Murat Bronz
email: murat.bronz@enac.fr

Antoine Drouin
email: drouin@recherche.enac.fr

Preliminary Design Estimation of the V/STOL Airplane Performance

A preliminary study on estimating aerodynamic forces of a Vertical/Short Takeoff and Landing (V/STOL) mini Unmanned Air Vehicle (UAV) configuration with Distributed Electric Propulsion (DEP) system is presented. The main objective is to offer the next generation fixed wing mini UAV aircraft configuration with high-speed cruise flight and vertical take-off capabilities. The proposed concept uses four electric motors and propellers combination located on the leading edge of the wing. The described method uses semi-empirical formulations in order to estimate the forces and moments generated by the wing immersed in its distributed propeller slipstreams. Actuator disk theory is used for the propeller slipstream, where the thrust is assumed to be known for the calculations. Upwash of the fuselage and each propeller slipstream are taken into account for the wing and propeller inflow angle calculations. The resulting method, which is written as a program, serves as a conceptual design program for this type of configuration. Additionally, the program will be used for generating data for flight dynamics simulations. A candidate design is also presented, which is being manufactured for the on-going developments and tests.

Introduction

In the past decade performance of small electric rotorcraft have improved vastly whereas performances of fixed wing vehicles have improved much less. For a number of applications that focus on high velocity and long range, fixed wing vehicles remain the best choice. The main limiting factor for the fixed wing configuration is the compromise between low and high velocity regimes. If the vehicle is optimized for low velocity (low wing loading, high static thrust), takeoff and landing will be easy but performances in endurance, range and high speed flight capability will be degraded because of unnecessary wing surface and low propeller efficiency dur-ing high speed flight. On the contrary, if the vehicle is optimized for speed and range (high wing loading, high pitch propellers), landing and takeoff become problematic, requiring the use of long runways and/or external devices like bungees or landing net. On large scale vehicles (often powered by combustion or jet engine), the problem is solved by the use of variable geometry (flaps, slats, variable pitch propeller). Those solution are incompatible with small scale UAVs in terms of added weight and complexity. Electric propulsion offers new possibilities compared to traditional jet or combustion engine solutions. NASA has started investigating DEP [START_REF] Mark | Misconceptions of electric propulsion aircraft and their emergent aviation markets[END_REF][START_REF] Stoll | Drag reduction through distributed electric propulsion[END_REF]and highlighted a significant increase of efficiency for the cruise. GL-10, shown in Figure 1 is being tested for vertical take-off capability with tilting its wing and an efficient cruise by adapting its multiple propellers that are located on the leading edge of the wing. On the small scale, ISAE's MAVION, also shown in Figure 1, is a good example of a hand-release vertical take-off and afterwards transition to cruise flight concept. However its relatively low-pitched propellers, required to fly stationary, and low aspect ratio wings, mainly a result of size restriction, limits its high speed capability as well as endurance and range performance.

Furthermore, recent progress on automatic control [START_REF] Ostermann | Control concept of a tiltwing uav during low speed manoeuvring[END_REF][START_REF] Nathan | Adaptive quaternion control for a miniature tailsitter uav[END_REF] allows the use of unstable aerodynamic configurations, as well as the use of electric motor for fast dynamic control (as is done on quadrotors). We believe that the combination of DEP and active control can be used to design the new generation of fixed wing vehicles offering superior endurance and range performance for wide velocity envelope. This includes a hand-release take-off, transitioning to level cruise flight while maintaining equilibrium through every attitude in between. Efficient high speed performances will be achieved

Background

The propeller wing interaction has been vastly studied for V/STOL vehicles. The problem is highly complex to solve without simplifications. Empirical formulas have been developed by Jameson [START_REF] Jameson | The Analysis of Propeller Wing Flow Interaction, Analytic Methods in Aircraft Aerodynamics[END_REF] in order to avoid massive calculations with the aim of estimating the generated lift and drag force. He relied on theoretical results for a rectangular wing in a constant and continuous rectangular jet slipstream. However, he has further improved the method by taking into account individual rectangular or circular slipstreams. De Young [START_REF] De | Propellers at High Incidence[END_REF] has developed a method for inclined propeller forces. Jameson's simplified formulas are verified by several experimental studies [START_REF] Richard | An investigation of a wing-propeller configuration employing large-chord plain flaps and large-diameter propellers for low-speed flight and vertical take-off[END_REF][START_REF] Page | Large-scale wind-tunnel tests of a deflected slipstream stol model with wings of various aspect ratios[END_REF] with good agreement. It should be noted that only the lift and drag forces were calculated in those studies, and the drag force included only the induced drag.

Present Work

This study focuses on a smaller scale vehicle, where the low Reynolds number flow regime plays a major role on the performances of the vehicle. We want to estimate the performances of the vehicle both in terms of aerodynamics and flight dynamics, so the stability is also taken into account in detail. Once the complete procedure finished, it will be possible to evaluate multiple design variables (span, surface, battery capacity,etc...) changes and their effect on the final performance of the aircraft for a given mission profile. As we concentrate on high speed computation with this simplified method, it will be possible to sweep through a wide range of candidate aircrafts individually and define the best performing one.

Aerodynamic Model for Propeller Wing Combination

The procedure developed by Jameson [START_REF] Jameson | The Analysis of Propeller Wing Flow Interaction, Analytic Methods in Aircraft Aerodynamics[END_REF] in order to estimate the aerodynamic forces and moments of a propeller wing combination will be described in detail for the consistency of this study. An arbitrary number of propeller slipstreams is defined, with individual thrust, actuator disk area, position and orientation. In this study, the fixation between the propeller actuator axis and the wing is fixed, however the presented model can be applied for tilting actuators as well. The method is mainly based on momentum theory, so that the swirl effects of the propeller slipstream are not modeled. DeYoung's method is used to estimate the inclined propeller thrust. Some of these previous methods are reformulated here in order to clarify the estimation procedure.

Blown Sections

Unblown Sections

Fig. 3: Showing the creation of wing sections according to the fully developed propeller slipstream width. Note that for each thrust value the sections will dynamically be changed in order to take into account the contraction.

Propeller Forces

The propeller forces are modeled according to actuator disk theory, for a given propeller thrust T, the ratio µ, between the free stream V ∞ and propeller jet slipstream V j , for a given actuator area of S p is given by

µ = V ∞ V j = 1 - T 0.5ρV 2 j S p (1)
Each individual slipstream is taken as circular form, and their contraction can be estimated with

b pc = b p 1 + µ 2 (2)
where, b p is the propeller disk diameter or width, and b pc is the fully developed contracted slipstream diameter or width.

Once the contracted slipstream diameter is calculated, the wing can be separated into sections, as shown in Figure 3, that are inside the propeller slipstream or outside. Note that the propeller slipstream is taken as fully developed for simplification reasons.

Propeller Downwash

Inclined propellers will deflect the free stream, which will change the angle of attack of the wing inside this slipstream. This downwash can be determined according to the inflow angle of the propeller α j .

= Eα j (3)
according to Ribner [START_REF] Herbert S Ribner | Notes on the Propeller Slipstream in Relation to Stability[END_REF] and De Young [START_REF] De | Propellers at High Incidence[END_REF] where,

E = E ∞ 2            2x b p + e + 1 + 2x b p + e 2 2x h p + e            (4)
E ∞ = 1 -µ 1 + µ 2 + µ 4 2 + µ + µ 2 1 + µ 2 4.25σ 1 + 2σ sin ( β + 8) (5) e = E ∞ 2 √ 1 -E ∞ (6)
As the slipstream form is taken circular, the propeller height h p is equal to the propeller width b p , and x represents the distance between actuator disk and the wing leading edge. Solidity of the propeller σ can be calculated by 4N b 3π cb b p , where cb is the average blade chord which can be estimated by (17). 4: Shows the wing incidence angle i w , jet incidence angle i j , angle of attack of the fuselage α with the resultant lift L, drag D, thrust T and the propeller normal force N, propeller downwash , jet slipstream V j .

∞ V L T j V ϵ N α + i w D α + i j Fig.

Actuator Inflow Angle Change due to Wing, Fuselage

and Other Propeller Jets Upwash Each actuator will be influenced by the fuselage, wing, and the other propeller jets. Taking these into effect, the inflow angle for each jet will be the sum of

α j = α + i j + U w (α + i w ) + U f α + ot her j et s U o j (7)
where, U w is the upwash due to wing,

U w = 2µAR 9( AR + 10) 1 x L.75/ c + 0.1 + 1 x R.75/ c + 0.1 (8)
U f is the upwash due to fuselage which is treated as an infinite falling cylinder,

U f = µ 8       D f us y L.75 2 + D f us y R.75 2      (9)
and U 0 j is the upwash due to the other propeller slipstreams treated as semi-infinite falling cylinders.

U 0 j = µ 16       b j ∆y L.75 2 + b j ∆y R.75 2      (10)
x L.75/ c and x R.75/ c are the distance between wing leading edge and propeller blade right and left 0.75 radius location. y L.75 and y R.75 are the distance from fuselage axis to the propeller blade right and left 0.75 radius location. ∆y L.75 is the lateral distance from one propeller axis to the other propeller's left blade 0.75 radius location, and ∆y R.75 is the right blade 0.75 radius location.

x L.75 y L.75 y R.75

x R.75 𝚫y L.75 𝚫y R.75

Fig. 5: Showing the incidence angles, angle of attack of the wing and actuator with the resultant lift, drag, thrust and the propeller normal force.

For each propeller slipstream , α j can be written as

α j1 = α + i j 1 + U w (α + i w ) + U f α + U o j 12 2 + • • • + U o j 1n n α j2 = α + i j 2 + U w (α + i w ) + U f α + U o j 21 1 + • • • + U o j 2n n α j3 = α + i j 3 + U w (α + i w ) + U f α + U o j 31 1 + • • • + U o j 3n n . . . α j n = • • •
for a half wing with n propellers mounted on the leading edge. U o j 12 presents the upwash effect of the second actuator on the first one. As long as there is a fuselage between the propellers separating the slipstreams, the upwash effects coming from the other wing can be neglected. Substituting from (3), results a set of linear equations in the form of Ax = b where,

x = [ 1 , 2 , 3 ,...] A =            -1/E 1 U o j 12 U o j 13 • • • U o j 21 -1/E 2 U o j 23 • • • U o j 31 U o j 32 -1/E 3 • • • . . . . . . . . . . . .            and b(1) = -[α + i j1 + U w1 (α + i w ) + U f 1 α] b(2) = -[α + i j2 + U w2 (α + i w ) + U f 2 α] . . .
Once the set of linear equations solved, and therefore the inflow angles α j can be found.

Similarly, wing inflow angles for sections that are not inside the propeller slipstream will be

α w j1 = α + i w + U f α (11)
and for the sections inside the slipstream

α w j µ = α w j1 -+ j et s U ∞ j (12)
where the upwash factor U ∞ j , due to other propeller slipstreams, is calculated as if they are infinite falling cylinders, resulting in

U ∞ j = 2U o j (13)

Propeller Normal Force

Once the actuator inflow angles α j determined, the normal force generated by the propeller can be calculated with the assumption of being proportional to inflow angle.

C N = C N α sin α j (14)
where, β is the propeller pitch angle measured at 0.75% radius blade location.

C N α = µ 2 1 + µ 2 + µ 1 + µ 2 4.25σ 1 + 2σ sin ( β + 8) (15

Equivalent Mass Flow Influenced by the Wing

The essential difference between a wing in free stream of speed V ∞ , and a stationary wing immersed in a slipstream of the same speed V, is the reduction of the mass flow outside the slipstream and also a reduction in the mass flow influenced by the wing. The wing in free stream is influenced from a mass flow that is passing through a tube surface S ∞ of πb 2 /4 containing the wing tips. However, the wing in a slipstream passing through surface S j influences a smaller mass flow resulting a reduction in the effective span or aspect ratio of the wing.

Stationary Wing in Jet-Stream

Wing in Free-Stream S j ∞ S Fig. 6: Mass flow influenced by the wings. On the left: stationary wing in a jet-stream passing through S j . On the right: wing flying in an equal velocity of freestream V ∞ .

In the case of a stationary wing immersed in a slipstream, compared to a wing in free stream, the same amount of lift has to be generated by deflection of a smaller mass flow through a greater downwash angle. Assuming that the additional downwash angle due to the slipstream is a constant fraction of the downwash of the wing in free stream, with a value of p, then the Aspect Ratio (AR) reduces to

AR 0 = AR 1 + p (18)

Resulting Lift Slope in a Slipstream

Considering lifting line theory, the lift slope (CL α 0 ) of this stationary wing in slipstream would be

CL α 0 = Cl α 2D 1 + Cl α 2D (1 + p) π AR (19)
where Cl α 2D is the lift slope of the two dimensional airfoil.

The calculations relies on the known performance values of the wing in the free stream, so comparing with the lift slope in a free stream which is

CL α ∞ = Cl α 2D 1 + Cl α 2D π AR (20)
Then, the lift slope CL α 0 in static jet slipstream can be calculated by

CL α 0 CL α ∞ = 1 + Cl α 2D π AR 1 + Cl α 2D (1 + p) π AR (21)
Assuming the two dimensional lift slope value 2π from thin airfoil theory, the ratio function becomes

CL α 0 CL α ∞ = AR + 2 AR + k (22)
where k depends on the slipstream jet aspect ratio. Jameson [START_REF] Jameson | The Analysis of Propeller Wing Flow Interaction, Analytic Methods in Aircraft Aerodynamics[END_REF] has found that a good approximation to the lift of a rectangular wing inside a cylindrical slipstream can be estimated by taking k = 3.54. Again, the lift slope CL α ∞ of the wing in free stream is assumed to be known.

Similarly, taking into account the forward speed, a wing that is in an elliptic jet slipstream of velocity V j , with a forward speed of V ∞ will have additional downwash angle compared to the same wing in V ∞ free stream only. This downwash increase is found [START_REF] Koning | Influence of the propeller on other parts of the airplane structure[END_REF] to be by the factor

λ + µ 2 1 + λ µ 2 ( 23
)
where µ is the velocity ratio of V ∞ /V j and λ is the ratio of the width to the height of the slipstream. This downwash increase results in an equivalent aspect ratio reduction of

AR µ = AR λ + µ 2 1 + λ µ 2 (24)
Using the lift slope of the wing in free stream CL α ∞ and stationary within a jet slipstream CL α 0 , the characteristics on forward speed can be expressed by

CL α µ CL α ∞ = 1 1 + C L α∞ C L α 0 -1 1-µ 2 1+ AR j µ 2 (25)
where AR j is the jet slipstream aspect ratio, and will be taken as 1 for circular slipstreams.

Partially Immersed Wing in Arbitrary Number of Slipstreams

The slipstream over the wing will be generated by individual propellers, and also there will be different propulsion configurations for different flight phases, hence an approximation in order to calculate the highly complex force, moments, and interactions. A simple estimation can be made by superposition of forces over the wing in free stream and the individual parts that are immersed in slipstreams. The individual parts that are immersed in slipstream are calculated as isolated planforms. Thus, the additional increase on each isolated planform will simply be the difference between the planform in free stream V ∞ , and the planform immersed in a jet slipstream V j moving with a forward speed of V ∞ . The difference in lift will be

∆L = 1 2 ρS w j (V 2 j CL α j µ α w j µ -V 2 ∞ CL α ∞ α w j∞ ) (26)
where CL α j µ is the lift slope of the wing part that is inside the jet slipstream with a velocity ratio of µ = V ∞ /V j by taking the aspect ratio as b j /S w j . CL α ∞ is the lift slope of the same wing part in a freestream, or in other words when µ = 1, α w j µ is the angle of attack of the wing in jet slipstream, and α w j∞ is the angle of attack of the same part in free stream. It should be noted that the angle of attack of the wing portion in jet slipstream is reduced compared to the angle of attack in the free stream by the slipstream downwash of as stated in equation 12.

Additionally, an inclined slipstream to the free stream will generate an external upwash, which can be approximated by assuming the slipstream as a falling cylinder model. The upwash at a distance y from the center axis of the slipstream is b 2 j /2/y 2 According to [START_REF] Jameson | The Analysis of Propeller Wing Flow Interaction, Analytic Methods in Aircraft Aerodynamics[END_REF], the average upwash over the external part of the wing will approximately be

S w j S
. Taking all upwash effects of propeller jets, the increase in lift can be calculated by multiplying the sum of all slipstream upwash angle with the unblown surface area and the lift slope of the complete wing in freestream CL α ∞ For the small angle of attack, lift force generated by the wing can be found by adding up the freestream lift of the complete wing, the additional lift created from the unblown parts of the wing because of the upwash effects of the jets, and finally the additional lift on the blown sections coming from dynamic pressure increase because of the jet velocities.

L = 0.5ρV 2 ∞ SCL α ∞ + 0.5ρV 2 ∞ SCL α ∞ S - jet s S w j jet s S w j S + jet s ∆L j (27)

Induced Drag

Let k denote CD i /CL 2 , k j 0 be the same ratio for a the wing in a static propeller jet slipstream, k j ∞ is the wing in a free stream, and k j µ is the wing in a slipstream with a forward flight velocity ratio of µ. Once again, the induced drag coefficient can be estimated by comparing with the values from freestream, that are assumed known or calculated by liftingline theory, or empirically. Jameson suggests

k = 1 + 0.006AR π AR (28)
for the sections inside the jet, the section's AR sect ion will be used. Once the k j ∞ calculated by

k j ∞ = 1 + 0.006AR sect ion π AR sect ion (29)
k j 0 and k j µ for circular slipstream can be found through

k j 0 k j ∞ = 1.68 (30) k j µ k j ∞ = 1.68 + 0.32µ 2 1 + µ 2 (31)
A similar approach can be used to calculate the additional induced drag for the wing section that are inside the slipstream. ∆D i can be calculated as the freestream lift of this section multiplied by the change in induced downwash angle, plus the new induced downwash angle multiplied by the change in the lift ∆L.

∆D i = 0.5ρV 2 ∞ S w j CL j ∞ (α i j -α i ∞ ) + ∆Lα i j (32)
where

α i ∞ = CL j ∞ k j ∞ (33) α i j = CL j µ k j µ (34)
Note that CL j ∞ and CL j µ were calculated during the ∆L, in (26)

CL j ∞ = CL α ∞ α w j∞ (35)
CL j µ = CL α j µ α w j µ (36)
Finally, induced drag D i can be found by summing up the induced drag of the whole wing in freestream as if there were no propeller slipstreams on it, and the additional induced drag

∆D i D i = 0.5ρV 2 ∞ SkCL 2 ∞ + j et s ∆D i j (37)

Viscous Drag

The interest while developing this semi-empirical method is to be able to use it for designing small scale V/STOL UAVs, where the low-Reynolds effects are significantly important and therefore viscous drag addition can not be ignored. Wing in isolation can be solved by a high-fidelity approach in order to have a basis estimate. However this will slow down the solution too much that the whole idea of being fast for rapid development and analysis for conceptual design will be vanished. With this in mind, the same procedure that is used in QPROP [START_REF] Drela | QPROP Formulation[END_REF], which is a polynomial fit to the lift-drag curve with an exponential correction coefficient for Reynolds effects is implemented.

Total Drag

Finally, the total drag force can be found as the sum of D 0 parasitic drag, D i induced drag, and D v viscous drag contributions.

D = D 0 + D i + D v (38)
2.11 Rotation of the Section Forces It should be noted that each wing section inside the propeller slipstream generates a lift force perpendicular to the local flow velocity and the drag force parallel to flow velocity. Therefore they should be rotated back by the propeller slipstream downwash angle and then summed in order to obtain the total lift force L ∞ and drag force D ∞ .

Effect of Flaps

The effect of flaps are modeled by an increase on the wing angle of attack as presented by Jameson [START_REF] Jameson | The Analysis of Propeller Wing Flow Interaction, Analytic Methods in Aircraft Aerodynamics[END_REF]. α/δ ∞ being the flap effectiveness of three dimensional wing in free stream, effective wing incidence angle i w ∞ becomes

i w ∞ = i w + α/δ ∞ δ e (39)
where,

α/δ ∞ = √ α/δ 2D + α/δ 2D AR+4.5 AR+2 AR √ α/δ 2D + AR+4.5 AR+2 AR (40)
Likewise for a wing section inside propeller slipstream, effective wing incidence i w j µ becomes

i w j µ = i w + α/δ j µ δ e (41)
and for a circular slipstream,

α/δ j µ = 1 -µ 2 + µ 2 α/δ ∞ (42)
i w ∞ and i w j µ should be substituted for wing incidence i w in [START_REF] Richard | An investigation of a wing-propeller configuration employing large-chord plain flaps and large-diameter propellers for low-speed flight and vertical take-off[END_REF], [START_REF] Drela | QPROP Formulation[END_REF], and (12).

Zero Lift Angle of Attack Determination

For cases where the propellers are not aligned with the zero lift angle of attack of the wing, the additional velocity imparted by the propellers will change the zero lift angle of attack of those wing sections. These angles for each section must be found separately. Lift slopes CL α j∞ and CL α j µ can be found by setting i w = i j = 0 and α = 1 in ( 7), [START_REF] Drela | QPROP Formulation[END_REF], and [START_REF] Draper | Investigation of the aerodynamic characteristics of a model wingpropeller combination and of the wing and propeller separately at angles of attack up to 90 degrees[END_REF] and calculating up to (27). After recalculating CL j ∞ and CL j µ with α = 0, correct wing incidence i w and actuator incidences i j , the zero lift angle of attack for each wing section can be found by

α 0 ∞ = CL j ∞ (α=0) CL α j∞ and α 0 j = CL j µ (α=0) CL α j µ ( 43
)
4 Wing Lift and Drag at High Incidence As mentioned before, the propeller slipstreams can significantly reduce the angle of attack of the blown wing sections. This will let the aircraft fly at very large angle of attack during transition and hovering flight phases. The added velocity imparted by the propeller slipstream keeps the flow attached on the blown wing sections where the other sections are already stalled. In such cases, the prediction of forces and moments becomes very difficult. However it is still possible to have a rough estimate which can give an idea about the performance of the vehicle in these phases.

Maximum lift angle of attack α ma x is defined for each wing section, and it is assumed that any wing section with a greater inflow angle compared to its maximum lift angle of attack (α w j∞ -α 0 j > α ma x ), is stalled. In this case, if the stall is on the unblown parts, V ∞ will dominate. Upwash effects are not taken into account as they do not contribute significantly. CL ∞ is thus,

CL ∞ = CL α ∞ tan(α ma x ) cos(α w j∞ -α 0 ∞ ) (44)
For the Stalled sections that are inside the propeller slipstream, the velocity becomes V j , the inflow angle α j µ and the lift coefficient becomes CL j µ . The lift will be calculated without ∆L contribution.

CL j µ = CL α j µ tan(α ma x ) cos(α w j µ -α 0 j ) (45)
Hence, for the drag, stalled wing section lift coefficients (44), (45) and k j ∞ , k j µ coefficients are used.

5 Total Forces and Moments

Forces

For the moment, only longitudinal flight dynamics is considered, so that the lateral force and moments are assumed to be zero F y = M x = M z = 0 as in equilibrium. Contribution of the wing lift L ∞ , drag D ∞ , propeller thrust T, and propeller normal force N will be taken into account as

F z = L ∞ + j et s T sin(α + i j ) + j et s N cos(α + i j ) (46) F x = D ∞ - j et s T cos(α + i j ) + j et s N sin(α + i j ) (47) ∞ V T L ∞ D ∞ d L d D d T M y L ∞ D ∞ T d L d D d T

Moment

The pitching moment is calculated by the resultant wing forces and moments as well. However, as the aircraft is capable of increasing its pitch attitude up to 90 degrees, the moment arm between the wing aerodynamic center and the center of gravity of the aircraft changes during this rotation as shown in Figure 7. The variation on pitch does also effects the position of aerodynamic center of the wing as experimentally tested by Draper and Kuhn [START_REF] Draper | Investigation of the aerodynamic characteristics of a model wingpropeller combination and of the wing and propeller separately at angles of attack up to 90 degrees[END_REF]. However we will assume it to be fixed. The thrust moment arm d T j does not change during the pitch variation. However lift force moment arm d L and drag force moment arm d D has to be calculated at every angle of attack as a result of moment arm length variation. Finally, the total pitching moment of the aircraft is found by

M y = M wing AC - jet s T j d T j -L ∞ d L + D ∞ d D (48)
where,

M wing AC = 0.5 ρV 2 ∞ S wing C M c (49) C M = sect ions C M sec S sec S wing V sec V ∞ (50) C M sec = C M 0sec + C M αsec α sec + C M δe .sec δ e.sec (51)
6 Equilibrium Calculations

In order to fly in equilibrium at every flight speed (V ∞ ), the aircraft should sustain F x = 0 , F z = 0 , M y = 0 via thrust (T), and elevator deflections (δ e ). For steady cases, this is obtained by finding the roots via a Newton-Raphson iteration. Figure 9 shows the estimated transition angle of attack of the example case aircraft versus horizontal flight speed, where every point is in equilibrium as stated in [START_REF] De | Propellers at High Incidence[END_REF].

Preliminary Results

Explained method is parametrized in order to accept multi-variable input, such as the number of propellers, diameter, pitch, position and orientations, wing surface, different thrusts, etc... and written into a FORTRAN code. The final program is capable of analyzing any given configuration within the explained limitations. An example configuration specifications are shown in Table 1.

Future Remarks

The propeller slipstreams are taken discrete even though they are really close to each other in some configurations. It could be modified such as that in certain cases with close slipstreams, a rectangular slipstream calculations can be used instead of circular ones as explained in [START_REF] Jameson | The Analysis of Propeller Wing Flow Interaction, Analytic Methods in Aircraft Aerodynamics[END_REF].

Conclusion

A preliminary study on force and moment estimation of a wing with distributed propeller is presented. The method takes into account low-Reynolds effects via airfoil viscous drag contribution. Further verification of the numerical results with wind-tunnel or flight test are required. However, once sufficient confidence is obtained, the method will be useful to design optimized vehicles using this propulsion system configuration, such as the proposed Next Generation Fixed Wing aircraft which offers a simplified solution to the widespeed envelope problem of a fixed wing UAV.

Fig. 1 :

 1 Fig. 1: Tilt-Body micro air vehicle MAVION and a small demonstrator of NASA's GL-10

Fig. 2 :

 2 Fig. 2: Transitioning from four propeller stationary vertical take-off to two propeller high speed cruise phase.

  ) which relies on the solidity σ of the propeller approximated by the blade number N b and the average blade chord cb σ = 4N b 3π cb b p (16) cb = 0.16 (1.25b 0.25 + 2b 0.50 + 2b 0.75 + b 0.95 ) (17)

Fig. 7 :

 7 Fig. 7: Illustration of the moment arm length variation during pitch attitude change.

Fig. 8 :Fig. 9 :

 89 Fig. 8: Representative CAD drawing of the conceptual design.


Stéphane Ronsseray
email: stephane.ronsseray@upmc.fr

Paramutation phenomena in non-vertebrate animals

. Thus it implies that the paramutated allele conserves its new properties on the long term over generations even in the absence of the paramutagenic allele and that it turns paramutagenic itself, without undergoing any changes in the DNA sequence. Some epigenetic interactions have been described in two non-vertebrate animal models, which appear to exhibit similar properties. Both systems are linked to trans-generational transmission of non-coding small RNAs. In Drosophila melanogaster, paramutation is correlated with transmission of PIWI-Interacting RNAs (piRNAs), a class of small non-coding RNAs that repress mobile DNA in the germline. A tandem repeated transgenic locus producing abundant ovarian piRNAs can activate piRNA production and associated homology-dependent silencing at a locus that was previously stably devoid of such capacities. The newly converted locus is then perfectly stable in absence of the inducer locus (>100 generations) and becomes fully paramutagenic. In Caenorhabditis elegans, paramutation is correlated with transmission of siRNAs, which are produced by transgenes targeted by piRNAs in the germline. Indeed, a transgenic locus, targeted by the piRNA machinery, produces siRNAs that can induce silencing of homologous transgenes, which can be further transmitted in a repressed state over generations despite the absence of the inducer transgenic locus. As in fly, the paramutated locus can become fully paramutagenic, and paramutation can be mediated by cytoplasmic inheritance without transmission of the paramutagenic locus itself. Nevertheless, in contrast to flies where the induction is only maternally inherited, both parents can transmit it in worms. In addition, a reciprocal phenomenon -(from off toward on) -appears to be also possible in worms as some activated transgenes can reactivate silent transgenes in the germline, and this modification can also be transmitted to next generations, even so it appears to be only partially stable. Thus, in a given system, opposite paramutation-like phenomena could exist, mediated by antagonist active pathways. As in plants, paramutation in flies and worms correlates with chromatin structure modification of the paramutated locus. In flies, inheritance of small RNAs from one generation to the next transmits a memory mainly targeting loci for repression whereas in worms, small RNAs can target loci either for repression or expression. Nevertheless, in the two species, paramutation can play an important role in the epigenome establishment.

1-

Introduction

Various strategies are used to recognize and repress mobile or foreign DNAs in genomes and to epigenetically transfer silencing memory over generations. In fly, transgenerational information seems to ensure predominantly gene repression. Indeed, systems based on the principle of genomic traps have been established in order to identify and further repress Transposable Elements (TEs).

The Drosophila melanogaster genome contains about 140 discrete loci composed of TE fragments which undergo non-canonical transcription. This results in the inactivation of the transcript of the locus itself and of all the homologous transcripts produced by the genome [START_REF] Brennecke | Discrete small RNA-generating loci as master regulators of transposon activity in Drosophila[END_REF][START_REF] Gunawardane | A slicer-mediated mechanism for repeat-associated siRNA 5' end formation in Drosophila[END_REF][START_REF] Mohn | The rhino-deadlock-cutoff complex licenses noncanonical transcription of dual-strand piRNA clusters in Drosophila[END_REF][START_REF] Zhang | The HP1 homolog rhino anchors a nuclear complex that suppresses piRNA precursor splicing[END_REF]. Therefore, this system based on the PIWI-Interacting RNAs (piRNAs) results in repression of all TE copies in the genome if at least one copy has inserted into a piRNA-producing locus. Euchromatic TE repression occurs at both the transcriptional and post-transcriptional levels [START_REF] Sato | Piwi-interacting RNAs: biological functions and biogenesis[END_REF][START_REF] Weick | piRNAs: from biogenesis to function[END_REF][START_REF] Thomas | Piwi induces piRNAguided transcriptional silencing and establishment of a repressive chromatin state[END_REF][START_REF] Sienski | Transcriptional silencing of transposons by Piwi and maelstrom and its impact on chromatin state and gene expression[END_REF]. Thus, when a TE copy is active, it will move and insert into a piRNA-producing locus and this "piRNA locus" copy will progressively establish repression of the entire TE family: the family gets trapped. An important functional aspect is that production of piRNAs by piRNA loci requires maternal transmission of piRNAs both for repressing TE activity in the embryo germline and for stimulating piRNA production by the piRNA loci in the adult gonads [START_REF] Brennecke | An epigenetic role for maternally inherited piRNAs in transposon silencing[END_REF][START_REF] Josse | Telomeric transsilencing: an epigenetic repression combining RNA silencing and heterochromatin formation[END_REF]. Thus, in flies, a catalog of potentially dangerous sequences is transmitted from one generation to the other via cytoplasmic inheritance of piRNAs within the embryo. Worms also have a piRNA machinery but the strategy of transgenerational inheritance appears to be different. Indeed, two large clusters of piRNA loci produce thousands of different piRNAs that associate with the PIWI protein PRG-1 and target many sequences, as mismatches between piRNAs and their targets are tolerated [START_REF] Batista | PRG-1 and 21U-RNAs interact to form the piRNA complex required for fertility in C. elegans[END_REF][START_REF] Bagijn | Function, targets, and evolution of Caenorhabditis elegans piRNAs[END_REF]. When a sequence is targeted by piRNAs, the signal is amplified by an RNA-dependent RNA Polymerase (RdRP) and further relayed to a small interfering RNA pathway based on double strand RNA slicing performed by WAGO proteins [START_REF] Bagijn | Function, targets, and evolution of Caenorhabditis elegans piRNAs[END_REF][START_REF] Luteijn | Extremely stable Piwi-induced gene silencing in Caenorhabditis elegans[END_REF][START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF][START_REF] Ashe | piRNAs can trigger a multigenerational epigenetic memory in the germline of C. elegans[END_REF][START_REF] Das | Piwi and piRNAs act upstream of an endogenous siRNA pathway to suppress Tc3 transposon mobility in the Caenorhabditis elegans germline[END_REF]. Once this silencing is established, the piRNA machinery is no longer necessary and the information can be maintained in further generations solely by the WAGO protein pathway. The piRNA machinery has thus a crucial role for the establishment of silencing but not for its maintenance. To avoid too extensive, unspecific attack of transcripts by piRNAs, an active pathway exists, linked to production of small RNAs associated with a protein called CSR-1, which counteracts the effect of the piRNAs and consequently licenses transcripts for expression [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF][START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF]. This CSR-1-associated RNAs are also transmitted from one generation to the other and allow transgenerational information of transcripts that have to be protected from degradation by piRNAs loaded onto PRG-1 [START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF].

It appears that in fly, one generation epigenetically transmits to the next a list of sequences to be repressed, whereas worms transmit information about both, correct repression or expression [START_REF] Conine | Argonautes promote male fertility and provide a paternal memory of germline gene expression in C. elegans[END_REF]. In both species, these systems were investigated using transgenes, and transgenic loci can exist at a given locus in opposite epigenetic states. In fly, clusters of transgenes can be stably maintained over generations, in either a quiescent or active state for production of abundant amounts of transgenehomologous piRNAs that establish trans-silencing of homologous transgene in the germline [START_REF] De Vanssay | Paramutation in Drosophila linked to emergence of a piRNA-producing locus[END_REF][START_REF] Ronsseray | P-Element repression in Drosophila melanogaster by variegating clusters of P-lacZ-white transgenes[END_REF]. In worm, the same transgene can exist in an active or repressed state for their expression depending on the line [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF]. The key point is that in both species, epigenetic conversion processes can occur in the germline between repressed and active loci, which can further be transmitted to the next generations in the absence of the converting locus. It results in a paramutation likephenomenon, resembling this classical epigenetic conversion as observed in maize [START_REF] Chandler | Paramutation: from maize to mice[END_REF][START_REF] Brink | A Genetic Change Associated with the R Locus in Maize Which Is Directed and Potentially Reversible[END_REF][START_REF] Coe | A regular and continuing conversion-type phenomenon at the B locus in maize[END_REF][START_REF] Brink | Paramutation at the R locus in maize[END_REF]. This review will describe properties of these epigenetic conversion processes and highlight the parallels and differences between the two models.

2-

Drosophila paramutation-like conversion

The piRNA pathway was discovered in fly in 2006-2007 [START_REF] Brennecke | Discrete small RNA-generating loci as master regulators of transposon activity in Drosophila[END_REF][START_REF] Gunawardane | A slicer-mediated mechanism for repeat-associated siRNA 5' end formation in Drosophila[END_REF][START_REF] Vagin | A distinct small RNA pathway silences selfish genetic elements in the germline[END_REF] and functionally validated with the use of genomic sites capable of transposon repression [START_REF] Brennecke | An epigenetic role for maternally inherited piRNAs in transposon silencing[END_REF]. Indeed, two TEs invaded the genome of natural D. melanogaster populations in the 20 th century, the P element (a DNA transposon) [START_REF] Engels | P elements in Drosophila[END_REF] and the I factor (a LINE retroelement) [START_REF] Finnegan | The I factor and I-R Hybrid Dysgenesis in Drosophila melanogaster[END_REF]. For the two TEs, it was shown that the cross of females devoid of TE copies (from lines collected before the invasion) with males carrying numerous copies of the TE (from lines collected after the invasion) produces progeny showing a syndrome of genetic abnormalities in the germline called hybrid dysgenesis (high mutation rate, chromosomal breakages, thermo-sensitive sterility) [START_REF] Kidwell | Hybrid dysgenesis in Drosophila melanogaster: a syndrome of aberrant traits including mutation, sterility, and male recombination[END_REF][START_REF] Picard | Non-mendelian female sterility and hybrid dysgenesis in Drosophila melanogaster[END_REF]. Cytoplasmic inheritance was shown to play a key role as reciprocal crosses (TE-bearing females x TE-devoid males) produced progeny without dysgenesis [START_REF] Picard | Non-mendelian female sterility and hybrid dysgenesis in Drosophila melanogaster[END_REF][START_REF] Engels | Hybrid dysgenesis in Drosophila melanogaster: rules of inheritance of female sterility[END_REF][START_REF] Engels | Extrachromosomal control of mutability in Drosophila melanogaster[END_REF][START_REF] Picard | Non mendelian female sterility in Drosophila melanogaster: sterility in the daughter progeny of SF and RSF females[END_REF]. Thus cytoplasm from females devoid of P or I elements was therefore missing "something" [START_REF] Ronsseray | Maternal inheritance of P cytotype in Drosophila melanogaster: a "pre-P cytotype" is strictly extra-chromosomally transmitted[END_REF][START_REF] Niemi | Establishment and maintenance of the P cytotype associated with telomeric P elements in Drosophila melanogaster[END_REF][START_REF] Bucheton | The I-R system of hybrid dysgenesis in Drosophila melanogaster: heredity of the reactive condition[END_REF], later shown to be P-or I-homologous piRNAs [START_REF] Brennecke | An epigenetic role for maternally inherited piRNAs in transposon silencing[END_REF][START_REF] Grentzinger | piRNA-mediated transgenerational inheritance of an acquired trait[END_REF]. For the P element, a master locus for repressing hybrid dysgenesis was identified at the telomere of the X chromosome [START_REF] Ronsseray | The maternally inherited regulation of P elements in Drosophila melanogaster can be elicited by two P copies at cytological site 1A on the X chromosome[END_REF][START_REF] Ronsseray | The regulatory properties of autonomous subtelomeric P elements are sensitive to a Suppressor of variegation in Drosophila melanogaster[END_REF][START_REF] Stuart | Telomeric P elements associated with cytotype regulation of the P transposon family in Drosophila melanogaster[END_REF][START_REF] Marin | P-Element repression in Drosophila melanogaster by a naturally occurring defective telomeric P copy[END_REF], within subtelomeric heterochromatin called Telomeric Associated Sequences (TAS) [START_REF] Karpen | Analysis of subtelomeric heterochromatin in the Drosophila minichromosome Dp1187 by single P element insertional mutagenesis[END_REF]. Such telomeric heterochromatin was shown to produce abundant ovarian piRNAs [START_REF] Brennecke | Discrete small RNA-generating loci as master regulators of transposon activity in Drosophila[END_REF].

In addition, P copies inserted in TAS were also shown to produce abundant ovarian piRNAs [START_REF] Brennecke | An epigenetic role for maternally inherited piRNAs in transposon silencing[END_REF][START_REF] De Vanssay | Paramutation in Drosophila linked to emergence of a piRNA-producing locus[END_REF][START_REF] Muerdter | Production of artificial piRNAs in flies and mice[END_REF]. A transgenic system based on P-derived sequences located in TAS was developed and used to study the phenotypic and genetic properties of piRNA-mediated repression in the germline.

In this system, called Trans-Silencing Effect (TSE), a P-transgene located in TAS can repress a homologous transgene in the female germline [START_REF] Josse | Telomeric transsilencing: an epigenetic repression combining RNA silencing and heterochromatin formation[END_REF][START_REF] Josse | Telomeric trans-silencing in Drosophila melanogaster: tissue specificity, development and functional interactions between non-homologous telomeres[END_REF][START_REF] Roche | Trans-silencing by P elements inserted in subtelomeric heterochromatin involves the Drosophila Polycomb group gene, Enhancer of zeste[END_REF]. Inheritance of this repressive capacity shows both a maternal effect and a partial persistence of the maternal effect over up to 6 generations [START_REF] Josse | Telomeric transsilencing: an epigenetic repression combining RNA silencing and heterochromatin formation[END_REF]. TSE studies and a mutant approach allowed to confirm that all the piRNA genes tested were necessary for the trans-silencing capacities of telomeric P insertions [START_REF] Josse | Telomeric transsilencing: an epigenetic repression combining RNA silencing and heterochromatin formation[END_REF][START_REF] Josse | Telomeric trans-silencing in Drosophila melanogaster: tissue specificity, development and functional interactions between non-homologous telomeres[END_REF][START_REF] Todeschini | The Epigenetic Trans-Silencing Effect in Drosophila Involves Maternally-Transmitted Small RNAs Whose Production Depends on the piRNA Pathway and HP1[END_REF]. Finally, the use of TSE also allowed to discover that some other structures in the genome can establish piRNAmediated repression [START_REF] Ronsseray | P-Element repression in Drosophila melanogaster by variegating clusters of P-lacZ-white transgenes[END_REF]. Such studies revealed puzzling situations as the two lines T-1 and BX2 carrying a similar cluster of P-lacZ-white transgenes exhibit different properties. Indeed the T-1 induces a strong TSE whereas BX2 showed no repression capacity [START_REF] Ronsseray | P-Element repression in Drosophila melanogaster by variegating clusters of P-lacZ-white transgenes[END_REF]. These P-lacZ-white clusters show stochastic on-off repression of the white marker in the eye (called variegation). This variegation results from Repeat Induced Gene Silencing (RIGS) [START_REF] Dorer | Expansions of transgene repeats cause heterochromatin formation and gene silencing in Drosophila[END_REF][START_REF] Dorer | Transgene repeat arrays interact with distant heterochromatin and cause silencing in cis and trans[END_REF] and is associated with the local binding of Heterochromatin Protein 1 (HP1) at the cluster, as tested by immuno-staining of salivary gland polytene chromosomes [START_REF] Fanti | Heterochromatin protein 1 binds transgene arrays[END_REF]. T-1 has the same cluster than BX2 but carries chromosomal inversions and translocations induced by X-ray treatment. The trans-silencing capacities of T-1 and BX2 appeared stable over more than one decade for the two lines. This allowed investigating possible factors that could activate piRNA production by the quiescent BX2 locus.

It was then tested if maternal inheritance of P-lacZ-white homologous piRNAs could de novo activate the production of piRNAs from an initially quiescent BX2 locus [START_REF] De Vanssay | Paramutation in Drosophila linked to emergence of a piRNA-producing locus[END_REF][START_REF] De Vanssay | piRNAs and epigenetic conversion in Drosophila[END_REF]. T-1 heterozygous females were crossed with BX2 males. Female progeny having inherited the BX2 locus and a T-1 cytoplasm, but not the T-1 locus, produced ovarian P-lacZ-white piRNAs and induced a complete trans-silencing (Figure 1). The phenomenon showed complete penetrance in each experiment. We called BX2* these paramutated BX2 females by contrast to the initial "BX2 naïve" (nonparamutated) flies producing no P-lacZ-white piRNAs. BX2* lines were established and further studied for their capacity to induce TSE and produce piRNAs. Again all the tested lines (more than 20) exhibited stable repression. One line was investigated for very long terms: it still induced complete TSE after more than 120 generations, and ovarian P-lacZ-white piRNA production was confirmed at G 42 and G 83 . It was also tested if the BX2* line is paramutagenic by crossing BX2* females at G 42 with BX2 naive males. The progeny (called BX2**) having inherited a paternal -but not maternal -BX2 locus showed complete TSE capacity and produced abundant P-lacZ-white piRNAs in ovaries (Figure 1). BX2* females are thus fully paramutagenic. Similarly, BX2** females are also completely paramutagenic. Therefore, epigenetic conversion occurs between BX2* and BX2 naive loci; the change is heritable, and the process can be repeated. This epigenetic conversion presents the properties of a paramutation which is mediated via cytoplasmic inheritance:

this excludes any role of pairing between the loci in the paramutation process. As control, T-1 males were crossed to BX2 females, and the progeny having inherited the BX2 locus did not show any trans-silencing capacities. Resulting flies carrying the BX2 loci failed to show silencing capacities in further generations (our lab, unpublished). Further, the paramutation process can be erased by crossing BX2* males with females that do not carry any P-lacZ-white transgene. This clearance is stable for over than 50 generations (our lab, unpublished). To exclude the hypothesis that an autoreproductive cytoplasmic component would be sufficient to induce paramutation, we also have performed a "passage à vide" (empty step) experiment [START_REF] De Vanssay | piRNAs and epigenetic conversion in Drosophila[END_REF]: BX2* females were crossed with males devoid of P-lacZ-white transgene and G 1 females which did not inherit the BX2* cluster were crossed with BX2 naïve males in order to test if their cytoplasm can induce paramutation. G 2 females, whose grand-mother produced P-lacZ-white piRNAs, but whose mother were unable to maintain such production due to the lack of P-lacZ-white transgene, showed no repression capacities confirming that this paramutation does not result from an autoreplicative cytoplasmic component.

BX2* females produce not only abundant P-lacZ-white 23-28nt piRNAs but also abundant 21nt

RNAs [START_REF] De Vanssay | Paramutation in Drosophila linked to emergence of a piRNA-producing locus[END_REF]. We have tested the effect of a homozygous mutation of Dicer-2, involved in the siRNA pathway on BX2* properties. The trans-silencing capacities were unaffected by a Dicer-2 loss of function, even after 50 generations in a homozygous mutant context. We have also tested the effect of a heteroallelic mutant context for the PIWI family gene aubergine on BX2* females: silencing capacities were completely abolished in such mutant females, showing that paramutation requires piRNAs but not siRNAs.

What is the molecular mechanism of paramutation linked to piRNAs in Drosophila? It can be assumed that maternally transmitted piRNAs are incorporated in Primordial Germ Cells (PGCs) in embryos and will potentiate piRNA production by homologous loci [START_REF] De Vanssay | piRNAs and epigenetic conversion in Drosophila[END_REF][START_REF] Thomas | Transgenerationally inherited piRNAs trigger piRNA biogenesis by changing the chromatin of piRNA clusters and inducing precursor processing[END_REF]. One possibility is that piRNAs associated with the Piwi protein reach the PGC nuclei and interact with the nascent transcripts on the piRNA locus to promote the binding of the Rhino protein, a member of the Heterochromatin Protein 1 (HP1) subfamily of chromo box proteins [START_REF] Volpe | Drosophila rhino encodes a female-specific chromo-domain protein that affects chromosome structure and egg polarity[END_REF], which was shown to have a causal role on piRNA production [START_REF] Zhang | The HP1 homolog rhino anchors a nuclear complex that suppresses piRNA precursor splicing[END_REF]. Indeed, PIWI loaded with a piRNA has the capacity to enter the nucleus. Such hypothesis is supported by chromatin immunoprecipitation (ChIP) experiments performed on BX2* vs BX2 naive ovaries showing an enrichment of posttranslational methylation of histone H3 (H3K9me3) on the cluster when the locus is paramutated [START_REF] Thomas | Transgenerationally inherited piRNAs trigger piRNA biogenesis by changing the chromatin of piRNA clusters and inducing precursor processing[END_REF]. H3K9me3 residues can indeed be targeted by the chromodomain of Rhino, resulting in Rhino-associated protein complex stabilization on the cluster. Alternatively, piRNAs loaded on the PIWI proteins Aubergine and Ago3 can also be transmitted to PGC in embryos where they could stimulate the amplification step of the piRNA biogenesis, which occurs in the nuage, a peri-nuclear diffuse structure surrounding the germline cell nucleus and enriched in PIWI proteins. In both models, paramutation would be induced by a diffusible cytoplasmic product, the piRNAs.

3-Worm paramutation-like conversions

Transgenesis in worms showed early on that not all single copy transgenes were expressed in the germline and that failure of expression appeared to be linked to the length of foreign DNA present in the transgene construct. Repression of the transgene occurred at both the post-transcriptional and transcriptional levels and is associated with H3K9me3 enrichment present on the silenced transgene [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF]. The cross of lines carrying expressed copies with lines carrying repressed ones surprisingly showed that, in a number of cases, the repressed state dominates in the progeny (Figure 2). For example, the cross of hermaphrodites carrying a gfp::csr-1 repressed transgene with males carrying an expressed gfp::csr-1 transgene produces progeny in which both transgenes are repressed in the germline (Figure 2-A) [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF]. The analysis of succeeding generations further revealed that the repressed state of both transgenes is maintained. The same dominance and conversion process was observed between repressed and active gfp::csr-1 transgenes located on different chromosomes (Figure 2-B). Furthermore, the newly repressed transgene conserved its properties over generations, in absence of the initial silencer transgene. Such conversion phenomenon can be mediated by passage of the silenced copy through both parents but it is less efficient via male transmission [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF].

In these experiments, the initial repressed transgene behaved as a paramutagenic locus and the newly repressed transgene, appearing stable for at least 10 generations in absence of the inducer locus, behaved as a paramutated locus. This silencing conversion was termed RNA-induced epigenetic Silencing (RNAe) [START_REF] Luteijn | Extremely stable Piwi-induced gene silencing in Caenorhabditis elegans[END_REF][START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF]. The repressed loci were termed gfp::csr-1(RNAe) and the active loci gfp::csr-1(+). The capacity of the paramutated locus to be paramutagenic was not tested, but it would probably work since gfp-transgene silencing mediated by gfp dsRNA in presence of a transgene sensitive to RNAe is stable over generations [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF]. Like in Drosophila, pairing between the two interacting loci during RNAe conversion is not likely to be necessary as conversion can occur when the transgenes are located on different chromosomes. This type of conversion was observed with different transgene structures (carrying cdk-1 instead of csr-1 with the gpf sequence).

The presence of an RNAe transgene in the genome does not appear to induce co-suppression of homologous endogenous genes, as tested by western-blot [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF].

Strikingly, not all transgenes undergo RNAe. Indeed, the gfp::wrm-1 and oma-1::gfp not only are resistant to the RNAe transgene-mediated repression but are able to switch some of them into an active state ( [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF], Figure 2 C andD). The activation process, called RNA-induced epigenetic gene activation (RNAa), is only progressive and not as fast as RNAe since several generations of coexistence of the two transgenes in the same genome are necessary to induce full activation of the repressed transgene or to confer it stability in next generations, after out-cross with the wild-type removing the initial active transgene [START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF]. For example, the combination of oma-1::gfp (RNAa)

with gfp-cdk-1(RNAe) results in activation of the latter transgene. Segregation after only one generation of contact between the two transgenes results in immediate reversion of the gfp-cdk-1 transgene to the repressed state. Segregation after ten generations of contact between the two transgenes provides stability for one generation to gfp-cdk-1, and 30 generations of contact provide a stability to the activated transgene for 8-10 generations after segregation away from the activating locus (Figure 2 C and D). Some transgenes, however are resistant to RNAa since a gfp::csr-1 (RNAe) transgene is insensitive to the presence of the oma-1::gfp transgene: in that case, the two transgenes keep their own properties in a double transgenic line and in succeeding generations after cross to wild-type [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF][START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF].

More recently, a case of "cascade" RNAe paramutation was described in Caenorhabditis elegans using a different combination of transgenes [START_REF] Sapetschnig | Tertiary siRNAs mediate paramutation in C. elegans[END_REF]. The first step involves on the one hand a "piRNA sensor" transgene carrying a gfp gene and a piRNA-targeted locus (21UR-1), and on the other hand an "operon" transgene which expresses mCherry and gfp mRNAs from a single primary transcript (Figure 3). mCherry is located upstream of gfp within this operon. The strain carrying the piRNA sensor transgene exhibits no gfp expression in the germline due to the targeting of the 21UR-1 sequence by piRNAs [START_REF] Bagijn | Function, targets, and evolution of Caenorhabditis elegans piRNAs[END_REF][START_REF] Ashe | piRNAs can trigger a multigenerational epigenetic memory in the germline of C. elegans[END_REF]. In contrast, the strain carrying the operon transgene shows strong gfp and mCherry expression [START_REF] Sapetschnig | Tertiary siRNAs mediate paramutation in C. elegans[END_REF]. Combining the piRNA sensor transgene with the operon transgene by crossing produces progeny in which the operon transgene is repressed for both gfp and mCherry expression in the germline. Therefore, the operon transgene is trans-silenced by the piRNA sensor transgene, and silencing propagates from the gfp sequence to the mCherry sequence in the operon.

Out-crossing this progeny with worms devoid of any transgene generates lines carrying only the operon transgene that remains completely repressed over at least 12 generations ("operon (OFF)" lines). In a second step, crossing the operon (OFF) worms with worms carrying an active mcherry::H2A transgene, but no gfp sequence, produces progeny in which mCherry expression of both the operon and mcherry::H2A transgenes is completely repressed. Further, removal of the operon silencer transgene by out-crossing results in lines carrying the targeted mcherry::H2A transgene alone, and this remains repressed at least for 10 generations. Thus, the operon (OFF) transgene, which was paramutated by the piRNA sensor transgene, is stably repressed over generations and appears strongly paramutagenic since it can transfer inheritable silencing capacities to the mcherry::H2A transgene. Finally, this repressed mcherry::H2A transgene, which is a "second-order" paramutated locus, was also shown to be able to trans-inactivate other transgenes carrying the mcherry sequence. This indicates that the epigenetic conversion process can be recurrent. The conversion processes described here exhibit the properties of a bona fide paramutation. In these experiments, it was shown that paramutation can be performed by both hermaphrodite and paternal transmission of the paramutagenic locus but the effect appears stronger via hermaphrodite inheritance (Nic Lehrbach and Eric Miska, personal communication). Further, crossing hermaphrodites carrying an operon (OFF) transgene at the heterozygous state with males carrying a mcherry::H2A transgene generated individuals which did not inherit the operon (OFF) transgene but carried a repressed mcherry::H2A transgene with properties stably transmitted over generations [START_REF] Sapetschnig | Tertiary siRNAs mediate paramutation in C. elegans[END_REF]. This indicates that, like in fly, paramutation can be mediated by cytoplasmic components without inheritance of the paramutagenic locus itself, excluding again of the need for pairing between the loci in the process. Importantly, this combination of structurally different transgenes shows that silencing propagation within a transgene, from the targeted transgene part (gfp) to the distal sequence (mCherry), is accompanied by production of paramutagenic signal from the distal sequence. Indeed, operon (OFF) worms produce siRNAs homologous to the mCherry sequence which are called tertiary siRNAs [START_REF] Sapetschnig | Tertiary siRNAs mediate paramutation in C. elegans[END_REF], by contrast to siRNAs produced by sequences located near the piRNA target site which are called secondary siRNAs [START_REF] Bagijn | Function, targets, and evolution of Caenorhabditis elegans piRNAs[END_REF]. These tertiary siRNAs can transfer heritable silencing capacities in trans and are thus paramutagenic.

Altogether, the different studies show that complete paramutation exists in worms and transgenes can occur in three different epigenetic states [START_REF] Luteijn | Extremely stable Piwi-induced gene silencing in Caenorhabditis elegans[END_REF][START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF][START_REF] Ashe | piRNAs can trigger a multigenerational epigenetic memory in the germline of C. elegans[END_REF][START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF][START_REF] Sapetschnig | Tertiary siRNAs mediate paramutation in C. elegans[END_REF]: RNAe and RNAa transgenes and neutral transgenes that are expressed, but can be sensitive to the presence of RNAe transgenes [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF][START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF]. However, these neutral alleles by themselves do not have the capacity to modify the expression of other homologous transgenes present in the same genome. What can be the mechanism of RNAe-and RNAa-linked epigenetic conversions? It appears that a complex balance of antagonistic systems determines the properties of a transgene and its capacity to affect expression of other homologous transgenes in trans. The establishment of the RNAe requires the PIWI protein PRG-1, and its maintenance depends on HPL-2, a HP1 ortholog, and several putative histone methyltransferases [START_REF] Luteijn | Extremely stable Piwi-induced gene silencing in Caenorhabditis elegans[END_REF][START_REF] Ashe | piRNAs can trigger a multigenerational epigenetic memory in the germline of C. elegans[END_REF]. In addition, maintenance of the RNAe state requires proteins involved in the WAGO-mediated RNAi pathway such as RED3, MUT7, WAGO-1 or WAGO-9 [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF]. The establishment of RNAa by contrast requires the Argonaute protein CSR-1 [START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF]. A dose effect is observed for CSR-1 since heterozygous individuals show impaired RNAa. CSR-1 engages siRNAs homologous to most of the germline-expressed genes [START_REF] Claycomb | The Argonaute CSR-1 and its 22G-RNA cofactors are required for holocentric chromosome segregation[END_REF][START_REF] Gu | Distinct argonautemediated 22G-RNA pathways direct genome surveillance in the C. elegans germline[END_REF] but CSR-1-interacting small RNAs (22G-RNAs) do not appear to induce silencing [START_REF] Claycomb | The Argonaute CSR-1 and its 22G-RNA cofactors are required for holocentric chromosome segregation[END_REF]. What could be the roles of these antagonistic systems at the genome level? Worms appear to have an opposite strategy to flies. In flies, the piRNA loci represent a repertoire of sequences that have to be repressed and are mostly homologous to mobile elements [START_REF] Brennecke | Discrete small RNA-generating loci as master regulators of transposon activity in Drosophila[END_REF]. Therefore, piRNAs mainly target mobile sequences although they can also target some gene transcripts containing TE fragments [START_REF] Rouget | Maternal mRNA deadenylation and decay by the piRNA pathway in the early Drosophila embryo[END_REF]. By contrast, in worms, the two piRNA loci located on chromosome 4 produce around 15,000 different piRNAs, which can target transcripts despite incomplete homology (up to 4nt out of 21nt) [START_REF] Batista | PRG-1 and 21U-RNAs interact to form the piRNA complex required for fertility in C. elegans[END_REF][START_REF] Bagijn | Function, targets, and evolution of Caenorhabditis elegans piRNAs[END_REF][START_REF] Das | Piwi and piRNAs act upstream of an endogenous siRNA pathway to suppress Tc3 transposon mobility in the Caenorhabditis elegans germline[END_REF][START_REF] Gu | Distinct argonautemediated 22G-RNA pathways direct genome surveillance in the C. elegans germline[END_REF]. Consequently, a very high number of gene transcripts can potentially be targeted by piRNAs, and a protecting system is thus required to ensure gene expression. This system appears to be mediated by the 22G

RNAs loaded on the CSR-1 protein, which might protect homologous transcript from the effect of 21-U PRG-1 RNAs. Antagonist 22G CSR-1 RNAs and 21-U PRG-1 RNAs would be therefore able to exert opposite effects on their common homologous transcript targets. If the effect of PRG-1 dominates, the transcript binds an RdRP that produces double-strand RNAs further targeted by the WAGO-RNAi machinery, leading to production of 22-G WAGO RNAs. These WAGO-RNAs can then induce both PTGS of homologous transcripts and TGS of homologous loci [START_REF] Gu | Distinct argonautemediated 22G-RNA pathways direct genome surveillance in the C. elegans germline[END_REF][START_REF] Buckley | A nuclear Argonaute promotes multigenerational epigenetic inheritance and germline immortality[END_REF]. If the effect of CSR-1 dominates, there is no double-strand RNA production by RdRP and the siRNA machinery is not activated. So, the piRNA machinery is required for the silencing establishment but not for its maintenance over generations, which relies on siRNA activation [START_REF] Luteijn | Extremely stable Piwi-induced gene silencing in Caenorhabditis elegans[END_REF][START_REF] Ashe | piRNAs can trigger a multigenerational epigenetic memory in the germline of C. elegans[END_REF][START_REF] Lee | C. elegans piRNAs mediate the genome-wide surveillance of germline transcripts[END_REF]. Cytoplasmic trans-generational transmission includes information carried in both WAGO interacting RNAs as a memory of silenced targets and CSR-1 interacting RNAs as a memory of targets licensed for expression. The PRG-1 system is involved in the foreign DNA detection step (which was not previously licensed) and the WAGO machinery is required for amplification and maintenance of the information and repression itself.

It appears that maintenance of the properties of epigenetically repressed RNAe or activated RNAa transgenes, each alone in a genome, involves not only cytoplasmic RNA molecules associated with WAGO (silencing) or CSR-1 (activation), but also chromatin marks on the locus deposited via either a WAGO RNAs or potentially a CSR-1 RNA-dependent mechanism for silencing or activation, respectively [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF][START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF][START_REF] Sapetschnig | Tertiary siRNAs mediate paramutation in C. elegans[END_REF][START_REF] Wedeles | Protection of germline gene expression by the C. elegans Argonaute CSR-1[END_REF]. Two opposite loops between small RNAs and chromatin similarly involved in a positive loop. In any case, this system implies that for a gene to be expressed, it is necessary that it produces sufficient quantity of RNA for first, establishing a population of CSR-1 RNAs to counteract silencing machinery and second, for being translated.

Neutral transgenes alone in a genome would escape RNAe silencing and could be thus expressed.

However, in the presence of strong RNAe, neutral alleles would be switched towards RNAe at the cytoplasmic and /or chromatin levels. When the RNAe-inducing allele is removed by crosses to wild-type, repression loops now associated to the repressed targeted transgenes could be maintained by themselves over at least some generations. It appears that the RNAe-induced conversion is relatively stable. This is probably due to the strength of the 22G-RNAs WAGO production based on RdRP activity. Finally, "adoption" of foreign sequences can be observed linked to cis-spreading of CSR-1 on a transgene which contains adjacent endogenous and foreign sequences [START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF].

Conclusion

Flies and worms can undergo epigenetic conversions showing paramutation-like properties. In fly, the conversion is unidirectional, corresponding to the transfer of a homology-dependent silencing capacity from one locus to the next, which reflects the capacity to produce piRNAs [START_REF] De Vanssay | Paramutation in Drosophila linked to emergence of a piRNA-producing locus[END_REF][START_REF] De Vanssay | piRNAs and epigenetic conversion in Drosophila[END_REF]. The conversion acts on the piRNA producing locus itself. It includes a change on the locus since the chromatin of the new piRNA-producing locus is associated with enriched H3K9 histone methylation marks [START_REF] Thomas | Transgenerationally inherited piRNAs trigger piRNA biogenesis by changing the chromatin of piRNA clusters and inducing precursor processing[END_REF]. In worm, the conversion can occur in two directions, probably reflecting the competition of two antagonist regulation loops whose strength can vary. Apparently, it does not involve the piRNA loci themselves but rather their targeted sequences. It appears, however, that the change toward the repressed state is more stable over generations than the opposite change. This RNAe conversion presents the stability of a true paramutation and can be recurrent. By contrast, the RNAa process appears not only less stable but the activated alleles are also not able to trigger further RNAa conversion [START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF]. So RNAa conversion does not exhibit all the properties of a complete paramutation. In fly, conversion is mediated only via maternal cytoplasmic transmission, in contrast to worms in which RNAe conversion can be mediated by transmission from both parents, possibly because of different proportions of paternal cytoplasmic transmission in the two species. A key point for future work will be to determine if some antagonistic forces may also exist in fly to counteract the action of piRNAs. Furthermore, in both species it will be essential to characterize the developmental events involved in the transgenerational transmission of these conversion processes. paternally inherited the BX2 locus and maternally inherited a BX2* cytoplasm -but not the locus -, which produce abundant ovarian piRNAs and induce strong silencing. BX2** lines (second order paramutation) stably maintain these properties over generations. This recurrent conversion process has been repeated five times "en cascade", generating BX2* 5 lines showing a complete transsilencing capacity [START_REF] De Vanssay | Paramutation in Drosophila linked to emergence of a piRNA-producing locus[END_REF]. Thus, this epigenetic conversion process presents functional properties of paramutation. This process does not require the transmission of the paramutagenic locus but requires cytoplasm inheritance. is immediately re-silenced [START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF]. Out-crossing after ten generations of double transgenic strains allows persistence of the gfp::cdk-1 active state for one generation, but then the effect is lost later.

(D) Propagation of the double transgenic strain for 30 generations allows maintaining of a gfp::cdk-1 fully active state for 8 generations after out-crossing, before transgene activation decreases. By contrast to RNAe, which can be stably established in one generation, RNAa needs a longer exposure and only results in a transitory active state. (Adapted from [START_REF] Shirayama | piRNAs initiate an epigenetic memory of nonself RNA in the C. elegans germline[END_REF][START_REF] Seth | The C. elegans CSR-1 argonaute pathway counteracts epigenetic silencing to promote germline gene expression[END_REF]).

  could exist for RNAe and RNAa transgenes, and the maintenance of the loop from one generation to the other would be established by cytoplasmic inheritance of WAGO RNAs for RNAe and CSR-1 RNAs for RNAa. When the two types of transgenes are present in the same genome, different small RNAs might compete both at the cytoplasmic and nuclear level. In the cytoplasm, a given transcript could be confronted with 21-U PRG-1 RNAs (and 22G WAGO RNAs) in one hand and with antagonist CSR-1 RNAs on the other hand. For RNAe conversion process, a strong RNAe transgene would generate a high quantity of 22G WAGO RNAs, which could potentially counteract a previously established presence of CSR-1 RNAs. By contrast, for an RNAa conversion process, a strong RNAa allele would generate a high quantity of CSR-1 RNAs that could counteract the effects of previously established RNAe alleles. In the nucleus, the 22G RNAs brought by RNAe or RNAa alleles could displace chromatin tags on the antagonist transgenes. For example, 22G WAGO RNAs could potentially trigger removal of CSR-1 from the chromatin of an RNAa allele and thus break a positive loop in which CSR-1 present on the locus favors the production of 22G CSR-1 RNAs. Reciprocally, 22G CSR-1 RNAs could displace chromatin tags on RNAe alleles

Acknowledgements:

  SR thanks Doug Dorer, Steve Henikoff, and the Bloomington Stock Center for providing stocks, and flybase.org for providing databases. SR thanks Nic Lehrbach and Eric Miska for personal communication. SR thanks Catherine Hermant for Figure 1, Safia Deddouche Grass, Laure Teysset, Antoine Boivin, Amna Asif-Laidin, Neel Randsholt and an anonymous reader for their help in preparing the manuscript. SR thanks all the authors of the de Vanssay et al. 2012 paper for their investigation of fly paramutation and for helpful discussions. SR especially thanks Valérie Delmarre for technical help and unpublished results. This work was supported by fellowships from the Ministère de l'Enseignement Supérieur et de la Recherche (ED515), by grants from the Association de la Recherche contre le Cancer (Fondation ARC, SFI 20121205921, PJA 20131200470), from the Fondation pour la Recherche Médicale (FRM -DEP20131128532) and from the Association Nationale de la Recherche (ANR, project "plastisipi").

Figure 1 :

 1 Figure 1: Paramutation linked to piRNAs in fly. A tandemly repeated P-lacZ-white transgenic locus, called T-1, which produces abundant piRNAs in ovaries and induces complete silencing of a homologous transgenic target in the germline was used as a paramutagenic locus. A similar transgenic locus, called BX2, located at the same genomic site, and stably devoid of piRNA production and trans-silencing capacities was used as paramutable locus. The mating scheme is shown with the number of generations indicated on the left. CyRoi and Cy are balancer chromosomes carrying distinct dominant phenotypic makers. Orange color indicates cytoplasm inheritance. Histograms show the length distributions (19-29 nt) of ovarian small RNAs matching P-lacZ-white. Positive (red) and negative (blue) bars correspond to sense and antisense reads, respectively. Trans-silencing capacities were measured by crossing tested females with males carrying a single P-lacZ transgene expressed in the female germline and by counting the percentage of egg chambers showing target transgene repression (n = total number of egg chambers counted). G 1 females having paternally inherited the BX2 locus and having maternally inherited a T-1 cytoplasm, but not the T-1 locus itself were generated. Lines established from G 1 individuals, called BX2* (first order paramutation), were further analyzed. BX2* females produce abundant transgene-homologous piRNAs and induce a complete trans-silencing in the germline as tested in G 2 and G 83 . Finally, females from BX2* lines (at G 42 ) were crossed with males of a BX2 line quiescent for piRNA production and trans-silencing. This generated BX2** females, having

Figure 2 :

 2 Figure 2: Reciprocal epigenetic conversions in worms. Single copies of the gfp::csr-1 transgene can exhibit gfp expression or repression depending on PRG-1-associated piRNAs targeting. At the same genomic location, the two states can exist and appear stable over several generations. RNAe (RNA-induced epigenetic silencing): (A) The cross of hermaphrodites worms carrying a gfp::csr-1(RNAe) repressed transgene (grey gfp box on the transgene map) with males carrying an expressed gfp::csr-1(+) transgene (green gfp box), both located on chromosome 2 (LGII), results in a progeny in which the two transgenes are repressed in the germline. Propagation of the derived lines shows that this repressed state is stable over generations at least until G 10 . (B) Similar silencing conversion can occur between transgenes located on different chromosomes. The cross of hermaphrodites carrying a gfp::csr-1(RNAe) repressed transgene located on chromosome 4 (LGIV) with males carrying an expressed gfp::csr-1(+) transgene located on chromosome 2, also results in progeny in which the two transgenes are repressed. The repressed state of the transgene located on chromosome 2 is maintained in successive generations after the removal of the silencer transgene located on chromosome 4 by crosses. Such RNAe conversion can occur during inheritance from both parents. RNAa (RNAinduced epigenetic gene activation): (C) Some active transgenes appear to be resistant to the effect of RNAe transgenes and show opposite properties. The cross of hermaphrodites carrying an active oma1::gfp(RNAa) transgene (chromosome 4) with males carrying a repressed gfp::cdk-1(RNAe) transgene (chromosome 2) results in progeny showing gfp expression of both transgenes. If the two transgenes are separated after one generation by out-crossing to wild-type, the gfp::cdk-1 transgene

Figure 3 :

 3 Figure 3: Cascade of RNAe paramutations in worms.The piRNA sensor transgene is targeted by an endogenous piRNA (21UR-1) specific for the "21U" site and shows no gfp expression. This repression correlates with production of siRNAs by the gfp sequence. Crossing worms carrying a piRNA sensor repressed transgene with worms carrying an operon expressed transgene generates individuals in which the operon transgene is repressed both gfp and mCherry expression in the germline. This repression correlates with cis-propagation of the capacity to produce siRNAs from the gfp until the mCherry sequence. This "operon (OFF)" transgene remains repressed in the absence of piRNA sensor transgene after outcrossing. Crossing worms carrying an operon (OFF) transgene with worms carrying a mcherry::H2A expressed transgene produces individuals in which both mCherry transgenes are repressed. As before, the mcherry::H2A transgene remains repressed in the absence of operon (OFF) transgene after outcrossing. Finally, crossing individuals carrying a repressed mcherry::H2A (OFF) transgene with individuals carrying a mcherry expressed transgene produces progeny in which both transgenes exhibit mcherry repression. The operon (OFF) transgene is thus paramutated by the piRNA sensor transgene (first order paramutation) and can paramutate a mcherry transgene (second order paramutation). (Adapted from[START_REF] Sapetschnig | Tertiary siRNAs mediate paramutation in C. elegans[END_REF]).

Figures 1- 3

 3 Figures 1-3

Ronsseray -Figure 2 Page 21 of 21 A

 221 : 70-30% GFP+ (n>40) gfp::cdk-1(RNAe) oma-1::gfp(RNAa) F3: 0% GFP+ gfp::cdk-1(RNAe) oma-1::gfp(RNAa) gfp::csr-1(+) gfp::csr-1(RNAe) gfp::csr-1(+) gfp::csr-1(RNAe)

Param-non-verteb

Param-non-verteb