingly caused a compromise of altitude accuracy. Hence, one can say that the ILC algorithm for the eight-shaped trajectory starts to become unsatisfactory as of A 4 =1.75m.

C. Square-shaped trajectory

A square-shaped trajectory is much harder to follow with precision compared to the eight-shaped trajectory if the UAV is required to fly continuously without stopping at the corners of the square. In different words, at the corners of the square Fig. 6. Filtered square reference trajectory the UAV is asked to perform a sudden change in its direction of movement which is a strenuous control task. Moreover, a prefiltering process similar to the one in Section III-B was also implemented on the square trajectory before beginning the ILC experimentation. Thus, the reference trajectory was made more real-like from the point of UAV dynamics and the thust level could be kept below the limit of saturation. Fig. 6 depicts the filtered square reference positions for X and Y axes as well as the corresponding velocity and acceleration curves. One can observe that the demanded acceleration from the UAV was kept within a range defined by a limit of ±25°in pitch and roll angles. In order to avoid saturations at sharp corner turns, this limit was made more strict compared to the one set for the eight-shaped reference, i.e ±35°.

The square trajectory has a period of 8s and it was simulated for 40s which corresponds to 5 loops. Fig. 7 demonstrates the evolution of the reference tracking according to the predefined data flow procedure and the plotted data represents only the fifth loop of the UAV's trajectory. It can be figured out that the most of the improvement in the tracking was obtained during the first 4 flights where the ILC algorithm used the predicted flight data. The rest of the flights were carried out with the real flight data using the traditional ILC update process and the precision of the tracking could be slightly improved.

D. Elliptical inclined trajectory

The final trajectory that was analysed is an ellipse with 0.8m semi-major axis, 0.4m semi-minor axis and 15°inclination. The altitude of the UAV was initially set to 1.5m and the UAV starts its flight from the center of the ellipse. Furthermore, the period of the ellipse and the flight duration were chosen to be 4s and 20s, respectively.

Due to the inclination of the reference, the UAV needs to allocate some of its total allowable thrust for altitude increment which limits the reachable accelerations for the maneuvers on the lateral plane. Accordingly, the reference was filtered in order to be sure that the demanded maneuvres stay below the saturation limits. Fig. 8 demonstrates the positions, velocities and accelerations for the filtered reference trajectory where one can also observe that the norm of the vector compound of the accelerations in each axis remains between a certain acceleration range. The absolute value of the maximum allowable acceleration of the UAV is 1.25 times the gravitational acceleration, i.e. 12.26m/s 2 . The evolution of the reference tracking is demonstrated in Fig. 9. The experiments were carried out according to the same data flow procedure used before and the represented data correspond to the 5th loop of the trajectory. Similar to the results of other reference trajectories, the largest improvement in tracking was seen to be during the first four flights where ILC used predicted data. Moreover, the seven flights performed afterwards using traditional update could only reduce a small amount of the remaining error.

VI. CONCLUSION

In this paper, we showed a practical procedure that can be utilized to reduce the time spent during ILC experiments. Our method is based on using predicted flight data when performing the ILC updates. The method showed to be efficient despite the low order linear UAV models used in the update process. The flight experiments with three different trajectories demonstrated that a large amount of tracking performance can be acquired in only 4 flight experiments. Furthermore, using the proposed ILC procedure it was possible to achieve almost the largest agility for our UAV which has already a very limited dynamic performance.

Fig. 1 .

 1 Fig. 1. NO-ILC experimental setup and control architecture.

Fig. 2 .

 2 Fig. 2. Data flow procedure for NO-ILC experiment

Fig. 3 .

 3 Fig. 3. Tracking results for the eight-shaped reference

Fig. 4 .Fig. 5 .

 45 Fig. 4. Evolution of the impulse response of the identified transfer function of the X-axis with the flights

Fig. 7 .

 7 Fig. 7. Tracking results for the square-shaped reference

Fig. 9 .

 9 Fig. 9. Tracking results for the elliptical reference

TABLE II MEAN

 II POSITION ERROR VS. REFERENCE AMPLITUDE (IN CM)

			Frequency, f =0.1333Hz
	Reference Mean Run Run Run Max. Run Run Run
	Amplitude error	1	2	3	error	1	2	3
		ēx 81.98 3.366 3.400 ex max 128.6 6.192 5.683
	A 1 = 1.00	ēy	80.29 3.504 1.292 ey max 126.3 7.831 3.363
		ēz	0.091 1.235 1.357 ez max 0.181 2.127 2.363
		ēx 102.7 4.082 4.084 ex max 161.3 7.687 6.985
	A 2 = 1.25	ēy	100.3 5.114 1.773 ey max 157.8 11.14 4.770
		ēz	0.142 2.001 2.260 ez max 0.284 3.435 3.864
		ēx 123.4 4.757 4.678 ex max 193.8 9.166 8.150
	A 3 = 1.50	ēy	120.2 6.899 2.363 ey max 189.3 14.69 6.361
		ēz	0.204 3.039 3.582 ez max 0.409 5.220 6.062
		ēx 144.3 5.399 5.140 ex max 226.4 10.67 9.455
	A 4 = 1.75	ēy	140.1 8.819 3.122 ey max 220.7 18.34 7.897
		ēz	0.277 4.405 5.244 ez max 0.557 7.669 9.288
		ēx 165.2 5.907 8.713 ex max 259.0 12.49 14.91
	A 5 = 2.00	ēy	160.0 10.26 15.26 ey max 252.2 21.24 32.30
		ēz	0.362 6.503 14.27 ez max 0.729 11.41 27.33

DTIS, Info, Processing and Systems. ONERA, The French Aerospace Lab, Toulouse, France. <first-name>.<lastname>@onera.fr

ACKNOWLEDGMENT

We would like to thank Angélique Beaucamp for her assistance at the beginning phase of the experiments. In addition, we thank Franc ¸ois Defay for letting us use the flight arena of ISAE-SUPAERO.


Aurélie Beaugency
email: aurelie.beaugency@u-bordeaux4.fr

Damien Talbot
email: damien.talbot@uca.fr

Cognitive proximity and knowledge spillover in the avionics industry An analysis from patents and scientific publications

Cognitive proximity and knowledge spillover in the avionics industry An analysis from patents and scientific publications

Introduction

The technological capabilities of a firm may be defined as the sum of its current know-how together with the know-how and knowledge acquired in the past. These technological capabilities influence the innovation pathways followed by the firm now and in the future. One major way of differentiating between firms is thus commonly considered to be by evaluating the volume of accumulated knowledge (knowledge base) and the diversity of this knowledge [START_REF] Dibiaggio | Substitutability and complementarity of technological knowledge and the inventive performance of semiconductor companies[END_REF]. In order to ensure their survival in a given market, companies constantly develop their store of knowledge using existing knowledge, exploring new fields of knowledge or acquiring new knowledge through partnerships, mergers or acquisition of other firms or business portfolios.

These developments generate significant knowledge flows within companies and within business ecosystems. Work on understanding cognitive distance/proximity tries to understand the origin of these flows and how they change. Thus, a first line of research studies the influence of geographical proximity on the generation of knowledge flows between stakeholders [START_REF] Almeida | Startup size and the mechanisms of external learning: increasing opportunity and decreasing ability?[END_REF]Gilly and Torre, 2000;[START_REF] Bathelt | Clusters and knowledge: local buzz, global pipelines and the process of knowledge creation[END_REF][START_REF] Boschma R | Proximity and innovation. A critical assessment[END_REF][START_REF] Rallet | Proximity and Localization[END_REF]: the fact of being physically close generates the possibility of significant contact and face-to-face meetings that favor knowledge transfers. In the same way, the search for partners for research and development activities always begins with stakeholders who are close by. Beyond the fact that it encourages knowledge flows between stakeholders that are physically close, geographical proximity encourages the formation of clusters specializing in one particular field, with the development of knowledge bases common to a locality and very close similarity between the knowledge bases of the stakeholders involved in the cluster. In this case, there is a combination of geographical, cognitive (common knowledge bases) and organizational (around a project) proximities.

A second line of research studies knowledge transfers between stakeholders who are not physically close but are partners in the same market. Firms can also deliberately seek to acquire knowledge that is available in their environment through research and development partnerships, mergers and acquisitions or by buying business portfolios, patents, etc. [START_REF] Pecqueur | Economie de Proximités[END_REF][START_REF] Rallet | Proximity and Localization[END_REF]. In this case, cognitive and organizational proximity combine in order to control the distribution of knowledge.

Finally, there is a third line of research, less studied by work on proximity, that deals with the case where cognitive proximity develops between competing stakeholders who are not partners but belong to the same industry. Numerous articles have highlighted the fact that, under certain conditions, competing firms within the same industry can have similar technological pathways because there is too great a proximity between their knowledge bases [START_REF] Patel | The Technological Competence of World's Largest Firms: Complex and Path Dependent, but not Much Variety[END_REF][START_REF] Nesta | Technology strategy and knowledge dynamics: the case of biotech[END_REF], particularly where there is a high level of technical specialization. This excessive proximity leads to an unintentional diffusion of knowledge (knowledge spillover) [START_REF] Nooteboom | Trust. Forms, Foundations, Functions, Failures and Figures[END_REF] which contributes to the development of these similar pathways. The current paper aims to contribute to this third line of research by describing the case of competing stakeholders from the avionics industry who share strong cognitive proximity leading to uncontrolled knowledge transfer. This is the first objective of this article.

However, it is also necessary to understand how such cognitive proximity has developed between stakeholders who are not engaged in any form of collaboration. Whereas it is to be expected that the effects of knowledge spillover will contribute, through a cause and effect mechanism, to strengthening such proximity once it has become established, the initial factors that could lead to its formation remain to be identified. The second objective of this paper is thus to answer the following question: how can we explain the existence of cognitive proximity (and thus of an unintended transfer of knowledge) between stakeholders who are not linked by any kind of cooperation arrangement, who are competitors and who are geographically remote from one another? In order to achieve this, we refer to evolutionary studies. An industry's innovation regime determines its component firms ' common characteristics (Grandstrand et al., 1997), placing them on industry-specific technological pathways within which they may be distinguished by their own learning processes and knowledge base management. The evolutionary studies dealing with technological regimes suggest that industry-specific factors influence the conditions under which knowledge is acquired, the structure of the industry's knowledge bases and the degree of accumulation of knowledge in the bases that leads them to converge [START_REF] Nelson | An evolutionary theory of economic change[END_REF][START_REF] Malerba | Technological regimes and firm behavior[END_REF][START_REF] Henderson | Scale, scope and spillovers: the determinants of research productivity in drug discovery[END_REF]. This paper is organized as follows: after defining cognitive proximity in the first part, the second part shows on the one hand that such proximity exists between the main avionics companies and highlights on the other hand the knowledge transfers made possible by this high degree of proximity. The third part discusses these two main results in the light of evolutionary studies dealing with industry-specific contingencies. The final part concludes.

Cognitive proximity and knowledge spillover

Knowledge lies at the heart of recent research into the performance of firms in a given industry [START_REF] Dibiaggio | Substitutability and complementarity of technological knowledge and the inventive performance of semiconductor companies[END_REF] both in terms of knowledge production (D'Este [START_REF] Cukierman | How do firms' knowledge bases affect intra-industry heterogeneity? An analysis of the Spanish pharmaceutical industry[END_REF] and the ability to acquire and absorb external knowledge and combine it with that already held [START_REF] Ahuja | Technological acquisitions and the innovation performance of acquiring firms: a longitudinal study[END_REF][START_REF] Fleming | Recombinant uncertainty in technology search[END_REF]. Each firm possesses its own knowledge capital, built up over a long period and consisting of a set of codified knowledge (patents, publications, documents) and non-codified knowledge (knowledge and know-how held by employees and managers). The development of this capital follows a pattern that is generally routine (pathway dependence) where the firm learns and develops knowledge linked to its activities and markets (Thomke et al., 1997) from knowledge and innovation patterns that it understands and capitalizes upon [START_REF] Cohen | Absorptive capacity: a new perspective on learning and innovation[END_REF][START_REF] Helfat | Evolutionary trajectories in petroleum firm R&D[END_REF]. Studies undertaken with the aim of understanding the dynamics of learning and knowledge management in accordance with industry-specific typologies [START_REF] Oltra | Sectoral systems of environnemental innovation: an application to the French Automotive Industry[END_REF][START_REF] Epicoco | Knowledge dynamics and sources of eco-innovation: mapping the green chemistry community[END_REF][START_REF] Dibiaggio | Substitutability and complementarity of technological knowledge and the inventive performance of semiconductor companies[END_REF] highlight the determining role of the diversity and depth of a firm's knowledge base in its performance.

Work by the Proximity School has shown that this base can be similar for several firms. Cognitive proximity underlines the differences in the abilities of different stakeholders to absorb knowledge, in particular because their knowledge bases are dissimilar [START_REF] Mattes | Dimensions of Proximity and Knowledge Bases: Innovation between Spatial and Non-spatial Factors[END_REF][START_REF] Capello R | Proximity and regional innovation processes: is there space for new reflections?[END_REF]. It refers to sharing of similar and/or complementary knowledge bases by the stakeholders, opening the way for knowledge transfer [START_REF] Boschma R | Proximity and innovation. A critical assessment[END_REF]. This proximity is an opportunity because collaborative innovation is conditioned by its very existence [START_REF] Markusen | Sticky places in slippery space: a typology of industrial districts[END_REF]. It is necessary so that stakeholders can absorb new knowledge [START_REF] Cohen | Absorptive capacity: a new perspective on learning and innovation[END_REF]: their cognitive bases must be sufficiently close to the knowledge to be acquired in order to understand and learn it. And if everyone goes to his partner to find new cognitive fields in order to have a large field of exploration [START_REF] March | Exploration and exploitation in organizational learning[END_REF], the stakeholders must remain capable of mutual understanding [START_REF] Nooteboom | Inter-firm Collaboration, Learning and Networks. An integrated approach[END_REF]. Firms then develop an absorption capacity understood as their capability to perceive, interpret and evaluate knowledge held by organizations [START_REF] Cohen | Absorptive capacity: a new perspective on learning and innovation[END_REF]. The objective of such a capability is to verify the usefulness and value of this knowledge with respect to that already held in-house, for example by a firm [START_REF] Zahra | Absorptive capacity: a review, reconceptualization and extension[END_REF]. There is thus a positive relationship between cognitive proximity, absorption capacity and knowledge transfer.

In more general terms, according to [START_REF] Nooteboom | Inter-firm Collaboration, Learning and Networks. An integrated approach[END_REF] it is necessary to be neither too close nor too far apart in cognitive terms in order for radical innovations to appear. Excessive cognitive proximity leads to cognitive short-sightedness: established routines prevent firms from seizing opportunities offered by emerging technologies. And it being understood that innovation is first and foremost a question of new combinations of knowledge, the development of new knowledge presupposes bodies of dissimilar and complementary knowledge -related variety -in order to avoid redundancy and bring out new ideas [START_REF] Boschma R | The spatial evolution of innovation networks. A proximity perspective[END_REF]. Cassi and [START_REF] Plunket | Proximity, network formation and inventive performance: in search of the proximity paradox[END_REF] have shown that such proximity has a positive effect on innovation up to a certain threshold, beyond which innovation-related performance decreases.

In cases where cognitive proximity has a positive effect on knowledge transfer, problems of governance appear. In order to benefit from the complementarity of knowledge, knowledge transfer is often based on collaboration between different categories of stakeholders with diverging interests (big groups, SMEs, public research institutions, universities, etc.) who can potentially enter into conflict [START_REF] Nooteboom | Inter-firm Collaboration, Learning and Networks. An integrated approach[END_REF]. All knowledge transfer carries three risks [START_REF] Williamson | The Economic Institutions of Capitalism[END_REF][START_REF] Nooteboom | Trust. Forms, Foundations, Functions, Failures and Figures[END_REF]:

first, if the collaboration breaks down, the stakeholders lose the investment made specifically for that transfer; -second, there is always the possibility of opportunist behavior where one partner captures the results of the exchange of knowledge for his sole benefit (holdup); -third, knowledge can be transferred unintentionally to competitors (knowledge spillover).

In order to contain these relational risks, it is necessary to develop organizational proximity that involves the sharing of systems, structures and processes. This type of proximity "…links the participating parties in a finalized activity within the framework of a specific structure.

[…]

[It] is deployed within organizations -firms, establishments, etc. -and, in certain cases, between organizations that are linked by a relationship of economic or financial dependence or interdependence -between firms that are part of the same industrial or financial group, within a network, etc. -" (Kirat, Lung, 1995, p.213). This type of proximity makes it possible to evaluate the degree of legal and economic autonomy that exists between the members of an organization or between organizations. Its existence leads to a reduction in the uncertainty inherent in any relationship and in the opportunism of participants [START_REF] Boschma R | Proximity and innovation. A critical assessment[END_REF] at the same time creating a climate of confidence between stakeholders who are organizationally close (Torre and [START_REF] Rallet | Proximity and Localization[END_REF]. This is particularly true when the collaborating stakeholders come from heterogeneous environments (for example public vs private) (Ponds, Van Oort and Frenken, 2007).

To summarize, according to the proximity literature, knowledge transfer supposes, in particular for organizations that share complex knowledge in order to undertake common projects, the construction of organizational control systems and sharing of closely-related knowledge bases.

In the case of the avionics industry we observe such cognitive proximity between stakeholders who do not otherwise share organizational proximity: unintentional knowledge transferknowledge spillover -then occurs.

Data and methodology

a. Data

The avionics industry emerged in the 1980s following the introduction of the first electronic systems into aircraft. The term "avionics" refers to all electronic systems produced for aeronautical applications and thus covers scientific and technical fields relating both to electronics technologies and to applications destined for systems (communication, navigation, surveillance, etc.). The proportion of the development costs of a civil aircraft (A380/A350, B787) devoted to systems has gradually risen so that today it represents between 30 and 35%.

In order to fully grasp the technological dimension of the industry-specific knowledge base, we have restricted our study to five major stakeholders (identified as Firms 1 to 5 in this paper) who, according to the "Decision" study (2012), account for more than 90% of market share. Moreover, these stakeholders are the only firms capable of producing several of the major systems and are among the aircraft manufacturers' first-tier contractors (Talbot, 2013;[START_REF] Kechidi | Resilience of organisations and territories: the role of pivot firms[END_REF][START_REF] Beaugency | Capacités dynamiques et compréhension des enjeux sectoriels : apports de l'intelligence technologique au cas de l'avionique[END_REF].

Scientific and technical production is generally measured in terms of the patents and scientific publications produced by firms, representing both the composition and development of their knowledge base and providing an understanding of its construction (capitalization, collaboration). Patents and publications represent a significant part of the codified knowledge produced and held by firms. Patents are used to help understand the firms' innovation pathways [START_REF] Griliches | Patent statistics as economic indicators: a survey[END_REF][START_REF] Oecd | Manuel de l'OCDE sur les statistiques des brevets[END_REF] with an appreciation of innovation based mainly on R&D activities. Because of the costs involved in filing and maintaining patents, they are most often held by firms and used to protect their inventions through the attribution of an exclusive, limited right to use. On the other hand, scientific publications provide information about innovationrelated knowledge at a much earlier stage (R&T), long before patents are invoked. They highlight the scientific production of researchers in a scientific or technical field, whether those researchers belong to a firm, a university or a research center. More generally, academic researchers prefer scientific publications to patents in order to make their results known for reasons of cost (publication costs little or nothing) and time (the publication process is shorter than that required for patents).

Using quantitative analysis to understand scientific and technical dynamics though databases of patents and scientific publication has numerous advantages. Such databases provide structured and easily exploited information about the knowledge produced within a given industry, by a given firm, about a given technology, etc. [START_REF] Ernst | Determinants of patent value: insights from a simulation analysis[END_REF][START_REF] Flamand | Le déploiement de l'intelligence technologique dans le processus d'innovation des firmes : quels objectifs, enjeux et modalités pratiques ? Une application à l'industrie automobile[END_REF]. The present study is based on the Fam Pat patents database using the Orbit1 tool. The database covers 99 patent offices and the patents are grouped into families, thus facilitating the exclusion of duplicates.

Given the complexity of the avionics industry and its close links with the aeronautics and electronics industries in terms of innovation [START_REF] Beaugency | Capacités dynamiques et compréhension des enjeux sectoriels : apports de l'intelligence technologique au cas de l'avionique[END_REF], we have preferred a case study approach [START_REF] Yin | Case study research: Design and methods[END_REF] carried out in two stages. First we carried out a general case study based on filing of patents by the five stakeholders covering the period 1980 to 2012 for 450 codes of the IPC. After subjecting the body of patents for each code to an examination by industry experts, 362 codes were retained as being useful in defining the technical perimeter of the avionics industry. For the second stage, we chose two case studies involving avionic systems (hereafter referred to as Systems 1 and 2, see Table 1) for which we studied the stakeholders' knowledge bases and knowledge transfers. We have adopted the approach traditionally employed in the literature that uses patents in order to understand knowledge flows between firms and we distinguish two categories of indicator:

the International Patent Classification. 2 The fact of belonging to the same sector of activity is an indicator of cognitive proximity, since it pre-supposes a similarity of technical knowledge [START_REF] Nooteboom | Optimal cognitive distance and absorptive capacity[END_REF][START_REF] Boschma R | Related variety, trade linkages, and regional growth in Italy[END_REF]Broekel and Boschma, 2009;[START_REF] Hautala | Cognitive proximity in international research groups[END_REF]. A comparison of major firms based on similarity between patent categories can bring to light similarities between their knowledge bases: by using the International Patent Classification it is possible to reconstitute the firm's patent portfolio by grouping the families by technical domain and to detect common knowledge bases by comparing the portfolios [START_REF] Breschi | Knowledge-relatedness in firm technological diversification[END_REF][START_REF] Bennera | Close to you? Bias and precision in patent-based measures of technological proximity[END_REF][START_REF] Diestre | Are all sharks dangerous? New biotechnology ventures and partner selection in R&D alliances[END_REF][START_REF] Ahuja | Technological acquisitions and the innovation performance of acquiring firms: a longitudinal study[END_REF]; -patent citations. Beyond the ability to produce useful knowledge in house, some stakeholders have developed the ability to identify and absorb external knowledge and to integrate it into their activities via knowledge flows [START_REF] Jaffe | Patents, Citations & Innovations: a Window on the Knowledge Economy[END_REF][START_REF] Hall B-H | Market value and patent citations: a first look[END_REF][START_REF] Moed | Handbook of Quantitative Science and Technology Research. The use of Publication and Patent Statistics in Studies of S&T systems[END_REF]. The identification and quantification of knowledge flows pre-supposes the use of indicators such as joint filing of patents or co-authoring of publications which give information about collaborations intentionally developed by the stakeholders [START_REF] Mowery | Technological overlap and interfirm cooperation: implications for the resource-based view of the firm[END_REF][START_REF] Breitzman | The Many Applications of Patent Analysis[END_REF][START_REF] Pavitt | Innovation processes[END_REF], whereas other indicators relating to patent citations offer a view of less easily-perceptible knowledge flows [START_REF] Jaffe | Patents, Citations & Innovations: a Window on the Knowledge Economy[END_REF]. These flows are important in the identification of technology transfers between science (public research) and technology as it is used for productive ends [START_REF] Narin | The Increasing Linkage Between U[END_REF] 3 .

b.ii. Data collection

Data collection took place in three stages:

first, a project team was created for each study. Each project team comprised a manager who had originated the request, an analyst who was in charge of carrying out the study and an expert providing support through technical knowledge. During this first phase the objectives and the limits of the study were fixed;

the second phase involved a two-hour interview between the analyst and the expert during which the expert provided technical knowledge of the system to the analyst that would be useful for data collection (in particular key words and the corpus of the company's patents that would be useful for the extraction of IPC codes); -in the third phase the information was collected from the structured patent databases, then subjected to statistical and cartographical analysis using MSExcel and Gephi [START_REF] Bastian | Gephi: an open source software for exploring and manipulating networks[END_REF] respectively.

Results: cognitive proximity resulting in unintended knowledge transfer between competitors

The study of the knowledge bases of the five major stakeholders in the avionics industry highlights the fact that, despite the fact that none of them belongs to the same organization, they share a similar innovation pathway. Thus, we first note that there is strong cognitive proximity between the two major industrial avionics firms given the high degree of similarity between their knowledge bases. Second, we observe the existence of unchecked knowledge flow between the firms.

a. The alignment of the avionics firms' technological pathways

On the basis of the IPC categories of patents filed by the avionics firms we observe strong similarity between their knowledge bases. Closer examination of the technological pathways followed by Firm 1 (European) and Firm 2 (American), two historical industry leaders, shows that they cover similar fields of knowledge (Figure 1).

the prior art of a patent differ from one patent office to another: for example, at the USPTO every patent application requires a very thorough examination of prior art, and the examiners may add references during their examination. These two firms have long been major stakeholders in the avionics industry, designing and manufacturing numerous systems in the different product ranges (surveillance, navigation, communications and information systems). For this reason, their knowledge bases have become particularly wide since the 1980s. In practical terms, the technological development of aircraft components towards a greater number of electronic systems has contributed to the extension of the firms' knowledge bases, particularly in the fields of numerical calculation (G06), transmission (H04), navigation and radio navigation (G01).

These firms are competitors in the industry and share neither development projects nor any other form of organized relationship which could explain this proximity. Cognitive proximity alone is observed here: there is no articulation with any organizational proximity. In other words, in the absence of any structured relationship, i.e. without organizational proximity, stakeholders can develop similar knowledge bases and follow the same technological pathways.

b. Unintentional knowledge transfers between competitors

In order to evaluate the degree of knowledge flow between these stakeholders, we refer to the patent citations for Systems 1 and 2. By comparing, for one avionics firm, the percentage of references to previous work by competing firms, we demonstrate the existence of an implicit sharing of knowledge between competitors. In the case of System 1, the authors quote many previous patents belonging to them or to their direct competitors: the proportion of these citations is significant (between 30 and 40% of prior art). A more detailed study of the citations brings out two distinct profiles (see Figure 2).

The first profile is that of Firms 1 and 4 which accord significant importance to prior art in their current developments, indicating a highly incremental innovation system. But at the same time, support from work carried out by competitors is just as important (around 25% of the patents cited belong to direct competitors).

The second profile (that of Firms 2 and 3) shows the importance of knowledge held by stakeholders who are not competitors. The weighting for knowledge already acquired is low, indicating a less incremental approach to innovation than that of the other stakeholders (particularly in the case of Firm 3). On the other hand, Firm 2 is more open to the outside world whereas Firm 3 has a percentage of citations to direct competitors' patents similar to that of Firms 1 and 4. Thus, Firm 2 draws a lot of knowledge from its environment and takes little from the industry, whereas for Firm 3, the approach to innovation is more heavily based on knowledge from the other stakeholders in the industry. Although the study of System 2 (Figure 3) shows a lower overall citation rate than for System 1, it confirms the previously-observed behavior of Firms 1 and 2, with a greater openness to external knowledge. In fact, we note once again that Firm 1 still capitalizes on previous knowledge but the percentage of prior art quoted falls from 22% to 11%. Although Firm 1 is among the stakeholders making the greatest use of knowledge from the leaders for this system, the proportion is nevertheless smaller in the case of System 2 (10% less than for System 1). Firm 2 accentuates its openness to external knowledge with a citation rate to prior art that is stable, contrary to that of the other leaders, whose level of openness is insignificant. In the case of Firm 3, there is a difference in the use of prior art, which appears to become more significant than for System 1 (13%) and approaches equality with the use of knowledge from other major stakeholders in the industry (16%) whereas Firm 4, although still making significant use of knowledge held by the major stakeholders, has a lower percentage of citations to prior art. To summarize, in System 1, the ability to exploit knowledge held by direct competitors is significant in the construction of the knowledge base necessary to the development of the system. In System 2, the stakeholders have tended to use knowledge from outside the closed circle of the leaders to build their knowledge bases.

c. Significant knowledge flows between aircraft manufacturers and avionics suppliers

In studying patents filed and their citations, we note that the architect-integrators Boeing and Airbus occupy an important place in the production of knowledge for the two Systems under consideration. Now, although Boeing and Airbus are not actually manufacturers of avionic systems, they are nevertheless responsible for defining the precise technical specifications of the systems and for managing their final integration into the aircraft. For this reason, they must be capable of evaluating the technological solutions proposed by their suppliers. Beyond any considerations of supplier evaluation, Airbus endeavors to design and produce certain "critical" avionic systems itself because of their decisive role in the success of a given program [START_REF] Beaugency | Outsourcing of strategic resources and capabilities: opposing choices in the commercial aircraft manufacturing[END_REF].

Figure 4 shows how the architect-integrators are ranked in terms of the number of patents filed in relation to Systems 1 and 2, particularly Airbus, which is very active in both cases. We have examined, from the patents filed by the four stakeholders being studied, the percentage of citations from patents filed by Airbus and Boeing (Figure 5). Here again we see that the architect-integrators are an important source of knowledge for the avionics firms. This is particularly the case for System 1, where 25% of the citations of prior art by the specialist firms concern Airbus patents, as against 15% from Boeing. In the case of System 2, on the other hand, the firms generally seem to manage without knowledge from the two architect-integrators (5%) despite the significant number of innovations that they have produced.

Discussion

How can we explain the existence of such cognitive proximity between stakeholders who are competitors and do not cooperate with one another? Of course, the unintentional transfer of knowledge that follows will later contribute strongly to the convergence of knowledge bases by a cause-and effect mechanism. But the initial factors must be sought in the industry-specific environment itself, as described by the evolutionary school.

Studies investigating technological regimes have proposed industry-specific typologies (Marsili and Verspagen, 2002): science-based regimes (electronics), product engineering regimes (instrumentation), process innovation regimes (chemicals), continuous innovation regimes (textiles) and finally those based on complex systems (automobiles, aeronautics).

Although, in overall terms, avionics belongs to the last category, it is necessary to analyze the special characteristics of the avionics industry in detail, i.e. the specific technological and technical conditions of avionic systems and the value chain in the aeronautical industry observed for recent programs.

The design and production of avionic systems involve highly specific processes, both in the very complex fields of knowledge that have to be combined and in the highly standardized monitoring of each stage (from the development of the system to its integration into the aircraft and its maintenance throughout the life of that aircraft).

a. Complex knowledge applied over a long period First, the knowledge that is useful for the development of avionic systems is highly specific. In fact, avionics depends on two industries that have opposing innovation dynamics: electronics, which is very dynamic and competitive and aeronautics, which operates over very long cycles and has a routine-oriented innovation regime and where competition is stable. Whereas in the electronics industry it is primordial for a firm to regularly renew its store of knowledge in order to innovate rapidly, in the aeronautical industry it is vital to capitalize on, and accumulate, knowledge without destroying any, so as to avoid endangering older programs.

Second, in the aeronautical industry the accumulated knowledge bases are complex and combine both technical know-how and knowledge of management of development programs for avionic systems [START_REF] Beaugency | Capacités dynamiques et compréhension des enjeux sectoriels : apports de l'intelligence technologique au cas de l'avionique[END_REF]. The technical know-how is based on the exploitation of electronics technologies in a restricted environment. On the one hand, the choice of components must be justified in relation to the particular characteristics of their use (lifespan and reliability of components and systems). Stakeholders in the avionics industry must have thorough knowledge of, and be able to ensure the availability of, the necessary technologies over a period of 30 years, the average lifespan of an aeronautical program. On the other hand, these components and systems must be designed with a view to their integration in the final machine (the aircraft) and their manufacturers must respect the conditions that ensure that the whole set of systems can interface without risk. In addition to this technical know-how, avionics suppliers must build on their experience in management of complex projects in order to meet the time and cost constraints imposed by the aircraft manufacturers. In order to achieve this, they rely on the years of experience acquired over previous programs. The avionics industry involves nearly 500 systems and sub-systems and each corresponds to a specific industrial development and organization procedure. For this reason, the ability of firms to capitalize on previous experience and the knowledge of systems engineers and experts is decisive, on the one hand for maintaining the systems during their operational life and on the other for identifying new, potentially useful knowledge within their environment [START_REF] Kogut | Knowledge of the firm, combinative capabilities, and the replication of technology[END_REF].

To summarize, it is necessary to be able to manage very rapidly-changing electronics technologies throughout the long lifetime of an aeronautical program. The management of knowledge bases by the historical leaders of the industry has thus taken place over the long term, in fact since the start of the avionics industry in the 1980s. New arrivals follow the same technology pathway by absorbing the leaders' knowledge, the whole industry contributing to a convergence of knowledge bases, thus explaining the diffusion of this knowledge.

b. Strong pressure for standardization

To this complexity may be added the strict control -through the application of standards -of the integration and application of new electronics technologies to the aeronautical context and of systems development -from design through to maintenance -over the whole life of the aircraft. The evaluation of the positive effect of standards on the radical nature of innovation in a given industry is a controversial question today in the literature and in the case presented here, we observe that the standards for the development of avionic systems represent a strong constraint, on the one hand on the stakeholders' technological choice and on the other on the degree to which their innovations are radical.

In fact, in order to develop these systems, avionics suppliers must scrupulously follow the specification defined by the architect-integrator so that they can prove that the new development conforms to the rules drawn up by the certifying authorities. The architect-integrator is the guarantor of respect for these standards and must convince the certifying authorities that the systems, and indeed the whole aircraft, comply in order to receive a marketing authorization. Numerous standards apply to the development of avionic systems both in terms of technological choice and of the design and assembly of the different sub-systems (standards relating to hardware and software interfaces). The standardizing constraints on the use of technologies imposed by the certifying authorities has an impact on the choices available to aircraft manufacturers and avionics suppliers for the design of systems.

But these standardizing constraints also act as a significant barrier to entry against any stakeholder possessing knowledge and capability in respect of the technologies used for the production of avionic systems. On the one hand, there is the question of the technological perimeter for the design of avionic systems which obliges any stakeholder wishing to penetrate the market to be thoroughly familiar with practically the whole field. Thus, a new stakeholder cannot be recognized by the aircraft manufacturer as a qualified supplier unless he provides proof of complete familiarity with the standardizing process for avionic systems. We note, as is the case for Firm 5, that competitors move up the value chain initially through an investment in non-critical systems (for which the constraints of standardization are less strict) before going on to more critical systems. On the other hand, the necessity to invest in these technologies over the long term creates a kind of dependence on a common pathway for all the avionics suppliers. The constraint of standardization creates strong similarities between the stakeholders' knowledge bases precisely because it sets technological orientations [START_REF] Acha | The Changing governance of knowledge in avionics[END_REF].

By limiting technical choice in this way, the sharing of international standards pushes avionics suppliers onto a single technological pathway leading to a similarity in knowledge bases.

c. Changes in the aeronautical industry

The constraints on the design and production of avionic systems have been accentuated by recent developments in the aeronautical industry [START_REF] Belin | Relational rent and underperformance of hub firms in the aeronautics value chain[END_REF]: because the architectintegrators have decided to concentrate on strategic activities, their first-tier contractors -such as avionics suppliers -find themselves entrusted with ever bigger and more financially onerous projects. The avionics suppliers have developed a strategy of moving ever higher up the value chain, thanks to the design and manufacture of major technical packages for which they have obtained responsibility (Amess et al., 2001). They have thus become the architects of a block of homogeneous knowledge and positioned themselves in a strategic segment of the supply chain (Talbot, 2008(Talbot, , 2013)). This new positioning is accompanied by strong constraints in terms of performance, volume, reliability, financial risk and the price of the systems supplied. Finally, there are few stakeholders who are able to bear these constraints on the development and production of avionic systems [START_REF] Beaugency | Capacités dynamiques et compréhension des enjeux sectoriels : apports de l'intelligence technologique au cas de l'avionique[END_REF]. The fact that such a small number of firms is capable of surviving at the highest level in the industry leads mechanically to greater and greater similarity in their knowledge bases: it is easier to all look alike when the group is small.

Conclusion

Hitherto there has been little research into companies involved in the technological regime of complex systems, such as those in the automobile or aeronautical industries. We have shown, through patent citations, that the stakeholders in these industries appropriate their competitors' knowledge independently of any contractual relationship thanks to the existence of strong cognitive proximity between them. A negative effect of cognitive proximity is thus brought to light because the flow of knowledge is uncontrolled (knowledge spillover). This is the main empirical result of our research. We have put forward several explanations for this phenomenon, all related to the avionics industry. First, the dependence on two industries (electronics and aeronautics) presupposes continuing mastery of rapidly-changing electronics technologies over a timescale of around 30 years and the need to capitalize on both past knowledge and recent developments in the aeronautical industry. Next, it accentuates the constraints to which avionics suppliers are subject, leading to a high degree of selectivity in the firms capable of becoming major stakeholders in avionics. Finally, the small number of stakeholders favors the similarity of their knowledge bases just as the strict standardizing constraints limit the choice of possible technologies. This similarity increases receptiveness to knowledge from competitors in the avionics industry. This can be understood: although cognitive proximity provides an opportunity to deliberately exchange knowledge, it also poses a problem because it can lead to unintentional transfer [START_REF] Nooteboom | Trust. Forms, Foundations, Functions, Failures and Figures[END_REF][START_REF] Capello R | Spatial Spillovers and Regional Growth: A Cognitive Approach[END_REF][START_REF] Boschma R | The spatial evolution of innovation networks. A proximity perspective[END_REF]. We thus observe here a negative effect of cognitive proximity (Gulati, 1998;[START_REF] Basile R | Technological interdependence and regional growth in Europe: Proximity and synergy in knowledge spillovers[END_REF].

Finally, we can identify two limits, which are also directions for future research. First, in studying the particular conditions related to the production and diffusion of knowledge peculiar to the manufacture of avionic systems we have provided a contribution by showing that competing firms tend to exploit the same knowledge in a similar way. Moreover, the study of patent citations shows that this similar use leads to an implicit sharing of knowledge because, in the absence of any proven scientific or technical collaboration, the firms use their competitors' patents and publications in order to innovate. It would thus be appropriate to investigate the circulation of knowledge in other industries with the same characteristics as avionics, i.e. technological regimes with complex systems (such as the automobile industry) and for which firms' technological pathways depend as much on endogenous as exogenous factors (standards, complexity of knowledge, etc.) [START_REF] Teece | Firm organization, industrial structure, and technological innovation[END_REF].

Secondly, although industry-specific factors can explain the existence of uncontrolled knowledge transfers in the absence of any organizational proximity associated with cognitive proximity, we must qualify our remarks: the flow of knowledge is controlled simultaneously via heavily structured client-contractor relationships between the architect-integrators and the avionics suppliers and via partnerships between the latter and various research institutions. In the aeronautical value chain, there is an intensification in exchanges of knowledge within the framework of client-contractor relationships [START_REF] Beaugency | Outsourcing of strategic resources and capabilities: opposing choices in the commercial aircraft manufacturing[END_REF]. During the preparation of projects, the architect-integrator requests the avionics suppliers to be present at a very early stage with other potential major suppliers who are their competitors. These preparatory phases aim to predefine projects on the basis of confrontation and exchanges between all the industrial stakeholders involved -this is known as co-specification. These upstream phases of strategic coordination lead, in terms of the design approach, to the development of long-term cooperative links with the architect-integrators (Gilly et al., 2011). These exchanges, which are highly organized, develop a strengthening organizational proximity between aircraft manufacturers and avionics specialists.

Moreover, since the beginning of the 2000s, partnership-based relationships have developed that channel the flow of information between avionics suppliers, architect-integrators and research institutions. The technological complexity of avionic systems requires an extension of knowledge bases and explains the development of relationships between scientific centers [START_REF] Kechidi | Resilience of organisations and territories: the role of pivot firms[END_REF]. In fact, avionics suppliers do not have all the knowledge necessary to explore several technological solutions in order to respond to a tender or to open new innovation pathways. For this reason, research partnerships are being created with scientific and technical research centers in order to acquire new knowledge while reducing both human and financial costs [START_REF] Beaugency | Capacités dynamiques et compréhension des enjeux sectoriels : apports de l'intelligence technologique au cas de l'avionique[END_REF]. Firms thus acquire new external knowledge that reinforces their knowledge bases and that they can use in the shorter or longer term [START_REF] Beaugency | Capacités dynamiques et compréhension des enjeux sectoriels : apports de l'intelligence technologique au cas de l'avionique[END_REF][START_REF] Flamand | Le déploiement de l'intelligence technologique dans le processus d'innovation des firmes : quels objectifs, enjeux et modalités pratiques ? Une application à l'industrie automobile[END_REF].

Finally, the existence of this uncontrolled diffusion of knowledge resulting from an intensive cognitive proximity explains the fact that, in order to guard against it, the industrial firms are developing organizational proximity not directly between each other but with the architectintegrators and the research institutions in order to limit the undesirable effects of too great a cognitive proximity. This is at least a hypothesis that should be verified.

Fig. 1 :

 1 Fig. 1: Changes in the knowledge bases of Firms 1 and 2 (in number of categories covered/period)

Fig. 2 :

 2 Fig. 2: Distribution of prior art cited by the firms in relation to System 1 (in %)

Fig. 3 :

 3 Fig. 3: Distribution of prior art cited by the firms in relation to System 2 (in %)

Fig. 4 :

 4 Fig. 4: Ranking of stakeholders, including Airbus and Boeing, for Systems 1 and 2 (by the number of families of patents filed)

Fig. 5 :

 5 Fig. 5: Percentage of citations of patents from the architect-integrators for Systems 1 and 2

Table 1

 1 Presentation of the System technical case studies

	Case	Study dates	Total duration (months)	Number of patents	Period studied
	System 1	Nov. 2012 Nov. 2013	12	2276	1980-2012
	System 2	June 2013 Dec. 2014	18	548	1980-2012
		Source: Beaugency (2015).
	b. Method
	b.i. Indicators of proximity

Commercial database available from Questel and accessible via the Orbit® software. Patents are grouped by family, which facilitates the evaluation of a given stakeholder's portfolio.

Established in 1971, the IPC or International Patent Classification enables all the patent offices in the world to classify patents into technological categories (there are currently nearly 70,000 categories) according to the nature of their contents.

However, the discretionary nature of the attribution of a citation of prior art has led certain researchers to question the importance of the results of such analyses[START_REF] Alcacer | Patent Citations as a Measure of Knowledge Flows: The Influence of Examiner Citations[END_REF]. In fact, the conditions for establishing