Hugues Mounier
email: hugues.mounier@l2s.centralesupelec.fr

Silviu-Iulian Niculescu
email: silviu.niculescu@l2s.centralesupelec.fr

Arben Cela
email: a.cela@esiee.fr

Marcel Stefan Geamanu
email: marcel.geamanu-renexter@renault.com

Flatness based longitudinal vehicle control with embedded torque constraint

Keywords: flatness based control, automotive control, input constraints

This paper aims at establishing a simple yet efficient solution to the problem of trajectory tracking with input constraint of a nonlinear longitudinal vehicle model. We make use of differential flatness, by embedding the constraint into the reference trajectory design.

Introduction

The aim of this paper is to come up with simple yet efficient control techniques for vehicle longitudinal speed control with constraint on its torque. More precisely, we consider a longitudinal nonlinear model including a simple adherence/friction law (see, e.g. [START_REF] Ellis | Vehicle dynamics[END_REF][START_REF] Gillespie | Fundamentals of Vehicle Dynamics[END_REF][START_REF] Kiencke | Automotive Control Systems: For Engine, Driveline and Vehicle[END_REF][START_REF] Henning Mitschke | Dynamik der Kraftfahrzeuge[END_REF][START_REF] Henning Mitschke | Dynamik der Kraftfahrzeuge[END_REF][START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]). For this model, we consider the problem of tracking a reference speed trajectory with constraint on the input torque. Traditional treatment of such a problem include model predictive control [START_REF] Li | Model predictive multi-objective vehicular adaptive cruise control[END_REF] and use of optimisation techniques [START_REF] Hsu | An optimal wheel torque distribution controller for automated vehicle trajectory following[END_REF][START_REF] Hsu | A constrained wheel torque controller for lane following system using control distribution[END_REF]) Some other works use adaptive anti-windup techniques [START_REF] Nazli | Cruise control with adaptation and wheel torque constraints for improved fuel economy[END_REF][START_REF] Tarbouriech | Anti-windup design: an overview of some recent advances and open problems[END_REF], saturated inputs [START_REF] Valmorbida | Design of polynomial control laws for polynomial systems subject to actuator saturation[END_REF] to name a few.

The constraint is embedded in the flat output trajectory design. Thus, the closed loop tracking controller naturally satisfies the required constraint, without the recourse to costly optimisation procedure.

A key advantage of the advocated technique is that the physical meaning is kept throughout the whole process, a feature often lost in MPC or other optimisation based techniques.

More precisely, a dynamical system with m inputs is differentially flat [START_REF] Fliess | Flatness and defect of nonlinear systems: introductory theory and examples[END_REF] if there exists a so-called flat output ω ω ω with m components ω ω ω = (ω 1 , . . . , ω m ) such that: first, these components are functions of the system's variables (endogenous character); second, the ω i s are differentially independent, i.e. they don't satisfy a differential equation involving themselves only (independent character); third, all the system's variables can be expressed as nonlinear functions of the ω i s and of a finite number of their derivatives (parametrisation property).

Thus, when a system variable is subject to a constraint, the latter is directly translated into a flat output constraint, thanks to the parametrisation property. The tracking problem with constraints is thus elaborated in two steps: first design a flat output reference trajectory ω ω ω r satisfying all the required constraints; second, design a closed loop feedback control law ensuring the tracking of ω ω ω r with stability. The constraints satisfaction is ensured by design, since it is embedded in the reference trajectory elaboration process.

The involved constraints can be given on any system variable, since all the system is parametrised by the flat output. The constraint is enforced on the reference variables, and is ensured practically on the actual variables since the tracking error is meant to tend to zero, in general exponentially.

Ensuring the constraints on the flat output is simplified by specialising the flat output reference trajectory to specific classes of functions with convenient properties, such as closedness wrt differentiation or being solution of a differential equation.

To the best of the author's knowledge, almost all the current work on differentially flat systems with constraints is managed through optimisation procedures [START_REF] Chamseddine | Active fault-tolerant control system design with trajectory re-planning against actuator faults and saturation: Application to a quadrotor unmanned aerial vehicle[END_REF][START_REF] Faiz | Trajectory planning of differentially flat systems with dynamics and inequalities[END_REF][START_REF] Flores | Trajectory generation for differentially flat systems via NURBS basis functions with obstacle avoidance[END_REF][START_REF] Keck | SAMMY -an algorithm for efficient computation of a smooth path for reference trajectory generation[END_REF][START_REF] Petit | Optimal drive of electric vehicles using an inversion-based trajectory generation approach[END_REF][START_REF] Ross | Pseudospectral methods for optimal motion planning of differentially flat systems[END_REF][START_REF] Tsuei | Trajectory generation for constrained differentially flat systems with time and frequency domain objectives[END_REF][START_REF] Walambe | Optimal trajectory generation for car-type mobile robot using spline interpolation[END_REF]. In [START_REF] Löwis | Real-time trajectory generation for flat systems with constraints[END_REF], no optimisation technique is used, but the flat output trajectory is not known on advance; thus, the trajectory is built step by step, by concatenating pieces The only work partially related to our approach is [START_REF] Ruppel | Analytical multi-point trajectory generation for differentially flat systems with output constraints[END_REF], where the constraints appear solely on derivatives of the flat output, which is specialised to piecewise polynomial functions. Preliminary results related to the present one have been presented for linear systems with delays in [START_REF] Bekcheva | Control of differentially flat linear delay systems with constraints[END_REF], and for an Euler Bernoulli beam in [START_REF] Bekcheva | Euler-bernoulli beam flatness based control with constraints[END_REF]. Other works related to the present theme include differential flatness based techniques for longitudinal and lateral vehicle dynamics [START_REF] Menhour | Coupled nonlinear vehicle control: Flatness-based setting with algebraic estimation techniques[END_REF].

The paper is organised as follows. In the next Section, the model is recalled. In Section 3, the flatness of the model is established, and a closed loop feedback tracking controller is given in Section 4. The torque constraint management is dealt with in Section 5.

Longitudinal model

The equations of the vehicle dynamics can be written as follows (see, e.g. [START_REF] Ellis | Vehicle dynamics[END_REF][START_REF] Gillespie | Fundamentals of Vehicle Dynamics[END_REF][START_REF] Kiencke | Automotive Control Systems: For Engine, Driveline and Vehicle[END_REF][START_REF] Henning Mitschke | Dynamik der Kraftfahrzeuge[END_REF][START_REF] Henning Mitschke | Dynamik der Kraftfahrzeuge[END_REF][START_REF] Rajamani | Vehicle Dynamics and Control[END_REF]) :

m Vx = F x (2.1a) I w ω = RT -rF x -F o (2.1b)
with the following slip ratio and forces :

F x = µ x (λ )F z , λ = V x -rω max(V x , rω)
(2.2a)

F z = mg (2.2b) F o = -F a -F s (2.2c) R x = mgC r , F a = ρ C a AV 2 x 2 , F s = mg sin α (2.2d)
The notations for the model (2.1a)-(2.1b) are: V x is the longitudinal speed of the vehicle, m its mass, F x the longitudinal tire force, I w inertia moment of the wheel, ω angular wheel speed, R the damping coefficient of the drive-line, T the engine torque, r the effective tire radius, F o the other forces exterted on the car body. The expressions of the forces are given in Equations (2.2a)-(2.2d), with the following notations: µ x is the adherence function, F z the normal force on the tire, λ the slip ratio, g the gravity constant, R x the rolling resistance force, F a the longitudinal aerodynamic drag force, ρ is the air volumic mass, A is

3 of 15 -1 -0.5 0 0.5 1 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 µ (adim) λ (adim) FIG. 1: Adherence function µ(λ ).
frontal area of the vehicle, C a is the drag coefficient, F s the force due to the road slope, and α the road slope angle.

A possible model for µ x (λ ) introduced by Kiencke and Daiß and depicted in Figure 1, is given by the function:

µ x (λ ) = aλ b + c|λ | + λ 2 (2.3)
One easily obtains that the maximum µ * of such a curve occurs at λ * with:

λ * = √ b, µ * = a c + 2 √ b
Conversely, the constants a, b, c can be expressed as functions of µ * λ * and µ 1 : 1) is the value of the function µ at λ = 1 (i.e. at wheel lock). Note that a and b are strictly positive constants. REMARK 2.1 Another, quite popular, model is the Pacejka one [START_REF] Bakker | Tyre modelling for use in vehicle dynamics studies[END_REF][START_REF] Pacejka | Tyre and Vehicle Dynamics[END_REF]. We have not used the latter, for simplicity reasons, but a similar, although more complex, analysis could be made with Pacejka's model.

a = µ * µ 1 (1 -λ * ) 2 µ * -µ 1 , b = λ * 2 , c = µ 1 (1 + λ * 2 ) -2µ * λ * µ * -µ 1 where µ 1 = µ(
The measured outputs are traditionally the wheel speed (e.g. through ABS encoders). We shall here suppose that the speed V x of the vehicle's center of gravity is either measured or reconstructed via an observer or an estimator (see, e.g. a previous work of some author of the present paper [START_REF] Villagra | Estimation of longitudinal and lateral vehicle velocities: An algebraic approach[END_REF]).

Differential flatness of the model

The model (2.1) is trivially flat, with flat output V x . Indeed,

Vx = gµ x (λ ) (3.1)
Then,

λ = µ -1 Vx g (3.2)
Now one has to distinguish two acceleration and deceleration cases (implied by the form of λ in (2.2a)):

• Acceleration case, where rω V x λ = V x rω -1 = µ -1 Vx g Hence ω = V x r 1 + µ -1 Vx g (3.3) And thus Vx = gµ x (λ ) λ = gµ x (λ ) 1 rω 2 ω Vx -ωV x • Deceleration case, where rω V x λ = 1 - rω V x = µ -1 Vx g Hence ω = V x r 1 -µ -1 Vx g (3.4)
And thus

Vx = gµ x (λ ) λ = gµ x (λ ) r V 2 x ω Vx -ωV x
Thus, one has the following dynamics in V x :

Vx = gµ x max rω 2 , V 2 x r ω Vx + V x I w mr Vx + F o + RT (3.5)
and the control input T is then obtained as

T = 1 R mr + I w ω V x Vx + F o - I w max r 2 ω 2 ,V 2 x grV x µ x Vx (3.6)
5 of 15 REMARK 3.1 The reader could have the (quite normal) feeling that the laws (3.3) and (3.4) yield a discontinuity when the vehicle switches from acceleration to deceleration (leading to a chattering like phenomenon). First note that this can only occur at extremely low slip, i.e. when rω -V x 1, where the µ() curve is in the linear zone (and thus the µ -1 also); thus

µ -1 Vx g ≈ β Vx g
Moreover, when the vehicle switches from acceleration to deceleration (or vice-versa), one has | Vx | 1. Thus, in (3.3), one has

1 1 + µ -1 Vx g = 1 -µ -1 Vx g + o Vx g 2
Thus, the expression of ω is

ω = V x r 1 + µ -1 Vx g = V x r 1 -µ -1 Vx g + o Vx g 2 whose term in o((V x /g) 2
) is exactly the one of (3.4). Thus, in case of acceleration-deceleration switching, the expression of ω is continuous and differentiable.

Trajectory tracking

Trajectory tracking control law

Recalling the flat output dynamics (3.5), and setting the right member equal to a new input v, one obtains the linearizing feedback

ω Vx + V x I w mr Vx + F o + RT = max r 2 ω 2 ,V 2 x grµ x v
tranforming the flat output dynamics (3.5) to

Vx = v Setting the new input v to v = Vxr -K p e V x -K d ėV x , e V x = V x -V xr
with K p , K d > 0 yield an exponentially stable error dynamics. The original input is then obtained as

T = 1 R mr + I w ω V x Vx + F o - I w max r 2 ω 2 ,V 2 x grV x µ x v (4.1) v = Vxr -K p e V x -K d ėV x (4.2)
REMARK 4.1 Note that, in (4.2), one could have used equally a second order sliding mode or a model free control law, for instance, in order to gain in robustness.

T r = 1 R mr + I w ω r V xr Vxr + F o - I w max r 2 ω 2 r ,V 2 xr grV x µ xr Vxr (4.3)
Thus, the Equations (4.1)-( 4.2) can be rewritten as

T = T r - 1 R (K p e V x + K d ėV x ) (4.4)
We thus see that, if the error e V x and its derivative ėV x remain small (which is the case when the tacking performance is good), the closed loop torque T remains close to the open loop one T r .

4.2 Trajectory tracking scenario 4.2.1 Trajectory form. We shall choose a trajectory V xr (t) of the following form is met, where

V xr (t) = Ω p p p u ,p p p d (t) = Θ p p p u (t) -Θ p p p d (t) (4.5) Θ p p p * * * (t) = V h * -V l * 2(t e * -t b * ) logCh σ * (t -t b * ) + logCh -σ * (t -t e * ) + V h * -V l * 2 (4.6) logCh σ (t) = 1 σ log cosh(
max λ ∈[-1,1] (µ x (λ )) = µ x (λ * ) = µ *
is given by (see Eq. (2.3) and below)

µ * = a c + 2 √ b , with λ * = √ b
We shall consider the following

max t∈R Vxr (t) = g(µ * -ε µ x ) gµ M (4.8)
where ε µ x is such that ε µ x /µ * 1. This corresponds to

λ M = µ -1 (µ M ) = λ * -ε λ (4.9)
where ε λ is such that ε λ /λ * 1.

Trajectory tracking.

The trajectory tracking of V xr = Ω p p p u ,p p p d is depicted in Figures 4 and5.

The chosen parameters are the following: initial conditions V x0 = 5m/s, ω 0 = 16.67rad/s, starting speed V lu = V ld = 5m/s, reached speed V hu = V hd = 15m/s. We see on Fig. 4 and 5 that the trajectory tracking is achieved with a very good precision, since the maximum error V x -V xr in Fig. 5 is 2.055.10 -5 . The slip ratio λ and the adherence function µ(λ ) are plotted in Figures 6 and7. Remark that this slip ratio λ remains very small (the maximum of λ is 4.613.10 -4 ). The parameters of the function µ(λ ) are: a = 3.661, b = 0.022, c = 5.153.

Torque constraint management

Since the constraints will be expressed in terms of the flat output V x and its derivatives, we have to compute analytically the first derivatives of V x .

Trajectory first derivatives

The derivatives of Ω are the following:

Vxr = Ω p p p u ,p p p d (t) = V hu -V lu 2(t eu -t bu ) tanh σ u (t -t bu ) + tanh -σ u (t -t eu ) - V hd -V ld 2(t ed -t bd ) tanh σ d (t -t bd ) + tanh -σ d (t -t ed ) (5.1) Vxr = Ω p p p u ,p p p d (t) = σ u (V hu -V lu ) 2(t eu -t bu ) tanh 2 -σ u (t -t eu ) -tanh 2 σ u (t -t bu ) - σ d (V hd -V ld ) 2(t ed -t bd ) tanh 2 σ d (t -t ed ) -tanh 2 -σ d (t -t bd ) (5.2)
For the example depicted in Figure 2, we get the derivatives in Figures 10 and11. The maximum and minimum of Ω p p p u ,p p p d and Ω p p p u ,p p p d are max( Ω p p p u ,p p p d (t We then set

)) = V hu -V lu 2(t eu -t bu ) , min( Ω p p p u ,p p p d (t)) = - V hd -V ld 2(t ed -t bd ) (5.3) max( Ω p p p u ,p p p d (t)) = max σ u (V hu -V lu ) 2(t eu -t bu ) , σ d (V hd -V ld ) 2(t ed -t bd ) (5.4) min( Ω p p p u ,p p p d (t)) = -max σ u (V hu -V lu ) 2(t eu -t bu ) , σ d (V hd -V ld ) 2(t ed -t bd ) (5.5)
∆ Vu = V hu -V lu , ∆ Vd = V hd -V ld , ∆ tu = t eu -t bu , ∆ td = t ed -t bd Vxm = - ∆ Vd ∆ td , VxM = ∆ Vu ∆ tu , Vxm = -max σ u ∆ Vu ∆ tu , σ d ∆ Vd ∆ td , VxM = -V xm

Torque expression and simple bounds

We shall give in this Subsection various bounds, postponing a discussion about them to Subsection 5.3, p. 12.

5.2.1

Torque expression amenable to be bounded. Recall the expression obtained for the trajectory tracking feedback law in Eq. (4.1):

T = 1 R mr + I w ω V x Vx + F o - I w max r 2 ω 2 ,V 2 x grV x µ x
Vx Then, we have:

• In the acceleration case, where rω V x , λ 0

ω V x = 1 r(1 + λ ) • In the deceleration case, where rω V x , λ 0 ω V x = 1 -λ r
Thus, the expression for the torque is

• In the acceleration case

T = 1 R mr + I w r(1 + λ ) Vx + F o + I w grµ x (1 + λ ) 2 V x Vx • In the deceleration case T = 1 R mr + I w (1 -λ ) r Vx + F o - I w grµ x V x Vx
5.2.2 Generic bound. We have the following bounds for |T |:

• In the acceleration case

|T | 1 R mr + I w r(1 + λ ) Vx + |F o | + I w gr|µ x |(1 + λ ) 2 V x | Vx |
(5.6)

• In the deceleration case

|T | 1 R mr + I w (1 -λ ) r | Vx | + |F o | + I w grµ x V x | Vx | (5.7) 5.2.3 A simplistic bound.
A simplistic bound is given by considering minimum (in denominators) and maximum (in numerators) values for the various expressions in the bounding formulas (5.6)-(5.7):

• In the acceleration case

|T | 1 R mr + I w r(1 + λ m ) VxM + I w gr|µ xm |(1 + λ m ) 2 V xM | VxM | (5.8) • In the deceleration case |T | 1 R mr + I w (1 -λ m ) r | VxM | + I w grµ xm V xM | VxM | (5.9)
with the following notations (see, in particular, Eq. (4.9))

VxM = max ∆ Vu ∆ tu , ∆ Vd ∆ td , VxM = max σ u ∆ Vu ∆ tu , σ d ∆ Vd ∆ td (5.10) λ m = -λ M = µ -1 (µ M ) = -λ * + ε λ , µ m = µ (λ * -ε µ ) (5.11)
5.2.4 A simple but realistic bound. We shall then consider the following more realistic bounding function:

• In the acceleration case

|T | mr R + I w rR(1 + λ m ) Vx + max I w V xr | Vxr | grR|µ xr |(1 + λ r ) 2 = ξ aM Vx + ζ aM
(5.12) 5.12)-(5.13) yields a maximum of 1.962N which is a much better bound than the previous one, wrt the real maximum of 1.948N.

REMARK 5.1 Note that the bounding functions (5.12)-(5.13) are valid for any type of reference trajectory, and not only the one given in (4.5), p. 6.

Recall the form of the bounds given in (5.3)

Vxm = - ∆ Vd ∆ td , VxM = ∆ Vu ∆ tu ∆ Vu = V hu -V lu , ∆ Vd = V hd -V ld ,
∆ tu = t eut bu , ∆ td = t edt bd and suppose ∆ Vu and ∆ Vd being given by practical considerations (e.g. speed limits). From the bounds obtained in (5.12)-(5.13), we then have In Figure 12, we have the bounds (5.12)-(5.13) in dashed line (ξ aM Vx + ζ aM and ξ dM Vx + ζ dM ) and the torque T in solid line, and in Figure 13 is depicted the error between the previous two. Note that the maximum error is 1.398.10 -2 , which is 0.18% of T r 's maximum. FIG. 13: Error between T and the bounds (5.12)-(5.13).

Conclusion

We have elaborated a simple yet efficient scheme for tracking a reference speed of a longitudinal vehicle model with torque constraint. The flatness character of the model enabled to embed the constraint fulfilment in the trajectory design. We considered a special class of functions for the class output, namely combinations of log(cosh(t)) type functions.

More general classes of functions will be considered in the future, together with some other types of constraints.

4. 1 . 1

 11 Open and closed loop tracking. Let V xr a reference trajectory for the flat output V x . Denoting by T r the following open loop control law, one has by direct substitution from (3.6):

FIG. 4 :FIG. 5 :FIG. 7 :

 457 FIG.4: Speed trajectory tracking; in blue V x and in red V xr , standard trajectory.

FIG. 9 :

 9 FIG. 9: Control error T -T r , standard trajectory.

FIG. 10 :

 10 FIG. 10:The first derivative Vxr = Ω p p p u ,p p p d (acceleration).

FIG. 11 :

 11 FIG. 11:The second derivative Vxr = Ω p p p u ,p p p d (jerk).

  FIG. 12: Bounds (5.12)-(5.13) on T .

  Since the µ x curve is imposed by the tyre/ground physics, we should ensure that Vx does not exceed the maximum (resp. minimum) of gµ x . In other words, the chosen trajectory will be such that the physical constraint

		15						15
		14						14
		13						13
		12						12
	(m/s)	10 11					(m/s)	10 11
	Vxr	9					Θp	9
		8						8
		7						7
		6						6
		5						5
		0	20	40	60	80	100	0	20	40	60	80	100
				time t (s)						time t (s)
	4.2.2 A physical constraint. Using Eq. (2.1a), p. 2, we have
							Vx = gµ x (λ )
						Vxr	g max λ ∈[-1,1] (µ x (λ ))					(4.7)

σt) p p p * ∈ p p p u , p p p d , p p p u = (t bu ,t eu ,V lu ,V hu , σ u ), p p p d = (t bd ,t ed ,V ld ,V hd , σ d )

The forms of Ω p p p u ,p p p d and Θ p p p are depicted in Figures

2 and 3

. The speeds V l * and V h * are the beginning and reached speeds, respectively; t b * and t e * are the beginning and ending times of speed change. The real σ * is a stiffness parameter: the higher σ * , the closer logCh σ * (t) is from |t|. REMARK 4.2 One could have chosen a tanh-like trajectory for V xr . The chosen form (which amounts to a combination of primitives of tanh) is a smooth (in fact entire) approximation of a trajectory yielding a piecewise constant acceleration. The difference t e *t b * is related to the acceleration, while the stiffness σ is related to the jerk. A tanh-like trajectory would furnish only a single design parameter (the stiffness).

The associated trajectory parameters are: σ = 0.5, t bu = 20s, t eu = 35s, t bd = 70s, t ed = 85s. FIG. 2: An example of V xr (t) = Ω p p p u ,p p p d (t) trajectory. FIG. 3: An example of Θ p p p (t) function.

  Simplistic bound. The simplistic bound of Equations (5.8)-(5.9) are far too pessimistic. Indeed, e.g. for the trajectory given in Figure4, p. 8, the above bound in the acceleration case is 9696.828N, when the real maximum on T is 1.948N. It is thus unusable. 5.3.3 A simple but realistic bound. The simple bound given in Equations (

	5.3 Discussion and bounds fulfilment
	5.3.1 Generic bound. The bound given in Equations (5.6)-(5.7) is rather generic, since it contains
	expressions in λ , yielding expressions in V x (see, e.g. Eq. (3.2)). Thus, it cannot be used very simply.
	5.3.2
	• In the deceleration case
	|T |	mr R	+	I w (1 -λ m ) rR	| Vx | + max	I w V xr | Vxr | grRµ xr	= ξ dM Vx + ζ dM	(5.13)

•

  In the acceleration case |T | ξ aM Vx + ζ aM ξ aM VxM + ζ aM = ξ aM ∆ • In the deceleration case |T | ξ dM Vx + ζ dM -ξ dM Vxm + ζ dM = ξ dM ∆ Vd ∆ td + ζ dM (5.15) Then, to ensure some prescribed bound on the the torque |T | T Ma on acceleration, and |T | T Md on deceleration (5.16)it is sufficient to impose the following bounds on ∆ tu , ∆ td :

					Vu ∆ tu	+ ζ aM	(5.14)
	∆ tu >	ξ dM ∆ Vd T Md -ζ dM	,	∆ ta >	ξ aM ∆ Va T Ma -ζ aM


Pierre Bricage
email: pierre.bricage@univ-pau.fr

Education for sustainability: lessons from living systems governance

Keywords: ARMSADA, fractal law, gauge invariance, governance, sustainability

).

Introduction

Complex systems, and particularly alive ones, can be represented and analysed as networks [START_REF] Almaas | Biological impacts and context of network theory[END_REF]. The availability of large-scale datasets that span the diversity of organisms has made possible to elucidate some of the organisational principles [START_REF] Bricage | La survie des organismes vivants[END_REF] and rules [START_REF] Bricage | La nature de la violence dans la nature : déterminismes écologique, physiologique et génétique de l'adaptation aux changements aux différents niveaux d'organisation des systèmes végétaux[END_REF] that govern their function, robustness and evolution [START_REF] Bricage | Systèmes biologiques : le jeu de la croissance et de la survie. Quelles règles ? Quelles décisions ? Quels bilans ? La Décision Systémique : du Biologique au Social[END_REF]. Variation in hundreds of species has been the subject of thousands of papers [START_REF] Eisler | Fluctuation scaling in complex systems: Taylor's law and beyond[END_REF] that evidenced laws of practical importance for designing efficient sampling of agricultural pests and insect vectors of human diseases [START_REF] Kaltz | Bacterial microcosms obey Taylor's law: effects of abiotic and biotic stress and genetics on mean and variance of population density[END_REF]. And log-log plotting may evidence which laws are power laws [START_REF] Eisler | Fluctuation scaling in complex systems: Taylor's law and beyond[END_REF][START_REF] Bricage | évolution créatrice : métamorphoses et phylotagmotaphologie du vivant. L'évolution du vivant a une direction[END_REF] or not [START_REF] Straatsma | Stretched exponential as one of the alternatives for the power law to fit ranked species abundance data[END_REF].

What operational definitions and general paradigms [START_REF] Bricage | La nature de la décision dans la nature ? Systèmes biologiques: production, consommation, croissance et survie. Quelles règles ? Quels degrés d'exigence ? Quels bilans ? La Décision Systémique: du Biologique au Social[END_REF][START_REF] Miller | Complex Adaptive Systems: An Introduction to Computational Models of Social Life[END_REF] can we use to built a useful model of living systems governance? What rules for their organisation [START_REF] Bricage | Pour survivre et se survivre, la vie est d'abord un flux, ergodique, fractal et contingent, vers des macro-états organisés de micro-états, à la suite de brisures de symétrie[END_REF] and survival duration can we evidence [START_REF] Miller | A Crude Look at the Whole: The Science of Complex Systems in Business, Life, and Society[END_REF]?

2 Materials and Methods. A meta-analysis of large-scale datasets.

What operational definition for every living system? A theory of living systems must explain simultaneously the adaptive matter and energy flows [START_REF] Bricage | Mobilisation de la matière et de l'énergie, et croissance, aux différents niveaux d'organisation des systèmes vivants : les principes organisateurs d'émergence des systèmes vivants[END_REF], the control and regulation of behaviour and their changes [START_REF] Bricage | Pigmentation and soluble peroxidase isozyme patterns of leaves of Pedilanthus tithymaloides L. variegatus as a result of daily temperature differences[END_REF], whatever the space [START_REF] Bricage | markers of surrounding and physiological changes, in situ in leaves and in vitro in calli of Pedilanthus tithymaloides L. variegatus: cell compartmentation and polyfunctionality, control of activity by phenols, specific roles[END_REF] and whatever the time [START_REF] Bricage | Chronobiology of the multiple molecular steps and pathways of in situ anthocyanin biosynthesis of Lathyrus macrorhizus Wimm leaves[END_REF].

1) How to define a living system? How to design it as a Whole?

As a Whole, every living system owns 7 functional capacities (figure 1): -the control of matter and energy flows, that eventually allows -the mass growth,the capability to respond to various stimulations, -the ontogeny of an internal organisation, -the capacity of integration into a peculiar ecoexotope of survival, and -the capacity of motion, that mutually eventually allow it survives enough time to get -the capacity of reproduction [START_REF] Bricage | Les Caractéristiques des Organismes Vivants[END_REF]. Structurally, every living system is composed of an endophysiotope (endo: internal, tope: space-time, physio: of functioning) that is integrated into an ecoexotope of survival (exo: external, tope: space-time, eco: of inhabitation). The ecoexotope provides a hosting capacity that allows the survival of the endophysiotope only if it gets a capacity to be hosted in adequacy: figure 2 [START_REF] Bricage | Héritage génétique, héritage épigénétique et héritage environnemental : de la bactérie à l'homme, le transformisme, une systémique du vivant[END_REF]. All these capacities are interrelated and linked together into a functional network (figure 3). All together they are mutually necessary and sufficient to be alive. Whatever the level of organisation of a living system [START_REF] Bricage | Pour survivre et se survivre, la vie est d'abord un flux, ergodique, fractal et contingent, vers des macro-états organisés de micro-états, à la suite de brisures de symétrie[END_REF], it must, sooner or later, along its life cycle, express all these capacities (figure 2b), which define the functionalism of a level of organisation [START_REF] Bricage | The evolutionary shuttle of the living systems[END_REF].

2) The gauge invariance paradigm.

For example, into the genome [START_REF] Bricage | Win-win not a solution. What next[END_REF], at the cell level, we can sort the genes into groups expressing these capacities (figure 1b). A lot of books have been written for each of these capacities and for different levels of organization (figure 1c). As a consequence a bee is not a living system but the swarm of bees is the living system [START_REF] Bricage | Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages ARMSADA. The way, to be resilient and self-sustainable, the living systems are running through[END_REF]. Only the swarm owns the 7 capacities (figure 1a). Indeed an atom is also a living system [START_REF] Bricage | Pour survivre et se survivre, la vie est d'abord un flux, ergodique, fractal et contingent, vers des macro-états organisés de micro-états, à la suite de brisures de symétrie[END_REF]: fusion is mass growth, fission is reproduction. All the 7 capacities are expressed at the atoms level of organization, but at space-time dimensions and at temperatures that are not ours [START_REF] Bricage | intégration et espace-temps des systèmes vivants[END_REF]. Other scales but the same gauge invariance paradigm! Whatever the level of organization of a system, whatever the scale [START_REF] Bricage | markers of surrounding and physiological changes, in situ in leaves and in vitro in calli of Pedilanthus tithymaloides L. variegatus: cell compartmentation and polyfunctionality, control of activity by phenols, specific roles[END_REF], to be alive a system must, as a Whole (figure 2b), sooner or later, express these 7 capacities (figure 2d). They are mutually necessary and sufficient. The gauge invariance paradigm (figure 3a) is the key to define the notion of scale invariant level of organization. The endophysiotopes of our cells (organization level i) are inhabiting our body endophysiotope (adjacent organization level i+1) which is their ecoexotope of survival (figure 4).

3) What is the keystone paradigm for sustainability?

Look at what a lichen is [START_REF] Bricage | La survie des systèmes vivants[END_REF]. A lichen is like a mille-feuille. The body of a fungus is hosting a population of green algal cells. Into the Whole, the lichen endophysiotope, the juxtaposed algal actors are embedded and protected by other actors, the cells of the multi-cellular fungal body. That is a great advantage for the algal cells, they can survive better than if they were free alone outside the lichens. They can escape the outside dangers of the ecoexotope of the lichen. But that is a disadvantage for the fungal partner. It must spend a great part of its matter and energy to allow the survival of the algal population partner. So its growth is reduced. For the Whole, that is a disadvantage [START_REF] Bricage | A new evolutionary paradigm: the Associations for the Mutual Sharing of Advantages and of Disadvantages[END_REF]: a lichen is a slow-growing organism. But it can survive into ecoexotopes where no other living form can. Lichens are living pioneers. That is a great advantage. But, sooner or later, fungal filaments are catching algal cells and they eat them. Now that is a great advantage for the fungal partner and a great disadvantage for the algal one. All that is an advantage for a partner is a disadvantage for the other one and reciprocally. A lichen is an association between partners of different levels of organisation that are fused together in a new whole for the best and for the worst. A symbiosis [START_REF] Margulis | Symbiosis in Cell Evolution[END_REF] is never an association for mutual benefits: advantages and disadvantages are reciprocally shared between local partners and mutually shared with the Whole (figure 5): if benefits they are only for the Whole, the lichen, which is an Association for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages (in brief: an ARMSADA). The same for a green earth newt or a green sea snail which bodies are, like the fungal body of a lichen, hosting a population of green algal cells. ARMSADAs are everywhere [START_REF] Bricage | La semi-autonomie du vivant : pour que l'un survive, il faut d'abord que l'autre survive, et réciproquement[END_REF]. There are never advantages without disadvantages. A win-win situation is not a systemic one [START_REF] Bricage | Win-win not a solution. What next[END_REF]. No living system can be seen outside the ecoexotope of survival it is sharing with other living forms. The partners of the first emergent lichen were ancient free living algal and fungal species that were sharing the same ecoexotope of survival [START_REF] Hom | Niche engineering demonstrates a latent capacity for fungal-algal mutualism[END_REF]. These founding ancestors don't exist anymore. They disappeared but their progenies always exist into the Whole of the current lichens, and only as lichens, never as free entities. But some brother species are already living freely. They have never met and merged to form a lichen. They probably will never. The fungal and the constrained embedded algal endophysiotopes cannot escape from the lichen. They cannot again be free to survive outside the lichen endophysiotope which is their common shared ecoexotope of survival [START_REF] Bricage | Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages ARMSADA. The way, to be resilient and self-sustainable, the living systems are running through[END_REF].

4) The ARMSADA paradigm: what really symbiosis is!

Viruses are eating bacteria [START_REF] Chen | Environmental T4-family bacteriophages evolve to escape abortive infection via multiple routes in a bacterial host employing altruistic suicide through type III toxin-antitoxin systems[END_REF]. Rarely, a virus that invades a bacterium (level i-1) is not able to eat it [START_REF] Erez | Communication between viruses guides lysis-lysogeny decisions[END_REF]. This defective bacteriophage is a predator that is unable to kill its prey. Sooner or later bacteriophage-bacterium interactions can give rise to new systems: when the genome of an invading virus is integrated into the bacterial genome, a new endophysiotope emerges in which the virus is embedded, and eventually juxtaposed to other previously embedded viruses. It is a change of scale for the virus. It is now surviving as long as its host survives too. A new system has emerged that is more than a bacterium and a virus. But this integrated Whole can be broken by outside dangers of the bacterium ecoexotope, because the virus is a constrained inside danger that can be released if the bacterial or cell endophysiotope is damaged by other dangers [START_REF] Bricage | Cancer is a breaking of the cell's ARMSADA through an aggression that results in a lack of non-autonomy[END_REF]. It is a symbiosis state, as in a lichen or mycorrhizae [START_REF] Bonfante | Mechanism underlying beneficial plant-fungus interactions in mycorrhizal symbiosis[END_REF]. 'To survive that is to eat and not to be eaten'. For the new Whole to survive both partners must survive: for the one to survive, the virus or the bacterium, the other one, the bacterium or the virus, must survive first.

A cell (i.e. level: i) is an ARMSADA too. The cell probably emerged through the merging of previous partners, of bacterial and archaeal types, from the adjacent inferior level of organisation of the Monera (level i-1), with the help of a RNA viral partner [START_REF] Bricage | The cell originated through successive outbreaks of networking and homing into Associations for the Reciprocal and Mutual Sharing of Advantages and of Disadvantages, between the partners, with a benefit only for their wholeness[END_REF]. The cell current endogenous membranes system is the result of that merging. And the fossil of the antic virus is the centrosome that is involved in cell division [START_REF] Bricage | Les systèmes agoantagonistes : l'origine endosyncénotique de la cellule. I n L a Gouvernance dans les Systèmes[END_REF]. Because of the cell origin our cells genome is hosting a lot of genomes of bacterial and viral origins (figure 1b). Cancer disease, which is an advantage for the survival of the cancer cells (level i) and a disadvantage for the survival of the organism (level i+1), is the result of the cell ARMSADA breakage [START_REF] Bricage | Cancer is a breaking of the cell's ARMSADA through an aggression that results in a lack of non-autonomy[END_REF]. Apoptosis is another kind of breakage, but which an advantage for the survival of the organism and a disadvantage for the survival of the apoptotic cell. Look at the functioning of a forest [START_REF] Bricage | Appraisement of the defoliator Lepidoptera associations in a hardwood forest[END_REF]. Like a viruses-bacteria system it is also a predators-preys interactions network (figure 5a). For caterpillars to survive that is to eat trees leaves. For trees to survive that is not to be eaten by caterpillars. To survive that is to eat and not to be eaten, but, sooner or later, it is impossible not to be eaten. The density (growth number) and the species diversity of the caterpillars predators are controlled by the density and diversity of the trees preys. An enough variety of trees species, the preys, is requisite for the survival of the Whole, the forest [START_REF] Bricage | Thinking and teaching systemics: bio-systemics in higher education[END_REF]. If not enough preys or too much the ecosystem is endangered. The Whole survival needs a not too much, not too little, but enough (meden agan), species variety. A requisite variety interval is the key. Too much variety can destroy variety. At the ecosystem level (i+2) a forest is also a system of systems [START_REF] Bricage | Approche systémique de l'évolution du vivant[END_REF][START_REF] Bricage | Évaluation des interactions entre les densité et diversité des chenilles de lépidoptères et les diversité et degré de défoliation des feuillus d'un bois. Mesure de la polyphagie et prédiction des pullulations potentielles[END_REF]. Organisms of the bacterial level (i-1), the cell level (i) and the meta-cell level (i+1) are juxtaposed and embedded to make a forest (level i+2) as a Whole and a forest is an ARMSADA too [START_REF] Bricage | Approche systémique de l'évolution du vivant[END_REF].

Whatever the level of organisation we are looking at, each living system is an ecosystem of ecosystems, with embedded and juxtaposed compartmented food networks [START_REF] Bricage | Win-win not a solution. What next[END_REF]. Living systems are systems of systems that are built by embedment and juxtaposition of previous less complex systems (figure 4) but according to the same functional law of merging and emergence: the ARMSADA paradigm. In every ARMSADA, like a lichen, a cell or a forest [START_REF] Bricage | Évaluation des interactions entre les densité et diversité des chenilles de lépidoptères et les diversité et degré de défoliation des feuillus d'un bois. Mesure de la polyphagie et prédiction des pullulations potentielles[END_REF], for one actor to survive, all the other ones must survive first. An ARMSADA is a 'pluribus unum' organism. Matter and energy flows are first for the survival of the Whole: 'unus pro omnibus omnes pro uno', 'in varietate concordia' [START_REF] Bricage | Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages ARMSADA. The way, to be resilient and self-sustainable, the living systems are running through[END_REF]. Into a lichen or a cell every actor gets its own space-time of survival and functioning: 'a space for each one and each one in its space' [START_REF] Bricage | Le langage du vivant : plurilinguisme, transfrontaliérité et associativité[END_REF], 'a time for each one and each one in its time' [START_REF] Bricage | La nature de la décision dans la nature ? Systèmes biologiques: production, consommation, croissance et survie. Quelles règles ? Quels degrés d'exigence ? Quels bilans ? La Décision Systémique: du Biologique au Social[END_REF]. Into an ARMSADA, advantages for a partner are always disadvantages for other ones and reciprocally. If benefits they are only for their Whole, for the mutual global association of the local actors: 'reciprocal interactions' means local interactions between partners, 'mutual interactions' means global interactions with and within the Whole (figure 5b). All actors and their Whole are making one, in a 'unity through diversity' way of survival [START_REF] Bricage | A new evolutionary paradigm: the Associations for the Mutual Sharing of Advantages and of Disadvantages[END_REF]. The merging into an ARMSADA is the result of 'a percolation process' (figure 5c): the same way neurones behave for the emergence and maintenance of neural networks, 'systems which wired together do fire together' and 'to wire together systems must fire together'. The percolation process is a metamorphosis [START_REF] Bricage | The metamorphoses of the living systems: the Associations for the Reciprocal and Mutual Sharing of Advantages and of Disadvantages[END_REF]: actors and properties of the previous step (before state) are lost, new ones are gained (after, at the end of the process), others are maintained, but transformed during the process. It is not a winwin process [START_REF] Bricage | Win-win not a solution. What next[END_REF]. There are never winners without losers [START_REF] Bricage | Living and banking systems comparison. Prisoners' dilemma "win-win" is not the solution[END_REF]. Every partner is both winner and loser [START_REF] Bricage | La survie des systèmes vivants[END_REF][START_REF] Bricage | Cancer is a breaking of the cell's ARMSADA through an aggression that results in a lack of non-autonomy[END_REF][START_REF] Bricage | The cell originated through successive outbreaks of networking and homing into Associations for the Reciprocal and Mutual Sharing of Advantages and of Disadvantages, between the partners, with a benefit only for their wholeness[END_REF][START_REF] Bricage | Living and banking systems comparison. Prisoners' dilemma "win-win" is not the solution[END_REF][START_REF] Bricage | About man Interventions in the living networks: modelling with a qualitative animated semiological holistic point of view, a systemic approach, an holistic way of education to explain the issues of the fighting steps and the escalade of violence between mankind and the wild[END_REF]. The only winner is their Whole (figure 5b) [START_REF] Bricage | An approach of organizations and management: systemic ethics, democracy and sustainability. Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages[END_REF].

5) The systemic constructal law and the emergence of new properties.

ARMSADAs are everywhere [START_REF] Bricage | Local versus global and individual versus whole competition between and within living systems. ARMSADA emergence and breaking[END_REF]! Viruses that are inhabiting bacteria, like algal cells are inhabiting the lichen fungus, give their host new properties that allow bacteria to eat new preys. To survive that is first to eat! Viruses that are inhabiting bacteria or eukaryotic cells, like our cells, give new properties that allow these bacteria or cells not to be eaten by other viruses or bacteria. To survive that is not to be eaten too! Endogenous integrated viruses are protecting their host against other viruses. These endogenous integrated constrained dangers (figure 1b) are not only necessary for their host to survive but also for their host to reproduce. And with its host survival, the integrated virus survives too. Living systems are systems of systems of adjacent levels of organisation. The functional structure, within or between systems, is the result of simultaneous reciprocal interactions: 'interaction is construction and construction is interaction', so, sooner or later, we don't know which are causes or effects: systemic constructal law (figure 6). For example, root nodules cells (level i) of leguminous plants own a new property of atmospheric nitrogen fixation, but none of the partners, neither the plant organism (level i+1), nor the invading population of bacteria (level i-1) can fix nitrogen from the air [START_REF] Bricage | Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages ARMSADA. The way, to be resilient and self-sustainable, the living systems are running through[END_REF].

Either with the leguminous plant nodules formation [START_REF] Madsen | The molecular network governing nodule organogenesis and infection in the model legume Lotus japonicus[END_REF] or with the early cell ontogenesis [START_REF] Bricage | The cell originated through successive outbreaks of networking and homing into Associations for the Reciprocal and Mutual Sharing of Advantages and of Disadvantages, between the partners, with a benefit only for their wholeness[END_REF], the first step of building an ARMSADA is an emergency situation [START_REF] Bricage | Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages ARMSADA. The way, to be resilient and self-sustainable, the living systems are running through[END_REF]. Free living bacteria (Rhizobium) invade plant roots hair cells. As every parasite, these bacteria eat the plant cells matter. That is a great advantage, they grow in mass, divide and grow in number, killing the cells and moving into the plant body. But sooner or later the invasion is stopped and the surviving bacteria are sequestered into plant cells vacuoles where they can survive, in the absence of oxygen only by nitrogen fixation. Now that is a great disadvantage. Only the new emerging tumorous nodule as a Whole owns the peculiar property of nitrogen fixation. Nowadays animal and plant oxygen respiratory cells are hosting an ancient free living invading bacterial species which gave rise to the current mitochondrial partner of these cells [START_REF] Bricage | Le langage du vivant : plurilinguisme, transfrontaliérité et associativité[END_REF]. The ancient parasitic bacterial ancestor species (level i-1) disappeared but its integrated descent lineage is still surviving within the cellular (level i) and meta-cellular (level i+1) organisms since hundreds millions of years. And it will survive as long as the cell species will survive, the same as for the viruses that are surviving into the cell nucleus (figure 1b) [START_REF] Bricage | The metamorphoses of the living systems: the Associations for the Reciprocal and Mutual Sharing of Advantages and of Disadvantages[END_REF][START_REF] Bricage | L'organisation spatiotemporelle des systèmes vivants[END_REF].

1) What law of governance does allow living systems of systems ontogenesis and evolution?

Like Rhizobium mutations are regulating the tumorous process of nodule emergence, mitochondrial mutations may give birth to tumorous cells [START_REF] Bricage | Cancer is a breaking of the cell's ARMSADA through an aggression that results in a lack of non-autonomy[END_REF]. Mitochondria may be invaded and eaten by viruses, like bacteria are. These viruses look like ancestral viruses that were invading and eating the mitochondrial bacterial ancestors. Nowadays when a cell is damaged, the inhabiting mitochondria will be killed except if they can integrate another hosting cell. Like bacteria, mitochondria always get invading properties and can move from one cell to another. When the mitochondria are damaged, the inhabited cell will be killed. During the apoptosis process, damaged mitochondria are eaten. The whole cell materials are eaten and recycled to make new cells. Into an ARMSADA disadvantages for a partner are disadvantages for other ones, and for the Whole. All partners are fused together in a new whole for the best and for the worst. Man species is not an exception [START_REF] Bricage | About man Interventions in the living networks: modelling with a qualitative animated semiological holistic point of view, a systemic approach, an holistic way of education to explain the issues of the fighting steps and the escalade of violence between mankind and the wild[END_REF][START_REF] Bricage | Living networks of networks: the societal and environmental responsibility of humanity in the fight between humans and the wild[END_REF]. [START_REF] Bricage | A new evolutionary paradigm: the Associations for the Mutual Sharing of Advantages and of Disadvantages[END_REF]. A new emergent adjacent superior level of organisation is always hosting previous adjacent inferior levels, that are juxtaposed and embedded in it [START_REF] Bricage | Pour survivre et se survivre, la vie est d'abord un flux, ergodique, fractal et contingent, vers des macro-états organisés de micro-états, à la suite de brisures de symétrie[END_REF]; hosted systems are embedded into the new hosting system-of-systems in which they merged into an ARMSADA. It is an iteration process (figure 4) with feedbacks between and within sub-systems (figure 5) and the system-ofsystems (figure 6). The hosted systems are more and more independent of their ancient ecoexotope of survival and more and more dependent of the endophysiotope of their Whole [START_REF] Bricage | Héritage génétique, héritage épigénétique et héritage environnemental : de la bactérie à l'homme, le transformisme, une systémique du vivant[END_REF], which is their new ecoexotope of survival (figure 6a). Increasing interactions and retro-controls (figure 6c) allow the endophysiotope of a i level to be the ecoexotope of survival of different i-j levels (figure 6b). And the ecoexotope of a i level, sooner or later, will be embedded into the endophysiotope of a i+k level organism.

The third paradigm is that 'all new living systems blueprints are emerging by merging of partners into an ARMSADA'

2) A periodic classification chart for living systems.

Due to the ARMSADA process of emerging of new blue-prints, life is not a tree but a coral [START_REF] Bricage | évolution créatrice : métamorphoses et phylotagmotaphologie du vivant. L'évolution du vivant a une direction[END_REF]. A lot of merging allowed new system-of-systems emergences. We can range the current known results in a table (figure 7) according to the scaling invariance [START_REF] Eisler | Fluctuation scaling in complex systems: Taylor's law and beyond[END_REF][START_REF] Barabási | Les réseaux invariants d'échelle[END_REF] for the definition of levels of organisation (figure 1). Each column represents the same kind of way of system-of-systems complexity enhancement and each line represents the same step of systems species evolution. Sub-steps into each step are not represented. For example within the step of Man species there are a great number of kind of societies [START_REF] Bricage | An approach of organizations and management: systemic ethics, democracy and sustainability. Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages[END_REF].

3) An invariant scaling relationship between living systems whatever the level of organisation.

According both to the gauge invariance paradigm of functioning and the ARMSADA paradigm of structuration we can draw a periodic classification chart of the levels of organisation of all known, or unknown, living systems, from the quantum of Planck to the Universe as a Whole (figure 7) [START_REF] Bricage | Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages ARMSADA. The way, to be resilient and self-sustainable, the living systems are running through[END_REF].

Every living system-of-systems can be characterised by its time dimension, in seconds, and its space dimension, its volume, in cubic meters (figure 8a) [START_REF] Bricage | rétrocession et émergence : organisation des systèmes vivants, éducation à la systémique, santé et sociétalité[END_REF]. But due to the dimensional wide scales we must use a logarithmic representation to plot all data (figure 8b) [START_REF] Bricage | évolution créatrice : métamorphoses et phylotagmotaphologie du vivant. L'évolution du vivant a une direction[END_REF]. Our ecoexotope of survival, the Universe, is always in its growth phase, expanding its volume (figure 8c). And every living system-of-systems in it are representatives of different steps of its expanding complexity. For every living species, space growth is governing time flow rate (figure 8c) like mass growth is governing time duration (figure 3b). It is a space-time co-evolution process [START_REF] Bricage | évolution créatrice : métamorphoses et phylotagmotaphologie du vivant. L'évolution du vivant a une direction[END_REF][START_REF] Bricage | Modelling space-time-action modularity and evolution of living systems[END_REF], time is a measure of space, and reciprocally (figure 8d). We may plot together the volume of the system at the end of its growth phase, VA the adult volume, at the sexual maturity [START_REF] Lee | Sexual maturity in growing dinosaurs does not fit reptilian growth models[END_REF], and the time that is necessary for the system to gain its capacity of reproduction, tg [START_REF] Bricage | Lathyrus macrorhizus : influence des facteurs stationnels sur la floraison in situ[END_REF].

The time of generation, tg, is also the duration of the growth larval phase (figure 3b), in a log-log plot we get a line with a 3/2 slope (figure 8b). If we now take subparts of these data, the sub-systems are governed by the same 3/2 power law that the system-of-systems is (figure 9). And if we plot again all the whole Universe system-of-systems data of the previous log-log plot, using the same log-log plotting we get again a 3/2 slope line (figures 8, 9). So the Universe as a Whole is a sub-system of an hyper-Universe which is governed by the same power law. Thus this power law is a scaling invariant fractal power law of governance of living systems of systems [START_REF] Bricage | Approche systémique de l'évolution du vivant[END_REF][START_REF] Bricage | Loi puissance d'invariance spatiotemporelle des systèmes vivants[END_REF]. 4) A hidden cryptic fundamental phenomenon of governance: the Brownian motion.

Brownian motion is a time dependent geometrical process that structures the Universe, from down to the top [START_REF] Bricage | évolution créatrice : métamorphoses et phylotagmotaphologie du vivant. L'évolution du vivant a une direction[END_REF], according to a 3/2 power law of time (figure 10). We can notice that V A 2 /3 = C. tg and, whatever the dimensional units, 2/3 is often a threshold value in the phenomena of percolation (figure 5). Brownian motion structures 3/2 or 2/3 power laws of co-relation (figures 10, 11).

5) Matter and energy controlled limits and limitations.

We can also say that all living systems, at their interfaces, along their life cycle as a Whole (figure 11a), are exchanging matter and energy [START_REF] Hulbert | Life and death: metabolic rate, membrane composition, and life span of animals[END_REF] at an average constant rate (figure 11b) and in a stochastic Brownian motion way of flows control (figure 11).

There are never advantages without disadvantages: when new abilities are gained, previous ones are lost. The new Whole results always from a percolation process (figure 5): every Whole is always both more and less than the sum of its parts [START_REF] Bricage | La nature de la décision dans la nature ? Systèmes biologiques: production, consommation, croissance et survie. Quelles règles ? Quels degrés d'exigence ? Quels bilans ? La Décision Systémique: du Biologique au Social[END_REF]. A neurone which expresses all capacities excepted the capacity of reproduction is not a new level of organisation, during its ontogenesis it gained new emergent properties, due to its new organisation, but it lost the capacity of division (figure 2b). 1) Modularity is the common rule for designing new Wholes and hosting ancient ones.

Juxtaposition and embedment are both the cause and the result of modularity (figure 4). Cell organisms (level i) are made of modules of Monera like structures (level i-1): the cell organites. These organites are made of clusters of macromolecules (level i-2). Macromolecules (level i-3) are embedding juxtaposed modules of atoms (level i-4) (figure 7). For example the starch grains of a plant cell which grow in number during the cell mass growth are made of an accumulation of starch molecules layers. Mass growth and number growth of different levels of organisation are linked together within and between levels. In terms of modules (figures 4, 11), we can consider either the spaces of interactions (figure 11e), to describe every living system-of-systems in terms of volumes (compartments space or mass), or the times of interactions (figure 11d), to describe in terms of time (process durations, flow rates) [START_REF] Bricage | Modelling space-time-action modularity and evolution of living systems[END_REF]. There are a minimum number (a threshold value) and a maximum one, of actors, of modules, of states, that are necessary for a controller (the Whole) to control a system (the Whole) which survival is depending from a limited number of interactions between the endophysiotopes of the actors as controllers of their common ecoexotope of survival (figure 5a).

2) Are power laws the common rules for governance control and homeorhesis?

Depending the way we are looking at the retro-action (feed-back) processes we may get inverse slopes, we can exchange the slopes, 2/3= 1/(2/3), but it is the same phenomenon of governance we are looking at (figures 8a, 10c). We can consider either the space or the time as a cause or an effect (figure 6). We can either consider the space if we look at the embedment and juxtaposition processes of ontogenesis of the subsystems into a new Whole (figure 4), or the time if we look at the flows of matter and energy (figure 11c), but it is the same phenomenon of governance and ontogenesis we are looking at (figure 8d).

We know a lot of such a kind of power law: -the Kepler's third law of motion governance, that relies the cube of the space dimension (the semi-major axis) and the square of the time dimension (the orbital period) in our solar system, -the law of matter and energy governance, law of irradiance that relies the mass to luminosity ratio of an object to its distance in our whole Universe system, which slope is 3/2 or 2/3 depending on what factor we suppose to be the cause or the effect (systemic constructal law), -the law of mass and number growths governance, between the endophysiotopes of species sharing the same ecoexotope of survival, an allometric scaling law between population density and energy use [START_REF] Marquet | Scaling and power-laws in ecological systems[END_REF], or the law of organisation governance of predator-prey communities across terrestrial and aquatic biomes [START_REF] Kant | Dynamics of a prey-predator system with infection in prey[END_REF], and again, depending which factor we consider as the cause or the effect we get a 3/2 or 2/3 slope power law [START_REF] Bricage | Loi puissance d'invariance spatiotemporelle des systèmes vivants[END_REF] (figure 10). Other similar power laws are governing the relationship between the hosting capacity and the capacity to be hosted of every living system (figure 6): for example, -the space linear dimension and the duration time of food networks extension in the boreal forest (matter and energy use and mass and number growths governance), and 'Man is not an exception', -the number of people and the time turnover of a society [START_REF] Bricage | Win-win not a solution. What next[END_REF][START_REF] Bricage | Man next challenge for survival: Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages. Las Asociaciones con Ventajas e Inconvenientes Recíprocos y Partidos[END_REF] obey the same power law. Whatever the system-of-systems, the same power law is evidenced. This scaling invariance is expressing a modular fractal organisation (figures 9, 10c).

We usually represent mass growth within time flowing. But indeed mass is controlled by matter and energy flows (figure 3b) and is controlling time duration of growth [START_REF] Bricage | Mobilisation de la matière et de l'énergie, et croissance, aux différents niveaux d'organisation des systèmes vivants : les principes organisateurs d'émergence des systèmes vivants[END_REF]. Mass is determining time! There is a mass threshold for the system to acquire its capacity of reproduction [START_REF] Tzur | Cell growth and size homeostasis in proliferating animal cells[END_REF]. Because to reproduce its self and eventually to grow in number (figure 2) has a cost which is paid by mass growth: mass growth stops and flows of matter and energy are invested into number growth. The Kleiber power law means the same [START_REF] Lloyd | Evolutionary entropy: a predictor of body size, metabolic rate and maximal life span[END_REF][START_REF] Dodds | Re-examination of the 3/4-law of metabolism[END_REF]. Mass is determining the metabolic rate with the same relationship independently of the level of organisation: a slope of 3/4 on a 18 dimensional world for animal livings [START_REF] Bricage | Mobilisation de la matière et de l'énergie, et croissance, aux différents niveaux d'organisation des systèmes vivants : les principes organisateurs d'émergence des systèmes vivants[END_REF]. All the metabolic processes in a cell obey power laws of different exponents. And the mean value [START_REF] Bricage | Mobilisation de la matière et de l'énergie, et croissance, aux différents niveaux d'organisation des systèmes vivants : les principes organisateurs d'émergence des systèmes vivants[END_REF] of all these measured processes is 3/2. These power laws are evidenced whatever the kind of metabolism. A power law of exponent 2/3 is representative of the simultaneous governance of nitrogen and phosphorus concentrations which are limiting factors of proteins and DNA metabolism [START_REF] Nasir | Phylogenetic tracings of proteome size support the gradual accretion of protein structural domains and the early origin of viruses from primordial cells[END_REF] and of matter growth and energy availability in plant cells [START_REF] Bricage | Lathyrus macrorhizus : influence des facteurs stationnels sur la floraison in situ[END_REF].

To survive is a game of chance. You need to be lucky, to be at the right place at the right time [START_REF] Bricage | Systèmes biologiques : le jeu de la croissance et de la survie. Quelles règles ? Quelles décisions ? Quels bilans ? La Décision Systémique : du Biologique au Social[END_REF][START_REF] Bricage | La nature de la décision dans la nature ? Systèmes biologiques: production, consommation, croissance et survie. Quelles règles ? Quels degrés d'exigence ? Quels bilans ? La Décision Systémique: du Biologique au Social[END_REF][START_REF] Bricage | The metamorphoses of the living systems: the Associations for the Reciprocal and Mutual Sharing of Advantages and of Disadvantages[END_REF]. Before the time is not the time but after the time is no more the time. How a system might increase durably either the hosting capacity of its ecoexotope of survival or the capacity to be hosted of its endophysiotope, to survive and live on? How to free its self, at least for a moment, from the space and time constraints? How to escape, at least for a moment, from the violence of the struggle for life [START_REF] Bricage | La nature de la violence dans la nature : déterminismes écologique, physiologique et génétique de l'adaptation aux changements aux différents niveaux d'organisation des systèmes végétaux[END_REF][START_REF] Bricage | A new evolutionary paradigm: the Associations for the Mutual Sharing of Advantages and of Disadvantages[END_REF]?

3) Brownian motion is the key governing process. Brownian motion was first observed, in 1827, by Robert Brown [START_REF] Kahane | Le mouvement brownien et son histoire, réponses à quelques questions[END_REF]. Through the microscope, he observed the motion of pollen grains (microscopic i+1 level) in water, but he was unable to provide an explanation. Brownian motion provided the evidence of molecular motion (picoscopic i-3 level) and the existence of infra-microscopic systems (figure 7) governing the functioning of macro-scopic living systems [START_REF] Rienzo | Probing short-rang protein Brownian motion in the cytoplasm of living cells[END_REF]. Norbert Wiener gave, in 1918, the mathematical definition and properties of the stochastic process (figure 10a), as the Wiener process [START_REF] Dunbar | The definition of Brownian motion and the Wiener process[END_REF]. Brownian motion emphasises the physical aspect of the process [START_REF] Perrin | Étude mathématique du mouvement Brownien de rotation[END_REF]. But, indeed, in 1900, Louis Bachelier had introduced the limit of random walk as a model for prices evolution on the Paris stock exchange and he is really at the origin of the Brownian motion mathematical model, now always occasionally found in financial literature [START_REF] Schilling R L | Brownian Motion. An Introduction to Stochastic Processes[END_REF].

For every living system-of-systems species, its time tg is a measure of its space VA, and reciprocally (figure 8d). The spaces embedment and juxtapositions emergence (figure 10) is a space-time co-evolution process (figure 9). So we can represent spaces embedment and juxtapositions either from a kinetic point of view (figure 11d) or from a geometric point of view (figure 11e). Whatever the scale, Brownian motion is structuring the geometry and rates of matter movements and interactions. Brownian motion can be described as a phenomenon of a 3/2 exponent of time (figure 10c). At the level of the Universe, the slope of the regression line between the distance of a light source and its red wavelength shift, which allows the experimental determination of the Hubble cosmological constant, is 2/3, or 1/(3/2). During their growth living systems exchange matter and energy at an average constant rate at interfaces (figure 11b). The 3/2 power law controlled flow is globally representative of the optimal ratio of the volume to surface area in a sphere. The big bang initial singularity is representative of an isotropic closed system [START_REF] Robredo | Le big bang, une idée tombée du ciel[END_REF]. Simulations of Brownian motion models at different scales (figure 10b) get pictures of living structures, from the quantum world to the whole Universe [START_REF] Bricage | Loi puissance d'invariance spatiotemporelle des systèmes vivants[END_REF]. Looking at giant living systems they usually originate from tiny ones! Referring to the gauge invariance paradigm (figure 1), -mobilisation of matter and energy is flow motion, -mass growth is volume motion, -reaction to stimulations is information motion, -movement is motion, -organisation genesis is space-time steps motion, -integration is interactions motion, -reproduction is generations motion. Motions governance is Brownian motion governance! 4) Why no other laws than a power law?

Looking at the sizes distribution (figures 8b) we must to question how to differentiate empirically a power law [START_REF] Clauset | Power-law distributions in empirical data[END_REF], a Log normal distribution and a Pareto distribution [START_REF] Pareto | Un applicazione di teorie sociologiche[END_REF][START_REF] Almaas | Power laws in biological networks[END_REF][START_REF] Karev | Analysis and simulation of power law distribution of file types in file sharing systems[END_REF]. Power laws has been discussed largely with income distribution [START_REF] Reed | From gene families and genera to incomes and internet file sizes: why power laws are so common in nature[END_REF][START_REF] Bricage | Living and banking systems comparison. Prisoners' dilemma "win-win" is not the solution[END_REF], Zipf-Auerbach city sizes [START_REF] Auerbach | Das Gesetz der Bevölkerungskonzentration[END_REF], Zipf-Estouf word frequency, Lotka bibliometrics and Mandelbrot information theory [START_REF] Mandelbrot | Les objets fractals : forme, hasard et dimension[END_REF]. In a Pareto distribution the Logcomplementary cumulative distribution function is exactly linear. Pareto has a linear Log-density. That is not the case (figure 8c). In a power law function, an infinite mean/variance is possible. That is the case in time evolving living systems. In a Log normal distribution the mean/variance is finite. Log-normal are more relative to multiplicative processes. But size changes rarely by a random multiplicative factor at each step [START_REF] Lloyd | Evolutionary entropy: a predictor of body size, metabolic rate and maximal life span[END_REF]. It is often claimed that living systems are thermodynamically optimised. The Zipf law [START_REF] Zipf | Human behaviour and the principle of least effort[END_REF], sometimes called the continuous Pareto distribution is observed when looking at frequencies. Sorting (figures 7, 8) may be looked either in an increasing or a descending order of VA. Zipf plot is a type of log-log scales plot diagram for the data sorted in the descending order, where the abscissa axis presents the value of a quantity, and the ordinate shows its rank. But neither the adult volume VA is sorted by classes nor the time of generation ordinate tg is expressing frequencies. We got a fractal organisation (figure 9). Either the fractal Mandelbrot model [START_REF] Mandelbrot | Les objets fractals : forme, hasard et dimension[END_REF] or the Zhu model are optimisation based [START_REF] Zipf | Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology[END_REF]. But [START_REF] Bricage | Mobilisation de la matière et de l'énergie, et croissance, aux différents niveaux d'organisation des systèmes vivants : les principes organisateurs d'émergence des systèmes vivants[END_REF], living systems optimisation is not the rule! Endophysiotopes are functioning in an interval of values (homeostasis) and are surviving in an ecoexotope with an interval of values too (homeorhesis), i.e. 'meden agan' (figure 5). The values are the most dependent of chance, 'to be at the right place at the right time', and 'not to be at the wrong place at the wrong time' [START_REF] Bricage | Modelling space-time-action modularity and evolution of living systems[END_REF]. Every living system is an open system-of-system, so, at every time, homeorhesis [START_REF] Margulis | The Symbiotic Planet: A New Look at Evolution[END_REF] and exaptation are the results of the percolation network dynamics of interactions (figure 5) between ecoexotope and endophysiotope [START_REF] Bricage | Héritage génétique, héritage épigénétique et héritage environnemental : de la bactérie à l'homme, le transformisme, une systémique du vivant[END_REF]. When processes are limited, with inferior and superior bounds, as that is always the case for every level of organisation (figure 4), Log-normal model easily pushed to a power law. So Brownian motion is a good model for a not trivial representation of a changing by chance process, it is consistent with the observed data and predictions (figures 8, 9, 10). And observations and experimentations cannot impact outcomes.

5) Another view about the significance of the golden number!

The golden ratio (golden mean or golden section, which symbol φ is the Greek letter "phi") is a number approximately equal to 1.618 which appears many times in geometry (figure 10d). It is commonly found in mathematics (e.g. Fibonacci series), nature sciences (e.g. the spiral arrangement of plant parts), and is very popular in art, architects or designers [START_REF] Van Mersbergen | Rhetorical prototypes in architecture: measuring the Acropolis with a philosophical polemic[END_REF][START_REF] Padovan | Proportion: science, philosophy, architecture[END_REF] have proportioned their works to approximate the golden ratio (especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio) believing this proportion to be the most pleasant. Its value, very near the ratio 5/3 (i.e. 1.666), is not far from 3/2 (i.e. 1.500), values that are difficult to distinguish through experimental plotting (figure 8). The golden ratio φ and inverse golden ratio 1/φ have a set of symmetries that preserve and interrelate them. Preserved by the fractional linear transformation, they are reciprocal and symmetric by interchanges, as cause and effect in the systemic constructal law (figure 6). So people could suggest the observed 3/2 slope value (figure 8) could be the golden ratio. But we could also say that phi is a mathematical artefact, it is 'man made' [START_REF] Markowsky | Misconceptions about the golden ratio[END_REF]. Brownian motion is a real natural process, everywhere, at every time, in the background from the origin of the Universe, even we don't know why it is like this. Maybe that is the reason why looking at Brownian motion controlled processes (i.e. b=1.50 or 1/b=0.66 values) we may think they are golden ratio designed ones (i.e. φ=1.618 or 1/φ=0.618 values), because the differences (between b and φ or 1/b and 1/φ) are between 5% and 10%, i.e. they are masked by the biological variability. But the reality is Brownian motion, not golden ratio, for eternity. Now we know the golden ratio is only 'a pleasant model' that is a consequence of 'the Brownian motion controlled process of governance' of the functioning of every level of organisation of living systems of systems [START_REF] Perez | Codon populations in single-stranded whole human genome DNA are fractal and fine-tuned by the golden ratio 1.618[END_REF].

The ultimate objective of the study of living systems is to find a general theory of Life that can explain and predict the dynamics of human and non-human systems [START_REF] Bricage | Modelling space-time-action modularity and evolution of living systems[END_REF][START_REF] Newman | Power laws, Pareto distributions and Zipf's law[END_REF][START_REF] Snooks | A general theory of complex living systems: exploring the demand side of dynamics[END_REF][START_REF] Bricage | Time management by living systems: time modularity, rhythms and conics running calendars. Methodology, theory and applications[END_REF][START_REF] Naryzhny | Zipf's law in proteomics[END_REF]. The ARMSADA paradigm has allowed to built a very realistic general dynamic theory [START_REF] Bricage | Living networks of networks: the societal and environmental responsibility of humanity in the fight between humans and the wild[END_REF]. 1) ARMSADA: the keystone for emergence and sustainability.

Ten thousands years ago, in different locations, Man species created different ARMSADAs with various wild species partners, ARMSADAs were emerging with the domestication of plants and animals. All the species partners simultaneously lose the ability to kill the other ones: an ARMSADA is long lasting as long as 'for the one to survive, the other ones must survive first'. But nowadays with Man species number growth and mass industrial agriculture, these ARMSADA deals are broken and Man is an endangered species because of its increasing parasitic behaviour [START_REF] Bricage | Win-win not a solution. What next[END_REF]. Symbioses are long lasting 'as long as they are supportable for every partner and supported by every partner': i.e. advantages and disadvantages are mutually shared and benefits are only for the Whole. Partners don't exist outside of their Whole. Symbioses are neither associations for mutual benefits [START_REF] Martin | Ancestral alliances: plant mutualistic symbioses with fungi and bacteria[END_REF] nor win-win deals; win-win is not a long lasting solution but rapidly a problem [START_REF] Bricage | Win-win not a solution. What next[END_REF]. ARMSADA is the key paradigm for sustainability [START_REF] Bricage | Systèmes biologiques : le jeu de la croissance et de la survie. Quelles règles ? Quelles décisions ? Quels bilans ? La Décision Systémique : du Biologique au Social[END_REF][START_REF] Bricage | La nature de la décision dans la nature ? Systèmes biologiques: production, consommation, croissance et survie. Quelles règles ? Quels degrés d'exigence ? Quels bilans ? La Décision Systémique: du Biologique au Social[END_REF].

2) ARMSADA: a fruitful predictive paradigm.

Cancer is the result of an uncontrolled cell growth. Tumour like structures as legumes nodules, and cancer cells, are controlled by viruses, either viruses from the ecoexotope that are damaging cells or endophysiotope constrained viruses that are freed. AIDS and cancer processes are similar in terms of hosted virus and hosting cell interactions [START_REF] Bricage | Cancer is a breaking of the cell's ARMSADA through an aggression that results in a lack of non-autonomy[END_REF]. Exceptionally a new whole may emerge in the emergency situation of viruses killing cells (level i) or cancer cells killing the organism (level i+1). Even if the probability is the lowest one, sooner or later, an ARMSADA balance will emerge from an emergency situation. Vaccine processes were proposed as a result of gauge invariance and ARMSADA paradigms: -a HIV curative vaccine, using stem cells cultivation and transplant technology with HIV auto-engineered selected HIV resistant stem cells [START_REF] Bricage | Le langage du vivant : plurilinguisme, transfrontaliérité et associativité[END_REF] and a cancer curative vaccine methodology with exogenous and endogenous lytic viruses [START_REF] Bricage | Cancer is a breaking of the cell's ARMSADA through an aggression that results in a lack of non-autonomy[END_REF]. They have been proved to work [START_REF] Germain | Une thérapie génique contre la drépanocytose[END_REF], and a procedure was patented by jennerex. As the result of billions years of sharing a common ecoexotope of survival, the Earth [START_REF] Margulis | The Symbiotic Planet: A New Look at Evolution[END_REF], the ARMSADA process is the key way for societal sustainability [START_REF] Bricage | An approach of organizations and management: systemic ethics, democracy and sustainability. Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages[END_REF]. It is a way of system management which aims to be the most open possible (requisite variety) in order to use in common shared resources, but with sharing both advantages and disadvantages, as within the forest ecosystem (figure 5). The collective management by the community (the actors and their Whole) has established rules of governance with the aim of protecting and perpetuating resources, everyone has the right to use it but within limits [START_REF] Bricage | Win-win not a solution. What next[END_REF][START_REF] Bricage | Thinking and teaching systemics: bio-systemics in higher education[END_REF]. These resources are a joint common property. They are necessary for the gauge invariance capacities (figure 1): -matter (air, water, food) and energy, for growing in mass and number, for moving, for reacting to changes (e.g. ecoexotope changes like climate change), -structures (of the every day life), for an harmonious compartmentation of spaces and times of actions, -information (creative commons), for the memory of the good and bad, past, interactions between the ecoexotope hosting capacity and the endophysiotope capacities to be hosted: 'interaction is construction, construction is interaction' (figure 6). Nowadays numerous parts of the joint property are threatened. They are removed from the Common, marketed and destroyed in an irreversible economical, without limits and limitations (figure 12), way of Nature and Life continuous destruction (figure 13a) [START_REF] Bricage | About man Interventions in the living networks: modelling with a qualitative animated semiological holistic point of view, a systemic approach, an holistic way of education to explain the issues of the fighting steps and the escalade of violence between mankind and the wild[END_REF].

3) Sustainability is variety, but not too much variety.

Sustainability needs an optimal interval balance, allowing an homeorhesis (figure 5), in-between efficiency and resilience. Too much efficiency and the predator (a virus, a caterpillar, man species) will kill too much preys (bacteria, trees, ecosystems) and die from hunger. For the predator to survive the prey must survive first. It is a who wins loses game. Too much resilience and actors (a cancer cell, an apoptosis cell) will not die and the Whole will die. It is a who wins loses game. ARMSADA is the key (figure 14). Indeed it is the core of the Taoism philosophy. There are never advantages without disadvantages. Limitations and control sharing (figure 15b) is the price to pay for surviving as a complex system (figure 15): to stay in-between, meden agan, in a window of viability (figure 5a) [START_REF] Bricage | Les communautés en Vic-Bilh : associations matrimoniales et patrimoine associatif. Journées Européennes du Patrimoine[END_REF][START_REF] Bricage | Sémiologique graphique de l'espace-temps-action du vivant : bilan épistémologique et praxéologique de sa modélisation systémique, co-déterminisme global, prédictibilité locale et imprédicativité glocale[END_REF][START_REF] Bricage | Un aspect de la flore et de la faune de la côte sableuse et rocheuse des mamelles. Quelques aspects des rapports entre les êtres vivants et leur milieu de vie: exemples d'actions des facteurs du milieu sur les êtres vivants[END_REF]. 4) Interactions between the hosting capacity and the capacity to be hosted: a selective screening.

Our ecoexotope of survival food volume and water and energy availability are limited. All the water of the Earth is only a droplet on a pebble [START_REF] Bricage | Thinking and teaching systemics: bio-systemics in higher education[END_REF]. The hosting capacity of the ecoexotope is limited.To increase always the hosting capacity of the ecoexotope of survival is not a solution but a problem. To increase the capacity to be hosted is the key [START_REF] Bricage | Win-win not a solution. What next[END_REF]. Limitations allow to survive only the endophysiotopes that get a capacity to be hosted in adequacy with the available capacity of hosting. Not enough water to use or too much use of water and no more survival. Too much plant density and no flowering, so no fruit, no seed and the plant population will die [START_REF] Bricage | Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages ARMSADA. The way, to be resilient and self-sustainable, the living systems are running through[END_REF][START_REF] Bricage | Thinking and teaching systemics: bio-systemics in higher education[END_REF][START_REF] Bricage | Sémiologique graphique de l'espace-temps-action du vivant : bilan épistémologique et praxéologique de sa modélisation systémique, co-déterminisme global, prédictibilité locale et imprédicativité glocale[END_REF][START_REF] Bricage | Un aspect de la flore et de la faune de la côte sableuse et rocheuse des mamelles. Quelques aspects des rapports entre les êtres vivants et leur milieu de vie: exemples d'actions des facteurs du milieu sur les êtres vivants[END_REF]. Dying is the rule for species which capacity to be hosted is not in adequacy with its ecoexotope hosting capacity [START_REF] Bricage | La semi-autonomie du vivant : pour que l'un survive, il faut d'abord que l'autre survive, et réciproquement[END_REF][START_REF] Bricage | About man Interventions in the living networks: modelling with a qualitative animated semiological holistic point of view, a systemic approach, an holistic way of education to explain the issues of the fighting steps and the escalade of violence between mankind and the wild[END_REF]. Whatever the size of the pie (figure 12), the numbers and sizes of the parts are limited according to an hyperbolic power law, as it is the case for supply-demand models (figure 12). You cannot eat the pie and have the pie. You cannot get both a high quality and a high quantity. Only a high capacity to be hosted allows the survival of endophysiotopes in weak hosting capacity ecoexotopes. That is a trivial rule in Nature, number growth and mass growth are limited by growth rate which is limited by the ecoexotope hosting capacity. We have to chose which capacity to be hosted we can express in which hosting capacity of the ecoexotope we want to support (figure 13a). It is a hosting-hosted co-evolution process like the host-parasite or predator-prey arms race [START_REF] Bricage | Cancer is a breaking of the cell's ARMSADA through an aggression that results in a lack of non-autonomy[END_REF][START_REF] Bricage | Le langage du vivant : plurilinguisme, transfrontaliérité et associativité[END_REF] (figure 14).

Figure 13

Sustainability: the 12 commandments for every system-of-systems governance.

Figure 13a

S ystem actors are taking, making, wasting, but recycling , matter, energy and processes.

1convergence: many causes can get the same effect, several ways of interactions can achieve the same result, 'interaction is construction, construction is interaction' (figure 6).

2contingence: the endophysiotope survival is always limited by constrained dangers, ecoexotope boundaries, barriers, and adverse situations (figures 14, 15).

3emergence: 'stressful emergency situations are situations of emergence' of new structures, processes, functions (i.e. exaptation), or actors; an emergency situation is always the first step of an ARMSADA emergence (figure 5).

4solidarity: 'e pluribus unum' and 'in variatate concordia', 'there are never advantages without disadvantages', good and bad choices are for everyone and the Whole. Everyone's growth is limited by that of all the others (local dependence) and the Whole (global dependence). "For the one to survive the other one must survive first" (figure 14).

5resilience: the resilience capacity is due to indispensable keystone actors, networks and situations (figure 5), but they can be identified only when they disappear.

6recycling: recycling processes, by embedment and juxtaposition into a new space-time, is a method of governance (figure 7).

7systemic constructal law (figure 6): when the capacity of hosting or the capacity to be hosted is changing, reciprocally the capacity to be hosted or the capacity of hosting must change too (i.e. homeostasis), to fit, the governance must eventually change to a new state (i.e. homeorhesis) (figure 5).

8sustainability: only the establishment of an ARMSADA allows the emergence, 'for the best and for the worst', of a sustained and sustainable governance, because it is sustainable for everybody and sustained by everyone, due to the everybody knowledge of the advantages and disadvantages flows, i.e. 'e pluribus unum' (figures 4, 5). 9co-evolution: every ecological, economical and educational system-of-systems and systems of governance is the result of a systemic interactive co-evolution process, i.e. 'interaction is construction, construction is interaction' (figures 5, 6).

1 0 -'meden agan': 'over the limits there are no more limitations', 'mutual survival depends on reciprocal limitations', to survive that is to transform disadvantages into advantages and to avoid advantages turn to disadvantages, 'for the best and for the worst' (figures [START_REF] Miller | A Crude Look at the Whole: The Science of Complex Systems in Business, Life, and Society[END_REF][START_REF] Bricage | Pigmentation and soluble peroxidase isozyme patterns of leaves of Pedilanthus tithymaloides L. variegatus as a result of daily temperature differences[END_REF].

11-'meden agan': 'no mass or number growth can increase without limits' (figure 3). 12-'meden agan': 'too much growth is killing growth' (figure 14).

Figure 13b

Transposition: what principles for education in systems thinking? [START_REF] Bricage | Guide Pour l'Enseignement de la Biologie Dans les Écoles Africaines[END_REF][START_REF] Bricage | La démarche scientifique expérimentale : un langage systémique[END_REF][START_REF] Bricage | Engineering health and social sciences curriculum: governance of the pedagogy, pedagogy of the governance[END_REF] 1convergence: several ways, more or less long, or effective, can achieve the same result. 2contingence: acquisitions of new skills and expressions of new competencies are limited by previous competencies limitations and unexpected adverse situations.

3emergence: stressful emergency situations may boost emergence of new pedagogic interactions, concepts and skills.

4solidarity: good and bad choices are for everyone (students and teacher) and their Whole (the class, the school, the enterprise, the social group).

5resilience: the resilience capacity is due to indispensable keystone actors, networks and situations (figure 5), but they can be identified only when they disappear.

6-recycling: recycling trans-disciplinary methods is a method of governance. 7systemic constructal law: when the capacity of hosting or the capacity to be hosted is changing, reciprocally the capacity to be hosted or the capacity of hosting are changing too, to fit, the governance must change to a new state. Whatever the cause an effect is needed.

8sustainability: 'e pluribus unum', the birth of an ARMSADA allows the emergence, for the best and for the worst, of a sustainable and sustained governance, because it is supportable for everybody and supported by everyone, due to the knowledge by everybody of the advantages and disadvantages for everyone, i.e. 'in variatate concordia'. 9co-evolution: every ecological, economical and educational system-of-systems or system of governance is the result of a systemic interactive co-evolution process, 'interaction is construction, construction is interaction'. 10-'meden agan': 'mutual co-existence depends on reciprocal limitations', for the best and for the worst', to survive that is to transform disadvantages into advantages and to avoid advantages turn to disadvantages.

11-'meden agan ': no process, no governance load can grow without limits. 12-'meden agan': 'too much power is killing power'.

5) Teaching systems thinking is the true key road for sustainability.

Nature seems very various but 'unity through diversity' is the rule. Reality is the result of necessity but chance is the law [START_REF] Thuan | Chaos et l'Harmonie : La Fabrication du Réel[END_REF]. To enter an ARMSADA is a way for a system (a species, a society) to limit the consuming of its hosting capacity and to increase its capacity to be hosted [START_REF] Bricage | An approach of organizations and management: systemic ethics, democracy and sustainability. Associations for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages[END_REF][START_REF] Bricage | Living networks of networks: the societal and environmental responsibility of humanity in the fight between humans and the wild[END_REF][START_REF] Bricage | Les communautés en Vic-Bilh : associations matrimoniales et patrimoine associatif. Journées Européennes du Patrimoine[END_REF]. It is 'an examination' every species has to pass sooner or later, again and again, for ever, and when failing only one time it is eradicated. Only will survive species that are embedded into an interactive ARMSADA network of ARMSADAs. Teaching 'systems thinking' is the key [START_REF] Bricage | Living networks of networks: the societal and environmental responsibility of humanity in the fight between humans and the wild[END_REF][START_REF] Bricage | Guide Pour l'Enseignement de la Biologie Dans les Écoles Africaines[END_REF][START_REF] Bricage | La démarche scientifique expérimentale : un langage systémique[END_REF][START_REF] Bricage | Engineering health and social sciences curriculum: governance of the pedagogy, pedagogy of the governance[END_REF]. According to the 2020 Strategic Framework for European Cooperation in Education and Training [START_REF] Council | Recommendation On Key Competences For Lifelong Learning[END_REF], systems thinking is a key competence to further develop and promote education for sustainable development. We need teachers of teachers [START_REF] Bricage | Thinking and teaching systemics: bio-systemics in higher education[END_REF] to seed systems thinking everywhere [START_REF] Bricage | The International Academy for Systems and Cybernetic Sciences[END_REF] in an interdisciplinary way (figure 13b) [START_REF] Lawrence | Interdisciplinary science: a coming of age?[END_REF], not only to train youngest in systems thinking approach practice [START_REF] Bricage | La démarche scientifique expérimentale : un langage systémique[END_REF] but first for a better human healthcare [START_REF] Bricage | Engineering health and social sciences curriculum: governance of the pedagogy, pedagogy of the governance[END_REF] and welfare [START_REF] Bricage | Use of chronolithotherapy for better individual healthcare and welfare[END_REF], not only to know Living systems history (figure 15a) [START_REF] Jeong | Organisms from all domains of life are scale-free networks[END_REF][START_REF] Bricage | Danger des représentations non-systémiques et pouvoir de prédiction des représentations systémiques en Sciences de la Vie. Les Représentations au Crible de l'Approche Systémique[END_REF] and fate [START_REF] Bricage | The modelling of the time modularity of the living systems: the time delay, time duration, time lag and the rhythms[END_REF].