César Sauvage
email: cesar.sauvage@meteo.fr

Cindy Lebeaupin Brossier

Marie-Noëlle Bouin

Véronique Ducrocq

6.2 ROLE OF THE SEA STATE ON THE AIR-SEA EXCHANGES DURING A MEDITERRANEAN HEAVY PRECIPITATION EVENT IN A KILOMETER-SCALE FORECAST SYSTEM

INTRODUCTION

During late

summer and fall, the Mediterranean region is prone to heavy precipitation events (HPEs) characterized by large rainfall amounts in a short period (typically more than 100 mm in less than 24 hours) which often lead to devastating flash-floods [START_REF] Ducrocq | Advances in understanding and forecasting of heavy precipitation in Mediterranean through the HyMeX SOP1 field campaign[END_REF]. For these events, the Mediterranean Sea is a source of heat and moisture that feed the mesoscale convective systems [START_REF] Duffourg | Origin of the moisture feeding the heavy precipitating systems over Southeastern France[END_REF]. The airsea exchanges are favored by a strong marine low-level jet (>20 m/s) blowing over a warm and thin ocean mixed layer. Frequently, such events are also associated with a sea surface elevation, submersion, which increase the coastal flooding risk, and rough sea that moderates the exchanges of heat, water and momentum at the air-sea interface.

The international HyMeX program (Hydrological cycle in Mediterranean Experiment, www.hymex.org) investigates the Mediterranean Sea hydrological cycle with an emphasis on the severe events that largely contribute to it [START_REF] Drobinski | HyMeX, a 10-year multidisciplinary program on the Mediterranean water cycle[END_REF][START_REF] Ducrocq | HYMEX-SOP1, the field campaign dedicated to heavy precipitation and flash flooding in the northwestern Mediterranean[END_REF]. A large part of HyMeX is devoted to the improvement of the prediction skill of highimpact hydro-meteorological events in the area, with notably the development of integrated (multi-components) forecast systems. Within this framework, the coupling between the Météo-France kilometer-scale AROME Numerical Weather Prediction (NWP) model [START_REF] Seity | The AROME-France convective-scale operational model[END_REF], the NEMO ocean model (Madec et al. 2016) and the WaveWatchIII (WW3) model [START_REF] Tolman | Validation of WAVEWATCH-III version 1[END_REF][START_REF] Tolman | User Manual and System Documentation of WAVE-WATCH III TM Version 3[END_REF] is currently developed.

As preliminary work for coupling, this study aims to investigate the representation of air-sea exchanges that occur during such events, with a focus on the role of the sea state. Several sensitivity tests to sea surface temperature (SST) and turbulent flux parametrization were run with AROME for a HPE occurring between 12 and 14 October 2016 in South-Eastern France.

SENSITIVITY EXPERIMENTS

Numerical sensitivity experiments were run with the high-resolution (1.3 km) non-hydrostatic AROME-France NWP model. The vertical grid has 90 η-levels with a first level thickness of ~5 m.

Operationally, AROME-France uses for the sea surface its own SST analysis [START_REF] Taillefer | CANARI (Code for the analysis necessary for Arpege, for its rejects and its initialization)[END_REF] that is kept constant during the forecast and the bulk iterative ECUME sea surface turbulent fluxes parametrization [START_REF] Belamari | Report on uncertainty estimates of an optimal bulk formulation for turbulent fluxes[END_REF][START_REF] Belamari | Validation of the optimal heat and momentum fluxes using the ORCA2-LIM global ocean-ice model[END_REF].

First, the sensitivity to the initial SST is investigated. For that, the SST analysis coming from the global operational analysis of Mercator-Océan

(1/12°-resolution PSY4 system, [START_REF] Lellouche | Evaluation of global monitoring and forecasting systems at Mercator Océan[END_REF]) is used instead of the AROME analysis. The sensitivity of HPE to SST in high-resolution simulations is already well documented in the literature (e.g. Rainaud et al. 2017 for AROME). So, this test serves here more as a 'gauge' for the following sensitivity tests (to the turbulent fluxes parametrization in this study, or, to interactive coupling, for example).

The second set of sensitivity experiments concerns the sea surface turbulent fluxes parametrization. First, the new version of ECUME, hereafter ECUME6 (Le Moigne 2018), is tested. The main difference is that ECUME6 uses for convergence, the three derived parameters P u 10 n , P θ 10 n , P q 10 n defined as:

P u 10 n = C D 10 n √C D10 n Δ u 10 n (1a) P θ10 n = C H 10 n √ C D 10 n Δ u 10 n (1b) P q 10 n = C E 10 n √ C D 10 n Δ u 10 n (1c)
and as polynomial functions of the neutral vertical wind gradient between the surface and 10 m Δ u 10 n , that are fitted with data collected during several campaigns (while ECUME uses a multi-campaign calibration of the neutral exchange coefficients at 10 m, i.e. polynomial functions of C D 10 n , C H 10 n , C E 10 n ). Then, the COARE 3.0 [START_REF] Fairall | Bulk parameterization of air-sea fluxes updates and verification for the COARE algorithm[END_REF], available in the surface scheme (SURFEX, Masson et al. 2012) of AROME, is used. And, finally, the innovative turbulent flux parametrization, named WASP (Wave-Age dependent Stress Parametrization), which takes into account directly the impact of the sea state, has been developed and introduced in SURFEX/AROME. The main principle of WASP is the following. The peak period T p is used to compute the Charnock's coefficient α ch :

c p = g T p 2 π ( 2
)
where g is the gravity and c p the phase speed;

α ch = A c p u * -B (3)
with u * the friction velocity, A and B coefficients depending on the first atmospheric level wind speed U a .

In the following, the peak period period T p is provided by wave model analyses or forecasts (called 'real waves' hereafter) or derived from U a (called 'ideal waves'), knowing that WASP is originally designed to be applied with a 'real waves' forcing or coupling.

In our experiments, AROME starts every day (12, 13 and 14 october 2016) at 00UTC, from ARPEGE [START_REF] Courtier | The ARPEGE project at Météo-France[END_REF] analyses and boundary conditions come every hour from the ARPEGE forecasts. Each AROME forecast duration is 42 hours.

In the latter sensitivity test, i.e. using WASP and a 'real wave' forcing, the period peak comes from WW3 simulations done in the frame of the french MARC (Modélisation et Analyses pour la Recherche Côtière) initiative at LOPS. This product has a 1/10°-resolution and is available with a three-hourly frequency.

RESULTS

In this part, all the results shown and discussed are from the forecasts starting on 13 October 2016, 00UTC.

Sensitivity to the SST

Figure 1a presents the differences between the PSY4 and the AROME SST analyses for 13 October 2016 at 00UTC. Large differences appear locally, in particular over the North-Western Mediterranean area. The PSY4 SST is higher by ~+0.5°C between the Balearic Islands and Sardinia and lower (~-1°C) in the Ligurian Sea and around Corsica. The largest differences (up to ±2°C) are associated with meanders of the North Balearic Front (NBF), which is not well represented in the AROME SST analysis. The SST differences directly impact the sensible heat flux and the latent heat flux (and evaporation), with an increase [decrease] in absolute value (up to 80W/m 2 ) over warmer [colder] sea surface (Fig. 1b). This result is robust whatever the sea surface turbulent flux parametrization used.

Comparing the Quantitative Precipitation Forecasts (QPF, Fig. 1c), large differences are found over sea related to a eastwards displacement of a first Mesoscale Convective System (MCS) occurring in the Gulf of Lion [5°E; 42°N]. Significant differences are also found over the Hérault region [2.5-3.5°E; 43-44°N] with an increase in QPF along the coast when the PSY4 analysis is used. Here, only one sea surface flux parametrization is considered (WASP with 'ideal waves'). But, the values of the differences the way the precipitating systems are moved are not similar when considering other pairs of SST sensitivity tests with the other sea surface flux parametrizations. This means that the SST has an indirect impact on precipitation through surface fluxes and several mechanisms acting notably on convection. Future work will investigate the possible involved mechanisms as the convergence, the stability and momentum mixing in the atmospheric boundary layer (ABL) and the pressure adjustment to SST anomalies.

Sensitivity to the sea surface turbulent fluxes parametrization

Figure 2 illustrates the sensible heat fluxes obtained when using the four different parametrizations described in section 2, i.e. ECUME, ECUME6, COARE 3.0 and WASP (with 'ideal waves').

Low to moderate changes are found between Sardinia and the Spanish coasts. Large modifications are obtained in the north-easterly to easterly flow over the Ligurian Sea (strong wind regime with cold and dry air at low-level). In particular, the three parametrizations ECUME6, COARE 3.0 and WASP, show a large decrease in absolute value (by 40, 80 and 100W/m², respectively) compared to ECUME, which is known to overestimate the sensible heat flux in such regime [START_REF] Rainaud | Characterization of air-sea exchanges over the Western Mediterranean Sea during HyMeX SOP1 using the AROME-WMED model[END_REF]. The same conclusions stand for the latent heat flux, i.e. generally small differences except in the strong, cold and dry 'Ligurian' easterly flow (not shown). Figure 3 shows the differences in wind stress and wind speed between simulations using ECUME and WASP parametrization. As for the heat fluxes, no significant wind stress differences are observed in the south-easterly flow. Large differences are found under the MCS [around 5.5°E-42.5°N] and the easterly flow, by more than ±0.3 N/m² for the wind stress and by more than ±3 m/s for the wind speed.

Comparing the QPF using WASP or ECUME parametrizations (Fig. 4), a strong impact is found locally over sea, with a westwards displacement of the rain bands. A lower but significant impact is also found for the inland rainfall amounts over the Hérault region (up to -80 mm in the western part and +40 mm along the coasts).

Sensitivity to the sea state: impact of the peak period of waves

In this part, we compare the two AROME forecasts both using WASP, but with a peak period as a function of the wind (hereafter 'ideal waves') or using the MARC WW3 three-hourly analyses (hereafter 'real waves'). Figure 5 illustrates the differences in the two Tp fields. In the case of 'ideal waves', large gradients and small scale patterns are obtained with the strongest Tp (>8 s) in the Ligurian Sea and the Gulf of Lion and very small Tp (<2 s) between Catalonia (Spanish coasts) and Sardinia (Fig. 5a). In the WW3 analysis, the gradients are smoother. The largest Tp are located in the north-western part and no Tp values go below 5 s (Fig. 5b). Figure 6 shows the latent (LE) and sensible (H) heat fluxes and the wind stress differences between the two simulations. The main differences appear for three areas that can be distinguish due to different causes possibly involved. In the Ligurian Sea, below the easterly flow, a decrease in absolute value of the heat fluxes is found, associated with an increased wind stress and a decrease in wind speed (about 1.5 m/s, not shown) in this area. Large differences are found below the MCS [around 5.5°E-42.5°N], possibly due to differences in the convection dynamics and the related low-level winds. For LE and wind stress, significant differences are also found in the western part of the Gulf likely related to the differences in Tp. In the Balearic Sea, large modifications of LE are found, possibly related to the large differences in Tp in the moist southerly flow.

Local changes on the QPF are seen (Fig. 7) mainly over sea. The precipitation inland seems not significantly affected by taking the sea state into account.

In fact, all the differences found between the 'ideal waves' and the 'real waves' forecasts are less important than when changing the SST or the parametrization of sea surface turbulent fluxes. Nevertheless, further investigation is needed to better attribute the processes leading to the heat fluxes and precipitation responses.

PRELIMINARY CONCLUSION AND FUTURE WORK

Several sensitivity tests were run in order to investigate the representation of the air-sea exchanges in the AROME model for the forecast of a Mediterranean HPE.

The sensitivity to the initial SST was reassessed, in particular the direct impact on the heat fluxes related to SST anomalies. Further work is now needed to identify what are the main mechanisms involved in the indirect impact on convective systems and precipitation for that case.

The choice of turbulent flux parametrization appears of great importance as large differences are found in terms of fluxes, low-level conditions and QPF. This will be now further examined through ocean -atmosphere -waves coupled simulations which ensure more consistency at the air-sea interface for the fluxes computation.

The sea state impact was finally investigated with WASP. The comparison of forecast using two different waves forcing shows significant differences related directly to difference in Tp but also some indirect effects such as modification of the low-level wind related to surface

FIG 1 .

 1 FIG 1. (a) Differences between the PSY4 and the AROME SST (°C) analyses. Differences between the forecasts using the PSY4 SST vs. the AROME SST (b) in the 24h-averaged latent heat flux (colors, W/m²) (the 24h-averaged latent heat flux in the reference forecast (using AROME SST) is indicated with contours, negative for ocean heat loss) and (c) in the 24h-cumulated rainfall amounts (mm) (the black contours indicate the 24h-cumulated rainfall amounts in the reference).

FIG 2 .

 2 FIG 2. 14 October 2016 00UTC: Sensible heat flux (H, in W/m²) in the AROME forecasts using the ECUME, ECUME6, COARE3.0 and WASP sea surface turbulent flux parametrizations. Arrows are the wind speed (m/s) at 5m above ground level.

FIG 5 .

 5 FIG 5. Peak period (Tp, in s) for 14 October 2016 00UTC: (a) for the 'ideal waves' case [Tp=f(Ua)] and (b) from the MARC WW3 product ('real waves' case).

FIG 3 .

 3 FIG 3. 14 October 2016 00UTC: Differences of wind stress (N/m²) and wind speed (m/s) between runs using ECUME and WASP parametrization.

FIG 4 .

 4 FIG 4. Differences in the 24h-QPF (mm) between runs using WASP and the ECUME parametrization -the black contours indicate the 24h-QPF in the reference (i.e. with ECUME).

FIG 7 .

 7 FIG 7. As Figure 3 but between forecasts using WASP with 'real waves' and 'ideal waves' -the black contours indicate the 24h-QPF in the simulation with 'ideal waves'.

roughness or of the MCS intensity/dynamics that must be studied in more details.


Gregory Beurier
email: beurier@lirmm.fr

Fabien Michel
email: fabien.michel@univ-reims.fr

Jacques Ferber
email: ferber@lirmm.fr

A morphogenesis model for multiagent embryogeny

This paper describes a bio-inspired method that enables the production of artificial multiagent organisms starting from a single agent. This method relies on two complementary computing approaches: (1) mimicking the functioning of segmentation genes and homeotic genes in the development of natural embryos and (2) using techniques from the evolutionary computing and the artificial embryogeny fields. The paper first details these mechanisms and then studies some possibilities of such a bio-inspired approach developing multiagent systems that evolve and self-organize in various flag patterns.

Introduction

Living systems outperform in many ways complex systems that man has produced. Seeking inspirations from these systems, several established and active research communities are organized around themes such as self-organization [START_REF] Camazine | Self-Organization in Biological Systems[END_REF], DNA computing, artificial neural networks [START_REF] Boers | Designing modular artificial neural networks[END_REF], morphogenesis [START_REF] Roggen | A Morphogenetic Evolutionary System: Phylogenesis of the POEtic Tissue[END_REF], evolutionary computation [START_REF] Koza | Introduction to genetic programming[END_REF], etc.

The problems tackled with evolutionary computation become increasingly complex and traditional approaches are becoming less efficient. In the nascent field of artificial embryogeny [START_REF] Stanley | A taxonomy for artificial embryogeny[END_REF], researchers explore new ways to outperform the classical direct mapping of evolutionary methods (from genotype to phenotype) by proposing various approaches to evolve and grow artificial organisms (indirect encoding).

This paper proposes an artificial embryogeny to explore possibilities of evolving a multiagent system (MAS) [START_REF] Ferber | Multi-Agent Systems: An Introduction to Distributed Artificial Intelligence[END_REF]). In our model, the agents behavior mimics the functioning of the segmentation genes and homeotic genes involved in the animals morphogenesis, based on the drosophila larva development model. Agents replicate and interact to construct organisms following morphogenetic rules.

The outlines of the paper are as follows: A review of some relevant works on artificial embryogeny is first presented. Secondly, a biological background is given to explain the role of segmentation and homeotic genes in the morphogenetic process. The MAS model is given in the third part:

we first define the cell-agents and then describe the way to make them evolve to construct multiagent organisms. Simulations of the model are developed and then discussed. Finally, we draw conclusions from this work.

Artificial embryogeny related works

Considering artificial embryogeny research, a clear distinction can be made between grammatical approaches and cell chemistry approaches [START_REF] Stanley | A taxonomy for artificial embryogeny[END_REF].

Using grammatical approaches, a number of researchers have studied the potential of Lindenmeyer systems (Lsystems) [START_REF] Prusinkiewicz | The algorithmic beauty of plants[END_REF] for generating Artificial Neural Networks (ANNs) which are a major challenge for artificial embryogeny. Boers and Kuiper used evolutionary algorithms to evolve the rules of L-systems that generate ANNs [START_REF] Boers | Designing modular artificial neural networks[END_REF]. Gruau abandoned Lsystems to develop a language called cellular programming based on the transformation of graphs [START_REF] Gruau | Genetic synthesis of modular neural networks[END_REF]. Cellular programming enables the controlling of the division of cells that grow into ANNs.

Grammatical approaches produce good results but do not seem to be well fitted for evolutionary processes [START_REF] Stanley | A taxonomy for artificial embryogeny[END_REF]. So, a number of researchers have managed to simulate the low-level aspect of natural embryogeny. One of the earliest works on cell chemistry approaches returns to Turing (Reaction/Diffusion) [START_REF] Turing | The chemical basis of morphogenesis[END_REF]. Turing proposed linear equations to achieve spatial differentiation, which is done by postulating two substances with mutual interaction and different spatial distribution, namely the morphogens. De Garis was one of the first to present a work based on cellular automata, cell chemistry and genetic programming [START_REF] De Garis | Artificial embryology and cellular differentiation[END_REF]. De Garis's work achieved to grow simple non-convex organisms. Moreover, de Garis extended his work to obtain convex organisms thanks to the addition of external sources of morphogens. In fact, exogenous sources of morphogens are commonly used in artificial embryogenies. For instance, Eggenberger used exogenous substances to induce a symmetry break in his digital organisms [START_REF] Eggenberger | Evolving morphologies of simulated 3d organisms based on differential gene expression[END_REF].

Fleischer and Barr [START_REF] Fleischer | A simulation testbed for the study of multicellular development: The multiple mechanisms of morphogenesis[END_REF]) developed a simulation framework for multi-cellular pattern formation including chemical diffusion. This framework also includes mechanical factors such as cell adhesion, genetic factors, etc. Fleischer and Barr showed the difficulty of maintaining the size and the shape of a multi-cellular organism and pointed out the necessity of combining multiple mechanisms in the pattern formation to guarantee the robustness of the organism. COMPUCELL 3D has been developed to simulate morphogenetic processes in different organisms and also implements phenomena such as cell growth, diffusion of chemical gradients, etc [START_REF] Izaguirre | Compucell, a multi-model framework for simulation of morphogenesis[END_REF]. COMPUCELL 3D highlighted the necessity of modeling each cell state of an organism to implement differentiation processes. Still, the morphogenesis model of COMPUCELL 3D is limited by the fact that it a priori assumes the shape of the organism as a function of time.

Inspired by the cell adhesion process, Hogeweg [START_REF] Hogeweg | Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation[END_REF] developed a model to simulate morphogenetic processes such as cell migration or engulfing. Using Boolean networks of genetic regulation, Hogeweg achieved to evolve complex artificial organisms. However, Hogeweg's model does not use morphogen gradients and cannot handle the simulation of phenomena such as chemotaxis or chemical genes regulation.

Miller developed artificial organisms based on Cartesian Genetic Programming which is an extension of Boolean networks [START_REF] Miller | Evolving developmental programs for adaptation, morphogenesis, and self-repair[END_REF]). Miller's goal is to evolve a developmental program inside a cell to create multicellular organisms. The obtained organism can be then considered as a program. Still, this method seems to be expensive in computing resources for simple problems for which developing a single program is easier.

Biological background Morphogenesis

The proposed chemical approach is a multiagent model directly inspired by the functioning of genes involved in the morphogenesis process of animals. To better describe this model, we now briefly introduce the biological concepts we will use later on.

Morphogenesis has been first studied via the observation of the alteration of the developmental process in species. At the end of the 19 th century, Bateson discovered few mutants drosophila (a fruit fly) which parts of the body were transformed into another ones. At the end of the 20 th century, Lewis discovered the genes involved in these alterations. These genes are known to be the same involved in the process of morphogenesis, the homeotic genes.

Genes are regions of DNA inheritance of living creatures. A gene basically encodes the chemical structure of a protein and the way this protein (the transcript) is produced. A protein is produced by a cell when the coding part (CP) of the gene is transcribed and translated. The transcription/translation process depends on interactions between regulatory elements (REs), which are other parts of the gene, and transcription factors which are cells internal or external molecules. The interaction process that takes place between a transcription factor and a gene is called the regulation process.

The homeotic genes encode transcription factors that control the expression of genes responsible for particular anatomical structures, such as wings, legs, and antennae. Basically, during the early phases of the development of animals, these genes are expressed within the organism to assign an identity to regions which are already established. In the case of the insects, these regions are called segments and are created by a cascade of regulations of genes, namely the segmentation genes.

Drosophila larva development model

To better understand the role of homeotic genes and segmentation genes, we will now briefly describe the early phases of drosophila larva development. For further information on this subject see [START_REF] Li | Alterations in development, behavior, and physiology in drosophila larva that have reduced ecdysone production[END_REF]. The genes that priorly act in the developmental process are already present in the egg before the embryo starts to transcribe its own genes. These maternal genes are expressed during oogenesis (production of female gamete) and they produce the mRNAs (maternal ribonucleic acids) which are stored within the egg. Initial asymmetries in the egg along the anterior-posterior axis (from head to tail) are set up by localization of mRNAs at the anterior and posterior poles of the embryo. These mRNAs are translated and diffuse through the embryo, forming two opposite long-range protein gradients (see Fig. 1.a.). These two protein gradients are transcription factors that regulate a first set of segmentation genes, the gap genes. A gene X may be active only at high concentrations of transcription factors, whereas a gene Y could also be active at lower concentrations, and therefore at a greater distance from the source of the transcription factors. It is the case for gap genes which roughly subdivide the embryo along the anterior/posterior axis (see Fig. 1.b.). The gap genes encode transcription factors that regulate the expression of a second set of segmentation genes, the pair-rule genes. The broad domains of gap gene expression are translated into a striped pattern and the embryo is divided into pair of segments (see Fig. 1.c.). Finally, the pair-rule genes encode transcription factors that regulate the expression of a third set of segmentation genes, the segment polarity genes. The segment polarity genes set the anterior/posterior axis of each segment (see Fig. 1.d.). Once established, the homeotic genes are regulated to assign each segment its own identity by regulating groups of functional/structural genes.

Proposed MAS organism model

The proposed model is a MAS based on reactive agents able to evolve and replicate. Our approach aims to closely mimic the role of segmentation genes and homeotic genes in the process of morphogenesis:

-Environment takes the role of egg/embryo, in which maternal gradients of morphogens/mRNAs are diffused.

-Agents take the role of cells and their behavior is an interpretation of a genome composed by segmentation genes and homeotic genes (behavioral genes). They are called cellagents.

Environment and information

The environment is a discretized rectangular surface (8connectivity) that primarily acts as interaction medium. Gradients of maternal morphogens are initially present to initiate the developmental process. These gradients are placed randomly or in an ad-hoc manner, depending on the organism adaptation objectives (see the evolutionary experiments section). Maternal gradients assume the role of biological mRNAs as in natural morphogenesis. An alternative to the use of an exogenous source of morphogens is discussed in the end of the paper. Nevertheless, maternal gradients are a fundamental feature of natural embryogenetic processes and must be considered when designing bio-inspired embryogenies.

The information management is comparable to a biological plain diffusion and involves equalizing the concentration of emitted proteins. The proteins diffuse at each time step according to a diffusion coefficient δ and a decay rate ρ. The physical mechanism of diffusion, when mapped onto a discrete system (space and time), may be expressed quite simply: at each time step, squares give out a fraction of the proteins they hold, in all "directions" (to each neighbor). The fraction is computed by using the diffusion coefficient δ. At the same time, the proteins also decay according to their decay rate ρ. Hence, for the simplest version of the plain diffusion algorithm, a square i that holds a quantity Φ i of a protein P, characterized by a diffusion coefficient δ p and a decay rate ρ p , will give a small fraction of P, ∆Φ i , at each time step to each of its neighbors, independently of squares, of neighbors, and of time. Each transfer of protein to a neighbor j can then be captured by the following equation:

∆Φ i→ j = (Φ i -(Φ i × ρ p )) × (δ p /8) (1)

Cell-agents

The proposed approach relies on extending classical regulatory networks [START_REF] Stanley | A taxonomy for artificial embryogeny[END_REF] by distinguishing morphogenetic interactions (segmentation genes) and functional interactions (homeotic genes). Each cellagent behavior is an interpretation of a genome composed by two types of genes: segmentation genes, which are involved in the patterning process of the organism, and homeotic/behavioral genes that encode the behavior of the agents and give the identity of the regions of the formed organism. Both homeotic/behavioral terms are used since some behaviors (such as the replicating one) are not dedicated to a particular region/segment of the organism. A gene is composed by two parts: (1) the coding part (CP) and ( 2) the regulatory elements (REs). The CP encodes the gene primary function. The REs encode the interaction properties that enable the gene regulation (as in classical artificial regulatory networks).

The CP of segmentation genes encodes protein properties. When a segmentation gene is activated, a parameterized diffusing protein is produced. The segmentation gene CP is implemented in a set of binary digits, namely a bitset. The diffusion coefficient and the decay rate of the protein are encoded in 7 bits (values ranged from 0.00 to 1.00 with a precision of one-hundredth). The CP can be easily extended to add extra properties to the produced proteins encoded in the same bitset (e.g. type, color, etc.).

In the case of behavioral genes, the CP type is related to the implemented function. Indeed, the CP works as an evolutionary computing standard tool. For instance, the CP can be a tree encoding a part of the cell-agent program (like in genetic programming [START_REF] Koza | Introduction to genetic programming[END_REF]), a bitset encoding a specific parameter/value of the cell-agent behavior (like in genetic algorithm [START_REF] Holland | Genetic algorithms and classifier systems: foundations and future directions[END_REF]), etc. For instance, we can imagine encoding the color of a cell-agent by using a set of 24 bits representing the RGB canal, or a moving behavior with simple commands encoded within a tree.

The REs encode the interaction between genes and protein gradients to enable the regulation process. The formal description of REs is inspired by the Reaction/Diffusion model [START_REF] Turing | The chemical basis of morphogenesis[END_REF] and encodes a chemical reaction involving genes transcription factors (the diffusing proteins). But, instead of encoding the chemical result of a chemical reaction, the REs encode the possibility of this reaction to appear. First of all, all the transcription factors of the gene are encoded within a bitset defining a set of transcription identifiers. The transcription factors of the gene are randomly chosen (C, B, D, A in Fig. 2). The REs second part is called the reaction part (RP) and encodes the chemical reaction itself. The RP is decomposed into equal parts representing reaction factors with each of the transcription factors. The last part encodes the reaction unit quantity, an integer that matches the perceived quantity of proteins with the reaction (as the mole unit in chemistry).

A cell-agent perceives all proteins in its square and applies the chemical reaction for all of its genes. For a given gene, the result of the reaction depends on the restricting chemical factor: let G be a gene, let H be the set of all transcription factors h of G, let F h be the reaction factor for h and Q h the quantity of h perceived. Let u be the reaction unit quantity of G. Then the reaction result r for the gene G is given by:

r = min ∀(h ∈ H), Q h u * F h (2)
The reaction result r can be interpreted in various ways. In standard reactions, if r > 1, the chemical reaction intervenes and the regulatory elements activate G: the cell-agent perceives a sufficient amount of transcription factors. If r = 0, the gene is inhibited.

The REs have been extended to perform more sophisticated tasks. For instance, a second RP can be added to inhibit the gene when r > 1. This permits to greatly increase the way a gene can be regulated but slows down the evolutionary process. Another extension deals with activation/inhibition thresholds. The quantities of perceived transcription factors may be high enough to react several times (e.g. r = 8). So, a part can be added to the REs to limit the regulation process to a certain number of reactions: under or over (or both) a threshold encoded in the gene, the CP is inhibited.

Genetic model

The evolutionary principles of the model are inspired by classical approaches of evolutionary computing. A standard evolutionary algorithm has been extended to encompass the notion of organism. Every cell-agent possesses a behavioral gene encoding the replication function (mitosis).

The evolutionary algorithm works as follows:

(1) Generate maternal gradients in the environment E.

(2) Generate a population P of cell-agents with random genomes.

(3) While (criterion not reached) { (4) Place each cell-agent of P in E and let it grow.

(5) Assign fitness to each genome of the cell-agents according to an objective function with respect to the formed organism.

(6) Select n cell-agents for reproduction with respect to the fitness of their genome.

(7) Reproduce cell-agents by taking two parents at a time and use reproduction operators on the set of genes of their genomes.

(8) Apply mutation operators on the genes of the offspring genomes.

(9) Replace old population by offspring according to replacement strategies. }

Step 1 is trivial: the generation of the maternal gradients can be done either randomly or by the simulation designer to accelerate the population convergence. In most of the cases, gradients are deposited according to symmetry axes. This phase intervenes at first in order to correctly initialize the regulatory elements of the generated genomes (transcriptions factors).

Step 2 consists in randomly generating coding parts and regulatory elements for every gene of the cell-agents. This generation can be different according to the nature of the gene (i.e. bitsets, tree of instructions, graphs of values, etc.).

Step 3: the criterion consists in reaching a pre-determined value of the fitness.

Step 4 and 5 are crucial ones. They consist in simulating each single cell-agent and evaluating the quality of the formed organism. Fitness is given by external(s) observer(s) based on the designer desiderata (task to achieve, size, color, etc.). The fitness is calculated on the formed organism but assigned to the genome of the single cell-agent that has given birth to the whole organism.

Step 6 involves selection methods of evolutionary computing and consists in choosing which cell-agents are allowed to reproduce thanks to the fitness of their genome. Several methods can be used here: Roulette Wheel Selection, Tournament Selection, Rank Selection, Boltzmann Selection, etc. [START_REF] Koza | Introduction to genetic programming[END_REF].

Step 7 consists in creating new cell-agents (with new genomes) starting from pre-selected cell-agents. The offspring are generated in the hope that they will be better than their parents (in the sense of fitness). Again, various techniques can be used depending on the type of the genes: Simple Crossing-over, Double Crossing-over, etc. (Koza, 1994).

Step 8 is used to alter genetic information on the genes of the genomes of the newly created cell-agents. This operation is used to prevent the evolutionary algorithm from stagnating at local optima.

Step 9 determines which offspring will replace old cellagents in order to generate the new population. Elitism, Steady State Replacement and CHC Selection are commonly used techniques for this purpose [START_REF] Koza | Introduction to genetic programming[END_REF].

Although this algorithm is a classical model of evolutionary programming, it has been designed to fit our embryoge-netic/organism point of view: the genomes of the cell-agents neither encode problem solutions nor methods for solving a problem, but rather encode the chemical interactions and the growth of an organism which is expected to have properties that will eventually resolve a problem from an external point of view.

Evolutionary experiments

To validate our model and evaluate its capabilities, classical artificial life experiments have been conducted creating organisms that construct flag patterns. The model has been implemented on the MAS platform MadKit [START_REF] Gutknecht | Integrating tools and infrastructures for generic multi-agent systems[END_REF] using the TurtleKit framework [START_REF] Michel | The TurtleKit simulation platform: Application to complex systems[END_REF].

Some modifications have been done to the model to ensure a faster convergence of the system. Firstly, four maternal gradients are deposited according to symmetry axes in order to bootstrap the morphogenetic process. The maternal gradients consist in linear gradients of proteins deposited from one side to the other side of the environment in arbitrary quantities (from 0 to 5000 in the presented simulations). In the drosophila larva model, these gradients are emitted by the mother during the early phase of the development according to the anteroposterior axis. Secondly, the coding parts of some genes are simplified by defining, in an ad-hoc manner, the encoded behaviors. When such genes are regulated, they directly activate the cell-agent behaviors instead of extracting these behaviors from an interpretation of the coding part of the gene.

The fitness of the organisms is calculated by an external observer-agent when the growing process stops or when the size of the organism reaches the size of the environment. This fitness is given by the observer-agent to the genome of the cell-agent which has formed the whole organism. The fitness consists in a percentage of similarity between the graphical representation of the formed organism and a predefined flag pattern. The simulation ends when an organism is at least similar at 98% to the predefined pattern. The cellagents which are eligible for reproduction are chosen via a roulette wheel selection with respect to the computed fitness. The mutation operator consists in randomly switching bits in the genes. At each new generation, the probability for a bit to mutate is 0.15%. The reproduction operator is a two-point crossover.

The French flag experiment

The French flag model of Wolpert [START_REF] Wolpert | The french flag problem: A contribution to the discussion on pattern development and regulation[END_REF]) has been the inspiration for the first task the model has to achieve. This model has already been studied by Miller [START_REF] Miller | Evolving developmental programs for adaptation, morphogenesis, and self-repair[END_REF] using CGP. The evolved organism has to grow a recognizable French flag.

To exhibit the role of maternal gradients, the first system has been implemented without segmentation genes. All the genes of the cell-agents are directly regulated by maternal gradients that are initially present in the environment. The genome of the cell-agents consists in four genes: mitosis, blue, white and red. All genes have been implemented in bitsets and the coding part simply activates a particular behavior of the cell-agents. The mitosis gene controls the replicating behavior. When the mitosis gene is activated, cell-agents replicate in the free neighbor spaces. When a color gene is activated, cell-agents take the corresponding color. By default, the cell-agents are green. Each transcription identifier of the transcription factors of the genes has been encoded in a set of 2 bits, the reaction factors of the reaction parts have been encoded in a set of 5 bits and the reaction unit quantity has been encoded in a set of 6 bits.

One hundred simulations have been made using 30 individuals as population, in a 100x100 environment. We obtained the growth of a French flag organism in all cases. We obtained the convergence of the population in an average of 250 generations. Figure 3 shows the growth of a mature French flag organism.

The Japanese flag experiment

This second experiment exhibits the role of segmentation genes in the patterning process. The genome of the cellagents consists in three genes: mitosis, segmentation and red. By default, the cell-agents are white. Each transcription identifier of the transcription factors of the genes has been encoded in a set of 2 bits, the reaction factors of the reaction parts have been encoded in a set of 5 bits and the reaction unit quantity has been encoded in a set of 6 bits. The same environment (size and maternal gradients) than in the French flag experiments has been used. It permitted us to reuse the mitosis gene of evolved French flag agents. Indeed, the mitosis gene specifically controls the size of the formed organism. So, we used a predefined Japanese flag pattern of the same size as the French flag pattern. It is a fundamental feature of the model: by reusing evolved genes, the performance of the evolution algorithm can be significantly increased and a step by step evolution is possible. Figure 4 shows the growth of a Japanese flag organism.

The formation of the red circle intervenes when (1) the

Experiments and model evaluation

Compared to other similar experiments which have been published in the literature, the obtained results are very promising. Firstly, the evolved organisms are almost equal to each predefined pattern. Secondly, these results have been achieved in a of generations which was less than expected. Finally, the Japanese flag experiment showed that it is possible to successfully reuse evolved genes within different organisms. This result has urged us to work on establishing a kind of gene library that be used to ease the design of new organisms based on the reuse of predefined/preevolved genes either (1) during the a priori design phase or (2) at runtime, directly within the evolutionary engine (manually or automatically).

A model limitation relies on the ad-hoc use of predefined maternal gradients. In fact, even if maternal gradients most likely are a fundamental feature of natural processes of morphogenesis, it would be very interesting to design organisms that do not require exogenous sources of morphogens prior to the emission of the cell-agents themselves. Considering this issue, we are currently working on applying Reaction/Diffusion techniques to define a better local control: substituting maternal gradients by the behavior of the agents. Indeed, [START_REF] Gierer | A theory of biological pattern formation[END_REF] have shown that interactions between heterogeneous gradients of morphogens can lead to symmetry breaks and polar-ity gradients formations.

Additionally, we are exploring some modifications of the reaction part of the genes: (1) we are extending the chemical reaction to transform the classical reaction factors into a polynomial function of the transcription factors, (2) this polynomial function is encoded and evolved within a node tree instead of a simple bitset. Preliminary experiments showed great improvements in the pattern refining and in the symmetry breaking of the simulated organisms.

Another way to improve the expressiveness of the model is to act on the mutation mechanisms. So, we plan to modify the mutation operators to permit modifications of the genome structure of the cell-agents. In fact, following the establishment of new sources of gradients in a pattern as a consequence of the regulation of segmentation genes, new gradients may be fired leading to more refined patterns. However, this refining may be insufficient and lead to local minima. So, we are exploring the introduction of new segmentation genes during the evolution process to ensure a better refining of complex organisms.

Conclusion

We have presented and discussed a bio-inspired developmental model of multiagent organisms. This model is an artificial embryogeny closely inspired by the morphogenetic process and is implemented using the multiagent paradigm. The evolved entities are reactive agents sensitive to protein gradients. The system has been simulated to exhibit its capabilities in evolving complex organisms.

Perspectives of such a work are numerous, but we are actually interested in three issues. The first one deals with multiagent systems design. We plan to construct swarm organisms giving the cell-agents low-level functions, enabling them to resolve simple tasks which require distributed resolution. Another interesting long-term perspective deals with data encryption and data compression. It can be interesting to consider predefined patterns of organisms as a data to compress or to encrypt. Evolved genomes would be thus considered as compressed data which have to evolve to be readable. In the same way, we can imagine to encrypt data in a genome. Then, the relevant key to decrypt data could be either the environment properties or the behavior of the agents.

Finally, we are very interested in refining our inspirations from biological processes. In a general way, the artificial embryogeny field can help in increasing knowledge on the mechanisms of complexity appearance in natural organisms. Seeking inspirations in these mechanisms can greatly contribute in designing complex systems. Indeed, Bentley and Kumar demonstrated that an evolutionary approach of embryogeny provides significant benefits to evolve complex solutions in evolutionary computation [START_REF] Kumar | Computational embryology: past, present and future[END_REF].

Figure 1 :

 1 Figure 1: A cascade of gene activation in the drosophila larva development.

Figure 2 :

 2 Figure 2: Example of regulatory elements.

Figure 3 :

 3 Figure 3: fittest program from a single cell-agent to a mature French organism.

Figure 4 :

 4 Figure 4: Growth of fittest program from a single cell-agent to a mature Japanese flag organism.