Christophe Gigot

Claude De Vallavieille-Pope

Marc Leconte

Claude Maumené

Laurent Huber

Sébastien Saint-Jean
email: sebastien.saint-jean@agroparistech.fr

Using 3D virtual plants to evaluate the canopy role in the progression of a splash-dispersed crop disease: a case study based on wheat cultivar mixtures

Keywords: cultivar mixture, splash dispersal, septoria tritici blotch, wheat, modelling, heterogeneous canopy

Highlights:

A model taking into account physical mechanisms involved in splash dispersal of pathogens and host cultivar quantitative resistance has been developed to study the potential of heterogeneous threedimensional crop canopies such as cultivar mixtures to prevent disease progression. We investigated different spatial organizations, proportions and resistance levels of wheat cultivars mixtures to allow better control of septoria tritici blotch.

INTRODUCTION

Increasing plant diversity within a crop by the use of cultivar mixtures is a strategy, that reduces severity of wind-borne diseases [START_REF] Wolfe | The current status and prospects of multiline cultivars and variety mixtures for disease resistance[END_REF][START_REF] Finckh | Plant competition and disease in genetically diverse wheat populations[END_REF][START_REF] Hau | Wind-dispersed diseases[END_REF]. The interest of cultivar mixture practice for the case of rain-borne diseases was controversial. Depending on the study, results are inconsistent, for example previous studies showed rather significantly benefits for reducing splash dispersed diseases [START_REF] Jeger | Disease progress of non-specialised fungal pathogens in intraspecific mixed stands of cereal cultivars. I. Models[END_REF][START_REF] Mundt | Choosing crop cultivars and cultivar mixtures under low versus high disease pressure: A case study with wheat[END_REF][START_REF] Mille | Influence of varietal associations on the development of leaf and glume blotch and brown leaf rust in winter bread wheat[END_REF][START_REF] Mille | Assessing Four-Way Mixtures of Winter Wheat Cultivars from the Performances of their Two-Way and Individual Components[END_REF] or rather non-significant effects [START_REF] Cowger | Effects of Wheat Cultivar Mixtures on Epidemic Progression of Septoria Tritici Blotch and Pathogenicity of Mycosphaerella graminicola[END_REF]. Septoria tritici blotch (STB), is one of the predominant foliar rain-born diseases on wheat crops caused by the fungus Mycosphaerella graminicola, and is regularly responsible for substantial yield losses up to 40% [START_REF] Oste | Bilan phyto-sanitaire de la campagne 1998/99[END_REF]. Findings of [START_REF] Mille | Assessing Four-Way Mixtures of Winter Wheat Cultivars from the Performances of their Two-Way and Individual Components[END_REF], show the interest of using wheat cultivar mixture to control STB. Recently [START_REF] Gigot | Protective effects of a wheat cultivar mixture against splash-dispersed septoria tritici blotch epidemics[END_REF] confirmed consistent reduction depending on disease pressure of STB disease severity by the use of cultivar mixture over four years. In this last study, it is also discussed that better control of STB should occur for specific proportions and resistance differences of wheat cultivar mixture of susceptible and resistant components. [START_REF] Newton | The effect of component number on Rhynchosporium secalis infection and yield in mixtures of winter barley cultivars[END_REF] also confirmed that for the splash-dispersed Rhynchosporium secalis on barley, increasing the number of components brought more benefits on disease control. Therefore, to take full advantage of cultivar mixtures, the design of cultivar mixture needs improvement. Relying only on experimental knowledge can be tedious and time-consuming, for example [START_REF] Mille | Assessing Four-Way Mixtures of Winter Wheat Cultivars from the Performances of their Two-Way and Individual Components[END_REF] had to test experimentally two component mixtures two by two for providing an optimal four components mixture.

We propose here to rely on modelling, to enhance and speeding up the process of designing efficient wheat cultivar mixtures on the control of STB. We investigated different mixture compositions such as spatial organizations, proportions and resistance levels. To do so, such model should at least take into account splash dispersal of spores and the inherently heterogeneous canopy properties of the cultivar mixtures [START_REF] Calonnec | Impacts of plant growth and architecture on pathogen processes and their consequences for epidemic behaviour[END_REF]. Because the spores are dispersed at short distances, due to the splashing mechanism from 0 to 20 cm [START_REF] Fitt | The role of rain in dispersal of pathogen inoculum[END_REF][START_REF] Huber | Environmental biophysics applied to the dispersal of fungal spores by rainsplash[END_REF], and plant organs of different resistant types, are spatially heterogeneous, it leads to consider a spatial scale less than 1 cm for modelling dispersal. To reach such requirement, one solution is to describe the physical scene with the help of virtual three dimensional plants [START_REF] Fournier | ADEL-Wheat: a 3D Architectural Model of wheat development[END_REF], as it has been used for light interception computations (e.g. [START_REF] Chelle | The Nested radiosity model for the distribution of light within plant canopies[END_REF].

MODEL DESCRIPTION

Here, we propose to focus on physical mechanisms involved in splash dispersal of a non-specialised pathogen within heterogeneous canopies of cultivar mixtures. For this purpose, we developed a framework that takes into account different mechanistic and stochastic models [START_REF] Saint-Jean | Role of rain-splash in the progress of Septoria leaf blotch within a winter wheat variety mixture[END_REF][START_REF] Gigot | Potentialités des associations de variétés pour limiter la progression épidémique de la septoriose du blé : rôle des mécanismes de dispersion des spores par la pluie dans un couvert végétal hétérogène[END_REF], including (i) the 3D spatial localization of wheat plant organs of at least two cultivars (periodic boundary conditions have been applied to simulate an infinite canopy); (ii) the calculation of droplet population dispersal based on Monte Carlo integration (Saint-Jean et al. 2004) within a 3D virtual scene; (iii) from this set of trajectories, the potential progression pattern of septoria tritici blotch is assessed on the whole canopy under several assumptions of cultivar resistance levels of the intercepted surfaces; (iv) the polycyclic nature of epidemics, forced by the rainfall occurrences, is modelled by iterating the previous calculations.

RESULTS AND DISCUSSION

Disease progression was computed for different wheat canopies. Highly susceptible pure stand, a moderately resistant pure stand, highly resistant pure stand and an equi-proportion mixture of the previous components have been tested. For those sets of canopies, initial inoculum was set at the fourth leaf (from the top) to 10% of leaf surface diseased. Three cycles of disease progression, i.e. pathogen generations or rain events, were computed. Evolution of disease severity (i.e. proportion of diseased surface over total leaf surface) was calculated on each leaf depending on their localisation in the canopy, level of resistance and the amount of the disease at the previous cycle. Here, we summed the disease of all the leaf levels of a plant to compute the progression of the disease at the canopy scale (Fig. 1). As it is expected, the more susceptible the cultivar is, the faster the disease progression is (Fig. 1). Comparatively to the mean of the pure stands, the progression of disease potential within the mixture was globally reduced by 35% after three dispersal cycles (Fig. 1). Such order of magnitude of disease reduction has been confirmed in field experiments [START_REF] Gigot | Protective effects of a wheat cultivar mixture against splash-dispersed septoria tritici blotch epidemics[END_REF]. Increasing both differences between resistance levels and proportion of the more resistant cultivar resulted generally in a higher expected protective effect against the pathogen. Nevertheless, this rule was not observed for very high proportions of a rather resistant cultivar. Our results illustrate that (i) mixture efficiency against a splash dispersed fungus may evolve differently across the successive pathogen generations, and (ii) optimal cultivar proportions can be established depending on resistance levels. Mixture component characteristics have to be precisely considered to find a compromise in terms of diversity within the field. Therefore such modelling approaches could be used for the design of cultivar mixture in order to find optimal and complementary properties of the mixture in order to integrate protective effects against splash-dispersed diseases among other beneficial properties of cultivar mixtures.

Fig. 1 .

 1 Fig.1. Disease progression within a wheat cultivar mixture for 4 wheat canopy types (from top to bottom, highly susceptible pure cultivar; moderately resistant pure cultivar; highly resistant pure cultivar and three cultivar mixture in equi-proportion of the previous cultivars). Grey scale represents from light to darker the resistance scale. Colour scale (from green to red) represents the increasing potential of disease severity.

ACKNOWLEDGMENTS

This work received financial support from the French Ministry of Agriculture (contract CTPS C032010) and from "Fondation pour la Recherche sur la Biodiversité-LU" ("Les Champs de Biodiversité"). Managed by the ANRT (Association Nationale de la Recherche Technique), the PhD grant of Christophe Gigot was cofinanced by ARVALIS -Institut du Végétal and the French Ministry of Research and Education.

LITERATURE CITED


Thomas Moulard
email: thomas.moulard@aist.go.jp

Eiichi Yoshida
email: e.yoshida@aist.go.jp

Shin ' Ichiro Nakaoka

Mvelocity,MtorqueMlimits M- M-Mlinkmlength M-Mjointsmposition

Optimization-based Motion Retargeting Integrating Spatial and Dynamic Constraints

In this paper, we present an optimization-based retargeting method for precise reproduction of captured human motions by a humanoid robot. We take into account two important aspects of retargeting simultaneously: spatial relationship and robot dynamics model. The former takes care of the spatial relationship between the body parts based on "interaction mesh" to follow the human motion in a natural manner, whereas the latter adapts the resulting motion in such a way that the dynamic constraints such as torque limit or dynamic balance are being satisfied. We have integrated the interaction mesh and the dynamic constraints in a unified optimization framework, which is advantageous for generation of natural motions by a humanoid robot compared to previous work that performs those processes separately. We have validated the basic effectiveness of the proposed method with a sequence of postures converted from captured human data to a humanoid robot.

I. INTRODUCTION

One of the advantages of human-size humanoid robots is its ability to generate whole-body motions maintaining similar dynamics to humans. This ability allows a humanoid robot to serve as an entertainer like a dancer of an actor [START_REF] Nakaoka | Intuitive and Flexible User Interface for Creating Whole Body Motions of Biped Humanoid Robots[END_REF], or also to use various machines and devices designed for humans [START_REF] Yokoi | A tele-operated humanoid robot drives a backhoe[END_REF]. As an extension of the latter use, a new application has recently been studied: a humanoid robot as an evaluator of human assistive devices [START_REF] Ogura | Development of a new humanoid robot WABIAN-2[END_REF], [START_REF] Miura | Humanoid robot as an evaluator of assistive devices[END_REF]. If a humanoid reproduces human motions faithfully, it can be used to test the devices instead of human subjects. This brings several benefits such as no need for ethical process, repeated test with exactly the same motions under the same conditions, and qualitative evaluation through sensory measurement like torque and force. It has been demonstrated that the humansize humanoid HRP-4C [START_REF] Kaneko | Cybernetic human HRP-4C[END_REF] can evaluate the effect of load reduction quantitatively by estimating motor torque [START_REF] Miura | Humanoid robot as an evaluator of assistive devices[END_REF], taking an example of a supportive wear called "Smart Suit Lite" [START_REF] Imamura | Motion-based-design of elastic material for passive assistive device using musculoskeletal model[END_REF] designed to reduce load at the lower back with embedded elastic bands.

The important issue in those applications is how to generate natural motions of a humanoid robot. There have been a number of studies on "motion retargeting" techniques in order to generate humanoid motions based on those of a human measured by a motion capture system. Retargeting captured motion to humanoids has been actively studied during the last decade, thanks to the progress of their dynamic capability. The work of Pollard [START_REF] Pollard | Adapting human motion for the control of a humanoid robot[END_REF] is one of the pioneering studies that enable reproduction of human motions by a humanoid, in this case the upper body of Sarcos humanoid robot, by taking into account various constraints. Nakaoka et al. developed a technique to transfer Japanese traditional dancing motions to a humanoid by introducing a notion of leg task model [START_REF] Nakaoka | Leg Motion Primitives for a Dancing Humanoid Robot[END_REF], [START_REF] Nakaoka | Learning from Observation Paradigm: Leg Task Models for Enabling a Biped Humanoid Robot to Imitate Human Dances[END_REF]. Miura et al. [START_REF] Miura | Human-like walking with toe supporting for humanoids[END_REF] devised a walking pattern generator that allows the humanoid robot HRP-4C to walk in a manner extremely close to humans, including stretched knees, swingleg trajectory and single support phase on the toe. Other imitation methods have been proposed based on a dynamic controller [START_REF] Yamane | Controlling humanoid robots with human motion data: Experimental validation[END_REF], [START_REF] Ramos | Dynamic motion capture and edition using a stack of tasks[END_REF], motion recognition and primitives [START_REF] Ott | Motion capture based human motion recognition and imitation by direct marker control[END_REF] and extraction of upper-body motion from markerless motion input [START_REF] Dariush | Online and markerless motion retargeting with kinematic constraints[END_REF], [START_REF] Do | Imitation of human motion on a humanoid robot using non-linear optimization[END_REF].

On the other hand, motion retargeting has been investigated intensively in computer graphics domain, typically to generate motions for new characters based on motion capture data using space-time constraints solver [START_REF] Gleicher | Retargetting motion to new characters[END_REF]. Recently, Ho et al. proposed a new retargeting method called "interaction mesh" that preserves the spatial relationship between closely interacting body parts and objects in the environments [START_REF] Ho | Spatial relationship preserving character motion adaptation[END_REF]. Nakaoka and Komura extended this method for retargeting to a humanoid robot by taking advantage of its capacity to adapt motions to a character with highly different physical properties [START_REF] Nakaoka | Interaction mesh based motion adaptation for biped humanoid robots[END_REF]. Usage of interaction mesh brings natural following of original human motion and self-collision avoidance. Although this method includes balance consideration by shifting the waist, this approach remains specific instead of general whole-body motion optimization and does not deal with dynamic constraints such as torque limits. In addition, those constraints are treated separately after generating retargeted motion to adapt to the humanoid.

Another related domain is the optimization technique that is more and more employed to generate robot trajectories minimizing certain cost function under mechanical or dynamic constraints. Miossec et al. applied nonlinear optimization to dynamic whole-body motion like a kicking motion of a human-size humanoid [START_REF] Miossec | Development of a software for motion optimization of robots -application to the kick motion of the hrp-2 robot[END_REF]. Recently the optimization is utilized for generation of multi-contact dynamic motion through modeling of dynamic constraints using Taylor expansion [START_REF] Lengagne | Generation of whole-body optimal dynamic multi-contact motions[END_REF]. For dynamic trajectory optimization for digital human, an efficient algorithm has been proposed [START_REF] Tassa | Synthesis and stabilization of complex behaviors through online trajectory optimization[END_REF], [START_REF] Erez | Trajectory optimization for domains with contacts using inverse dynamics[END_REF]. Suleiman et al. proposed another trajectory optimization technique based on Lie algebra that allows efficient computation through analytic integration of dynamics [START_REF] Suleiman | On humanoid motion optimization[END_REF] and applied it to human motion imitation [START_REF] Suleiman | On human motion imitation by humanoid robot[END_REF]. The latter research aims at optimizing the humanoid trajectory to be as close as human motion, but self-collision avoidance is incorporated as a post-processing to the optimized motion like previous work

Post-processing

MotionMconversionMtoM robot jointMtrajectory Fig. 1. The two step retargeting process. The final inverse kinematics step is only here to convert the final motion to joints trajectory. [START_REF] Nakaoka | Interaction mesh based motion adaptation for biped humanoid robots[END_REF]. This is disadvantageous because separate application of collision avoidance may lead to unnatural motions.

Methods in previous research are, therefore, still lacking the capability to optimize humanoid motions by taking into account the associated problems for retargeting in a unified manner. The main contribution of the paper is the optimization process integrating retargeting, dynamics constraints and self-collision at the same time, in order to create the humanoid motion as close to human motions as possible. In this paper, we address this retargeting by formulating it as a nonlinear optimization problem under spatial and dynamic constraints. First, the captured motion is pre-processed to provide better initial guess for the optimization. Then the full optimization problem is solved considering the spatial relationship and dynamic robotic constraints simultaneously. The spatial relationship between body parts of captured motion is reserved by using interaction mesh as introduced by [START_REF] Ho | Spatial relationship preserving character motion adaptation[END_REF], which achieves self-collision avoidance in consequence.

This paper is organized as follows. Section II describes the overall method and in particular how the retargeting is performed. Section III describes the details of each step of the optimization-based retargeting method. Section IV introduces RobOptim, an optimization framework for robotics used to implement the proposed method. Section V presents the results of retargeting with validation of dynamic simulations, before concluding the paper.

II. METHOD OVERVIEW

The proposed retargeting framework consists of three steps as shown in Fig. 1 and takes a time series of captured marker positions to generate a retargeted robot joint trajectory. The main part of the retargeting is the second step, which is the main optimization process whereas the first and last steps are additional data processing for efficient optimization and motion conversion respectively.

The first pre-processing takes care of initial guess for the optimization. It takes care of retargeting problem only to fit the marker positions to the target robot structure, to obtain the initial state that helps the optimization process converge quickly. This geometric problem can be represented as a linear problem using the interaction mesh [START_REF] Ho | Spatial relationship preserving character motion adaptation[END_REF] with a quadratic cost rendering its resolution extremely efficient.

The main optimization process is initialized using the result of the first step and then takes the full problem into consideration. This optimization incorporates robotic constraints such as motion balance and torque constraints together with the spatial relationship modeled also by interaction mesh. The previous work [START_REF] Nakaoka | Interaction mesh based motion adaptation for biped humanoid robots[END_REF] adopts a twostep approach for this optimization: first the markers were optimized before adapting the motion by optimizing joint angles for the robot in order to satisfy robotic constraints. In contrast, in the proposed method the optimization variables are the marker position throughout the retargeting process until it is converted to joint angles at the last step. This is advantageous to make the constraint matrix sparse [START_REF] Ho | Spatial relationship preserving character motion adaptation[END_REF] and also to maintain a global optimization framework unifying all the constraints simultaneously. Inverse kinematics computation of the target robot is employed in order to estimate the nearest robot configuration from the marker positions at each time step. This allows evaluating robotic constraints such as dynamic balance or joint torque limit by using deduced joint velocity and acceleration. The robotic constraints being non-linear, this main optimization problem is much more computationally intensive.

The third post-processing step is conversion of the resultant marker positions into the robot joint configurations that is done in a straightforward manner using inverse kinematics. Fig. 2. Examples of interaction mesh representing the spatial relationship between body parts, applied to a digital character and a humanoid [START_REF] Nakaoka | Interaction mesh based motion adaptation for biped humanoid robots[END_REF].

III. OPTIMIZATION-BASED RETARGETING METHOD

As described in the previous section, our retargeting method has two main components: motion retargeting and robotic motion generation that are integrated in the optimization. This section will detail their computational aspects.

A. Motion retargeting

The retargeting algorithm employed in the first two steps in the framework of Fig. 1 relies on the notion of "interaction mesh" to ensure that spatial relationship between bodies is preserved. We will briefly describe how it is incorporated in the optimization based on previous work by Ho et al [START_REF] Ho | Spatial relationship preserving character motion adaptation[END_REF].

By applying Delaunay Tetrahedralization [START_REF] Si | Meshing piecewise linear complexes by constrained delaunay tetrahedralizations[END_REF] on the marker set, one can generate a mesh which is parameterized by the marker positions

V i = (p i 1 • • • p i m )
where 1 ≤ i ≤ n. n denotes here the number of frame composing the motion and m the number of markers in each frame. p i 1 represents the position of the first marker in the i-th frame.

Given a particular interaction mesh, one can compute the "Laplacian Coordinate" of one marker as follows:

L(p i j ) = p j i - l∈Nj w j l p i l (1)
In Eq. ( 1), N j is the one-hop neighborhood of the marker j in the interaction mesh and w j l is the weight of the marker l when computing the Laplacian Coordinate of marker j. This weight is inversely proportional to the distance between j and l.

Considering these two notions, it is possible to introduce the "Laplacian Deformation Energy" associated to a marker set which serve as a cost function in this problem:

E L (V ′ i ) = j ||L(p i j ) -L(p i j ′ )|| 2 (2)
The Laplacian Deformation Energy is the square of the norm of the difference between the Laplacian Coordinates of the original marker set and the updated marker set

V ′ i = (p i 1 • • • p i m ).
In practice, this cost function penalizes motion of highlyconnected markers whereas isolated ones will move for a lower cost.

A second cost function is added to the first one to smooth the motion. To achieve this goal, the marker set acceleration energy is considered:

E A (V ′ i-1 , V ′ i , V ′ i+1 ) = 1 2 ||V ′ i-1 -2V ′ i + V ′ i+1 || 2 (3) V ′ i-1 , V ′ i , V ′ i+1
being the new marker set position for the frame i -1, i and i + 1. Acceleration energy is always null for first and last frame.

The final cost function C is by consequence expressed by:

C(V ′ i-1 , V ′ i , V ′ i+1 ) = E L (V ′ i ) + αE A (V ′ i-1 , V ′ i , V ′ i+1 ) (4)
where α is the weighting coefficient. Additionally, a link length constraint is defined. This constraint aims at retargeting the motion so that it fits the robot morphology. It is defined as follows:

||p 1 e -p 2 e || 2 = l e (5)
Whenever there is a need for some part of the robot body to stay fixed, an optional positional constraint is also provided through an equality constraint:

V ′ i = P i (6) With 0 ≤ i ≤ m.
The quadratic problem is then solved to generate a new set of marker positions. The goal of the first pre-processing step in Fig. 1 is to obtain the marker positions that fit the robot structure sufficiently well. Of course, the resulting motion may still not be feasible due to physical constraints. The output marker positions from the pre-processing is used as the initial guess for the main optimization process considering robotic constraints and retargeting at the same time, as explained in the next subsection.

B. Robotics motion generation

We here define a non-linear optimization problem using the motion derived with the pre-processing. The same optimization variables, namely the set of marker positions, are used also with the cost function and the constraints introduced in the previous section. By keeping the previous constraints, one can make sure that the good properties ensured by the previous pre-processing are kept during this optimization step. Moreover, the constraint matrix can be kept sparse by using the marker positions as optimization variables [START_REF] Ho | Spatial relationship preserving character motion adaptation[END_REF], which makes the optimization computation efficient, whereas the joint Jacobian matrix for the robot is dense.

To ensure that the motion is feasible by the robot, two additional constraints are added in the main optimization process:

• Dynamic balance constraint.

• Joint angle, velocity and torque constraints. We here need robot configuration q from the marker positions to calculate the following constraints with dynamic property like mass and moment of inertia of each link. Since the output marker positions from the pre-processing are close enough to the feasible robot configuration, we can benefit from the joint angle fitting using damped least square method introduced in [START_REF] Nakaoka | Interaction mesh based motion adaptation for biped humanoid robots[END_REF]. Figure 3 shows the kinematic structure of the humanoid HRP-4C [START_REF] Kaneko | Cybernetic human HRP-4C[END_REF] the proposed retargeting is applied to. Once the robot configurations are obtained, the following constraints are evaluated on the numerical basis, by using joint velocity and acceleration computed with finite difference.

The first constraint constrains the ZMP (zero moment point) position so that it stays into the robot support polygon: where (x ZM P , y ZM P ) is the ZMP position on the ground with the coordinate system shown in Fig. 3, σ the variation of the kinetic momentum around the center of mass, and (x G , y G , z G ) the center of mass position. The gravitational constant is denoted by g. Here we assume that the robot is moving on a flat floor. The ZMP acts as a criterion that allows deciding whether a motion can be executed stably or not. As long as it stays inside the convex hull of the robot contact points with the floor, the motion is dynamically stable. Knowing which foot of the robot is in contact with the floor and the foot geometry, it is possible to insert this as an inequality constraint (x ZM P , y ZM P ) ⊂ S(x rf oot , y lf oot ) [START_REF] Nakaoka | Leg Motion Primitives for a Dancing Humanoid Robot[END_REF] to make sure that the ZMP is staying inside the current support polygon, denoted by S(x rf oot , y lf oot ) that is determined by the right and left positions (x rf oot , y lf oot ).

x ZM P = x G -σy + m z G ẍG m (z G +g) y ZM P = y G + σx -m z G ÿG m (z G +g) (7)
The second robotic constraint we take into account in this problem is the joint limitations. Given (q, q, q), the set of torques τ = (τ 1 , • • • , τ o ) applied to each robot joint can be computed using the classical equation of motion:

M(q)q + C(q, q) + G(q) = τ (9)
where M(q) is the system mass matrix, C(q, q) is the vector of Coriolis and centrifugal forces and G(q) the vector of gravitational forces. Other robotic constraints for limits of joint rotation, velocity and torque are expressed as:

q min ≤ q ≤ q max dq min ≤ q ≤ dq max τ min ≤ τ ≤ τ max (10)
As mentioned earlier, the output of the main optimization process is the set of marker positions. As we have already applied the robotic constraints, the resultant motion can be easily converted to the joint trajectory to be executed by the robot through inverse kinematics.

IV. IMPLEMENTATION OF THE OPTIMIZATION PROBLEM USING ROBOPTIM

RobOptim is a general framework to assist the development and resolution of optimization problems applied to robotics. The optimization is more and more applied to robotics field to solve complex problems of motion planning and generation with many constraints, as mentioned earlier.

Although number of state-of-the-art optimization solver tools and libraries are now available, they are not necessarily ready for immediate use for robotics.

RobOptim has been developed to allow roboticists to prototype their optimization applications easily by providing necessary interfaces specific to robotic problems in the form of C++ libraries. It has a three-layer architecture: the core, the solver and the application layers. The core layer provides a way to define mathematical function and their associated derivatives, while the solver layer encapsulates different state-of-the-art solvers so that they can solve problems defined using the representation proposed by the core layer. The application layer contains dedicated mathematical functions which can be embedded into different optimization problems. An overview of the framework architecture is shown in Fig. (4).

The core layer offers some useful higher-level tools that help users define the functions such as costs and constraints introduced in the previous section. By implementing those functions inherited from the basic mathematical functions of the core layer, RobOptim ensures the compatibility with a number of state-of-the-art solvers whose plug-ins are provided in the solver layer. Those tools include function definition itself and also differentiation of the functions that can be computed analytically, or numerically when no analytical gradient is provided by the user. Even if the gradient is provided, numerical differentiation can be used to ensure the computation correctness. The user can benefit from the transparency of those higher level tools to prototype their problem without thinking about individual solvers used for optimization.

Although not really utilized in our problem of retargeting, the application layer is convenient especially for planning purpose. One of the practical tools is the trajectory toolbox, which allows representation of robot motion using B-spline. Since these are associated with mathematical functions of the core layer and others like of minimal-time optimization.

RobOptim is distributed as an open-source library (LGPL-3) through its website: http://www.roboptim.net/ V. RETARGETING RESULTS

The proposed algorithm has been applied to a whole body motion taken from CMU motion capture database [START_REF]Carnegie mellon university motion capture database[END_REF]. We have integrated a RobOptim plug-in for nonlinear optimization tools of NAG optimization library [START_REF]Numerical algorithms group[END_REF] to solve the problem while using sparse matrices computation. This is particularly useful for trajectory optimization where large matrices are involved as some constraints are only considering one frame and thus associated Jacobian are containing a large proportion of null values. In order to validate its basic capacity of dynamic constraint consideration, we have applied the proposed method to a sequence of several human postures to be converted into stable humanoid configurations. In this validation we use the Laplacian Deformation Energy E L in Eq. ( 2) only with α = 0 in Eq. ( 4), with dynamic balance constraint with ZMP of Eq. ( 7). The support polygon S(x rf oot , y lf oot ) for the stability is the square of 15 cm around the center of feet.

The result after the optimization process is illustrated by Fig. 5 (pre-processing) and Fig. 6 (final result). In Fig. 5 we can observe that the markers positions are displaces to fit to the robot whose size is much smaller than the digital character. In the optimized posture in Fig. 6(b), the configuration is modified so that robotic constraints such as joint limits or link length can be satisfied. We also verified the dynamic balance during the motion sequence by computing the resultant ZMP as shown in Fig. 7. As can be seen, the ZMP stays inside the support polygon of the area ±7.5 cm along each x and y axis as specified in the constraints. Although the profile in Fig. 7 is a bit shaky as we have not yet integrated Acceleration Energy E A in Eq. ( 3), the balance constraint itself is satisfied. We therefore believe that more smooth trajectory will be obtained as the optimized trajectory by taking account Acceleration Energy.

VI. CONCLUSION

This paper presented a unified approach combining retargeting and robotics constraints into one single nonlinear optimization problem. For efficient computation, a three-step approach is adopted including pre-and post-processing of the motion. After obtaining pre-processed marker positions approximately fitted to the robot structure, the main optimization process generates also marker motions that respect the original spatial relationship of body parts as much as possible based on interaction mesh, by satisfying the robotic dynamic constraints throughout the motion. The optimization output motion can be converted to the robot trajectory in a straightforward manner by the last step. The fundamental effectiveness of the proposed method has been validated by converting a sequence of human postures into humanoid configurations by minimizing the cost of spatial relationship with robotic constraints.

Future work includes extensions to take into account different cost functions such as human-likeliness, or additional constraints such as collision avoidance or others depending on the task of the humanoid. Application to walking motion retargeting will also be addressed in future work.

Fig. 3 .

 3 Fig. 3. Humanoid robot HRP-4C and its structure.

Fig. 4 .

 4 Fig. 4. RobOptim architecture.

Fig. 5 .Fig. 6 .

 56 Fig.5. The marker set before (purple markers) and after (white markers) the initial preprocessing phase.

Fig. 7 .

 7 Fig. 7. ZMP values during the motion sequence of 10 frames.

ACKNOWLEDGMENT

This research was partially supported by the Japan Society for the Promotion of Science (JSPS; Grant-in-Aid for JSPS Fellows P12803).


Patrice Salzenstein
email: patrice.salzenstein@femto-st.fr

Vitaly B Voloshinov

Arseniy S Trushin

Investigation in acousto-optic laser stabilization for crystal resonator based optoelectronic oscillators

Keywords: Integrated optics, acousto-optics, optoelectronics, oscillators, engineering, micro-optics

Potentialities are investigated for using acousto-optic cells based on a TeO 2 crystal to stabilize a microwave signal generated by an optoelectronic oscillator (OEO). Bulk acoustic waves at two radio frequencies (RF) near 60 MHz are launched in the two identical cells providing a required locking on of a microwave signal. Differences between RF signals are up to 400 kHz to follow quality factor of the optic resonator typically in the range of 5x10 8 . Critical alignment of the two cells is performed thanks to an extraordinary polarized laser beam launched at very low Bragg angle of light incidence. Moreover, the system is operating for any resonator to be inserted into the optoelectronic oscillator with a Q factor in the range 2x10 7 -10 11 .

Introduction

In order to improve stability of an optoelectronic oscillator (OEO) based on an optical resonator [1][START_REF] Ilchenko | High-Q microsphere cavity for laser stabilization and optoelectronic microwave oscillator[END_REF][START_REF] Volyanskiy | Compact Optoelectronic Microwave Oscillators using Ultra-High Q Whispering Gallery Mode Disk-Resonators and Phase Modulation[END_REF][START_REF] Tavernier | Magnesium Fluoride Whispering Gallery Mode Disk-Resonators for Microwave Photonics Applications[END_REF][START_REF] Schliesser | Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators[END_REF][START_REF] Chiasera | Spherical whispering-gallery-mode microresonators[END_REF][START_REF] Maleki | The optoelectronic oscillator[END_REF], it is necessary to stabilize optical frequency of the input laser at 1.55 µm. Although Pound-Drever-Hall technique [START_REF] Drever | Laser phase and frequency stabilization using an optical resonator[END_REF][START_REF] Black | An introduction to Pound-Drever-Hall laser frequency stabilization[END_REF] can be used for the purpose, we investigate in this work the opportunity of using acousto-optic cells (AOC) based on a paratellurite TeO 2 crystal [START_REF] Voloshinov | Acousto-optic cell based on paratellurite crystal with surface excitation of acoustic waves[END_REF][START_REF] Gupta | Optical transmission of single crystal tellurium for application in acousto-optic cells[END_REF][START_REF] Bechtold | Analytic and experimental investigations on influence of harmonic generation on acousto-optical modulation[END_REF] to stabilize the microwave signal generated by the OEO. Although Acousto-optic modulator was already proposed for frequency stabilization of a diode laser system for atom trapping [START_REF] Mcdowall | Acousto-optic modulator based frequency stabilized diode laser system for atom trapping[END_REF], to our knowledge, it is the first time that it was proposed the use of AOC pairs for OEO stabilization. Bulk acoustic waves at two radio (RF) frequencies near 60 MHz are launched in the two identical cells providing a required locking of the microwave signal. For an optical resonator with quality factor of the order 2x10 7 -10 11 , the difference between the two RF signals should be varied from 2 kHz to 10 MHz as it is explained in section 4. In our case [START_REF] Voloshinov | Acousto-optic cell based on paratellurite crystal with surface excitation of acoustic waves[END_REF][START_REF] Gupta | Optical transmission of single crystal tellurium for application in acousto-optic cells[END_REF], an extraordinary polarized laser beam on the cells ultrasound is sent at Bragg angle of light incidence corresponding, at the RF frequency 60 MHz, to a deflector regime of the cells operation. It helped to perform a critical alignment of the two cells. To generate radio frequency (RF) signals, a Voltage Controlled Oscillator (VCO) is locked to a micro-controller following the microwave frequency generated by the OEO.

Operation of the optoelectronic oscillator

An OEO is generally an oscillator based on an optical delay line and delivering a microwave signal [1]. This delay line is equivalent to an optical resonator with a quality factor Q=2πFT where F is the microwave frequency and T the delay induced by the delay line [START_REF] Volyanskiy | Compact Optoelectronic Microwave Oscillators using Ultra-High Q Whispering Gallery Mode Disk-Resonators and Phase Modulation[END_REF]. The loop of the oscillator consists of an optic and an electric part as schematically represented in figure 1. Light from the laser goes through a modulator driven by a signal from the detected light at its output, hence generating the oscillation. This light is then stored in the resonant element or delay line, and detected by a fast photodiode. The resulting microwave is then amplified and filtered. OEO can have optical output with the modulated optical signal and microwave output through a directional coupler. Instead of an optical delay line, an ultra-high Q whispering gallery-mode optical resonator allows a much more compact setup and an easier temperature stabilization. In order to be introduced into the loop, the fabricated resonator has to be coupled to the optical light coming from a fiber. When OEO begins to work, some phenomena limit the ability to keep the resonance. In a previous publication, we reported difficulties in stabilizing the generated signal [START_REF] Volyanskiy | Compact Optoelectronic Microwave Oscillators using Ultra-High Q Whispering Gallery Mode Disk-Resonators and Phase Modulation[END_REF]. Thermal effects can certainly cause a drift of the the frequency so it is even possible to loose quickly the resonance after few minutes, making the measure of the phase noise too difficult. Therefore it is necessary to stabilize the laser by locking it on the generated microwave frequency. AOCs are inserted to drive the laser frequency in order to improve its stability. It has to be underlined that a Erbium Doped Fiber Amplifier (EDFA) is needed to amplify the optical signal.

Main principle of the acousto-optic cell operation

Our goal is to use a radio frequency signal to generate acoustic waves in the crystals. The AOCs are to be inserted at output of the laser and in front of the modulator. Concretely, the incident light delivered by the laser is diffracted by the phase grating created in the cell by the acousto-optic effect. It diffracts and shifts the frequency of light using sound waves at radio-frequency. We are especially interested in one property. The light beam is scattered from the moving periodic planes of expansion and compression that change the index of refraction. Consequently, the frequency of the diffracted beam in a diffraction order m will be Doppler-shifted by an amount equal to the frequency of the sound wave F, which is a radio frequency signal. The drift of the frequency of the light wave υ = c/λ will be: υ → υ + mF, where m = ...-3, -2, -1, 0, 1, 2, 3 ... is the order of diffraction. We must take into account that light will not only be shifted in terms of frequency, but also deflected at an angle θ depending on the wavelength of light λ relative to the wavelength of the sound Λ. The light beam emerges from the cell in form of a diffracted beam. The Bragg regime corresponds to a particular incidence angle where only one diffraction order is produced. In that case, the other diffraction orders are annihilated by destructive interference. The refractive indexes of the incident and diffracted beams are different in an anisotropic medium because of a change in polarization direction associated with the interaction.

Installation of acousto-optic cells in the oscillator

Alignment of the AOCs

As mentioned, AOCs are driven by RF signals. To shift the optic frequencies, we must choose the RF signal according to the quality factor of the resonator described in section 2 of this manuscript.

The wavelength of light is λ = 1.55 µm. The velocity of light in the vacuum is c ≈ 3x10 8 m/s. So the frequency of light is υ = c/λ ≈ 2x10 14 Hz. Considering a resonator with its Q ≈ 5.10 8 , we typically need to apply two RF signals to the cells in the range of F 1 = 60 MHz and F 2 = F 1 + ΔF, where ΔF = υ/Q = 400 kHz. At this acoustic frequency, we need to apply only 6 Volts to each cell.

One of the difficulty is to select the good mode. If α is the angle of the incident beam arriving of the cell, we get:

n 0 = sinα/sinα 0 = 2.2597 (i)
for the TeO 2 cell. n e = 2.4119 at 630 nm [START_REF] Shakolskaya | Acoustic crystals" (Акустические кристаллы)[END_REF]. For the wavelengths close to 1.55 µm, we find interesting to select the first order extraordinary polarized mode (+1e mode) because the Bragg angle versus RF frequency presents a floor at zero incidence angle for RF frequency between 55 and 65 MHz as shown in figure 2.

The curves reported in this figure present the Bragg angle. They are obtained by measuring the deviation of the laser spot after going through an AOC. It has been determined for first order ordinary and extraordinary polarized modes -1o, -1e, +1o and +1e by applying RF frequencies between 10 and 65 MHz.

The RF signals can then be shifted between 55 and 65 MHz. This 10 MHz maximal amplitude between the two RF signals allows to work with a resonator with Q-factor no worse than 2x10 7 . If we can expect ultra high Q-factor in the range 10 11 to be achieved and inserted in the OEO, it should require a 2 kHz difference between the two RF signals. So the system is operating for any resonator inserted in the OEO while its Q-factor stay in the range 2x10 7 -10 11 .

Another difficulty is alignment of the two cells and their insertion between the laser and the modulator. The light is in the orange-red at 630 nm but it is not visible at 1.55 µm. Furthermore, the diameter of the beam delivered by the laser must be in the range of 1.0 -1.5 mm. This value is larger than the core diameter 10 µm in the fiber. This fact impacts the dimension of the system: 30 to 50 mm are necessary in front and after the cells, and a typical distance of 50 mm separates the two cells. Even if the +1e mode enables better alignment of the acousto-optic cells, the two cells are slightly misaligned and need to be rectified with a rotation stage. The optical frequency at output of the first cell after the first cell driven by F 1 RF signal is υ + F 1 while the diffracted light propagates at a narrow angle relatively to the incident beam. Similarly, after the second cell mounted at output of the first cell, the frequency of light is υ + F 1 -F 2 while the diffracted light at output of the two cells propagates along a direction only slightly different from the direction of the radiation incident on the first cell. So it is easy to understand that the alignment is relatively a critical step. The beam is then focused into an optical fiber at the input of the modulator.

Locking the AOCs

Both RF signals set to the acousto-optic cells must be driven by a Voltage Controlled Oscillator (VCO) as the frequency need to be adjustable. We use a synthesizer to change both frequencies.

Micro-controller Atmel "ATMega48" is used to control the synthesizer and also to measure the frequency if we do not use a Phase Lock Loop (PLL). ADF4001 is a frequency synthesizer produced by Analog Devices. It consists of a low noise digital Phase Frequency Detector (PFD), a precision charge pump, a programmable reference divider, and a programmable 13-bit N counter. In addition, the 14-bit reference counter (R Counter), allows selectable reference frequencies at the PFD input. A complete PLL can be implemented if the synthesizer is used with an external loop filter and VCO or Voltage Controlled Crystal Oscillator (VCXO). To control ADF4001 we use Serial Peripheral Interface (SPI). We need to have an access to 24-bit register to set values of the Ncounter and the R-counter.

Estimation of the benefit on OEO stabilization

The reference frequency is taken from the special clock output of the micro-controller. Stability of the frequency of our VCO is limited by the quartz stability. Yet it is enough for driving the acoustooptic cells. Indeed the best quartz oscillators are very stable [START_REF] Kuna | Lowest Flicker-Frequency Floor Measured on BVA Oscillators[END_REF][START_REF] Salzenstein | Significant step in ultra high stability quartz crystal oscillators[END_REF]. Concretely, when operating with a frequency stability of 10 -13 at 1 s at 60 MHz, in such a good case, it corresponds to -130 dB.rad²/Hz at 1 Hz from the carrier in terms of phase noise. RF reference signal is to be driven by a synthesis chain described in reference [START_REF] Lardet-Vieudrin | Design and realisation of a 100 MHz synthesis chain from an X-band reference signal[END_REF]. Thanks to this synthesis chain, the spectral density of phase noise S φS can then be expressed in equation (ii), by considering a time constant τ that depends on the characteristics of the synthesis chain:

( ) 2 0 . 4 . ² 1 . ² ² ² 4 1 1 . ² ² ² 4 1 ² ² ² 4 x SPD DDS ref S S S S S n f S f f S ϕ ϕ ϕ ϕ τ π ϕ τ π τ π ϕ + + +       + +       + = (ii)
where f is the Fourier frequency, τ the integration time, and S φ0 , S ref , S DDS , S SPD , S x2 are spectral density of phase noise respectively of the OEO, the VCXO, the Direct Digital Synthesis (DDS) referenced to a 200MHz signal coming from the VCXO frequency multiplied by 2, the sampling phase detector (SPD), the x2-multiplier.

The microwave signal of the OEO should be the main limiting contribution according to the best expected phase noise considered in microwaves for such a device: in case an OEO reaches the noise mentioned in reference [START_REF] Maleki | The optoelectronic oscillator[END_REF], phase noise is still respectively in the range of -110 and -160 dBc/Hz at 100 Hz and 10 kHz from the 60 MHz signal. It is much more than the noise introduced by the synthesis chain which can be respectively better than -135 and -165 dBc/Hz at these Fourier frequencies. Thanks to the use of the synthesis chain to drive AOCs, the expected phase noise should not be degraded by the electronics.

Conclusion and further work

We have presented here a description of advantages and disadvantages of a pair of AOCs to stabilize a signal delivered by an OEO. Without any stabilization, we see that this signal is not sufficiently stable to allow phase noise measurement close to the carrier. The system operates in a proper manner only when the OEO is kept locked on the resonance. As result of this study, two RF signals in the range of 60 MHz presenting a difference no higher than 400 kHz were demonstrated to allow a significant better alignment of the two inserted AOC cells thanks to the +1e mode. We would like to underline the fact that the use of AOCs for locking an OEO is particularly interesting in case of testing various resonator with different Q factors between 2x10 7 and 10 11 . The RF to be applied on the cells just need to be adjusted. Electronics is ready and will soon be useful for locking the loop and stabilize the OEO with the cells. A further goal is to measure phase noise of the stabilized OEO at Fourier frequencies between 10 Hz and 100 kHz away from the carrier. To achieve our goal, we plan to use a dedicated optoelectronic phase noise measurement bench [START_REF] Römisch | Performance evaluation of an optoelectronic oscillator[END_REF][START_REF] Salzenstein | Realization of a Phase Noise Measurement Bench Using Cross Correlation and Double Optical Delay Line[END_REF][START_REF] Salzenstein | Estimation of the uncertainty for a phase noise optoelectronic metrology system[END_REF]. Although the phase noise measurements are not yet available experimentally, we expect the noise of the signal to be better matched with respect to the carrier.

Acknowledgements

This work was supported for French partner, by the French National Research Agency (ANR) grant #ANR 2010 BLAN 0312 02. The Russian partners acknowledge the support of Russian Foundation for Basic Reasearch (RFBR) grant #10-00683.

References:

[1] Yao X. S. and Maleki L., "High frequency optical subcarrier generator," Electronics Letters,

Legends:

Fig. 1 .

 1 Fig. 1. Schematic representation of an OEO stabilized by acousto-optic cells.

Fig. 2 .

 2 Fig. 2. Bragg angle (radian) versus RF frequency (MHz) for λ = 1.55 µm for first order ordinary

Biographies:

Patrice Salzenstein


J M Dudley

V Sarano

F Dias

On Hokusai's Great Wave off Kanagawa: localization, linearity and a rogue wave in sub-Antarctic waters

The Hokusai woodcut entitled the Great Wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics [J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc. 63 119-135 (2009)]. In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great Wave's simultaneous transverse and longitudinal localisation, we show that the purely linear mechanism of directional focussing also predicts characteristics consistent with those of the Great Wave. In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut.

The Great Wave off Kanagawa is arguably the most famous of the many woodblock prints made by the Japanese artist Hokusai. The print (shown in Figure 1a) shows an enormous wave on the point of breaking over cargo boats that are being sculled against the direction of the wave's travel. The wave itself is often assumed to be associated with a tsunami but, as examined in detail by Cartwright and Nakamura in this journal [START_REF] Cartwright | What kind of a wave is Hokusai's Great wave off Kanagawa?[END_REF], the Hokusai print is far more likely to show an extreme plunging breaker, a large storm wave on the point of breaking over the approaching boats. The location of the wave is estimated to be 3 km offshore within Tokyo Bay, and the estimated wave height of around 10 m leads to the conclusion that this would be an exceptionally large amplitude wave for this area and likely to fall into the category of a rogue or freak wave.

Rogue waves are large-amplitude surface waves that represent wave-height outliers for a particular sea state. This means that they possess height and steepness much larger than the average values of other ocean waves in the surrounding environment. It is important to distinguish rogue waves from tsunamis [START_REF] Synolakis | Tsunami and Seiche[END_REF]. A rogue wave is a strongly localized wave in space and time on the ocean's surface, whereas a tsunami is caused by massive water displacement. After their initial stage of generation, tsunamis propagate at high speed over long distances at low amplitude, typically as low as tens of centimeters on the open ocean where they are generally unnoticed. Tsunamis only become destructive as they run up to the shore and grow to great height as the water depth decreases.

The dynamics of tsunamis is very well understood: they propagate as linear waves on the ocean [START_REF] O'brien | The force of a tsunami on a wave energy converter[END_REF] until, at a distance from shore of about a seventh of their wavelength some nonlinear processes may play a role [START_REF] Kajiura | Local behaviour of tsunamis[END_REF]. On the other hand, a consensus concerning the physics of oceanic rogue waves is only just beginning to be developed. Rogue waves are now generally considered to form a distinct class of ocean waves, but it seems likely that they arise from a variety of different physical mechanisms [START_REF] Kharif | Physical mechanisms of the rogue wave phenomenon[END_REF]. In particular, both linear and nonlinear effects have been shown to lead to unusual wave amplification under many different conditions. For example, linear effects that can generate rogue waves include: spatial focusing due to refraction in the presence of varying topography; wave-current interactions; dispersive focusing of a chirped wave train; directional focusing of multiple wave trains. Nonlinear effects have also received much attention, especially the process of exponential amplification of random surface noise through modulation instability, and the development of high amplitude coherent structures and related soliton dynamics. Note that whether the generating mechanism is linear or nonlinear does not enter into the definition of a rogue wave; the only criterion is whether the wave is statistically much larger than the other waves in the immediate environment. Reviews of the subject of rogue waves are given in [START_REF] Kharif | Physical mechanisms of the rogue wave phenomenon[END_REF][START_REF] Dysthe | Oceanic Rogue Waves[END_REF][START_REF] Kharif | Rogue Waves in the Ocean[END_REF].

A possible generation mechanism for Hokusai's Great Wave in terms of nonlinear soliton collisions was discussed in [START_REF] Cartwright | What kind of a wave is Hokusai's Great wave off Kanagawa?[END_REF] and indeed, the important role of nonlinear dynamics in wave amplification has been confirmed in a number of recent studies [START_REF] Rainey | Weak or strong nonlinearity: the vital issue[END_REF][START_REF]Special Issue on Rogue Waves -Towards a unifying concept[END_REF][START_REF] Chabchoub | Rogue wave observation in a water wave tank[END_REF]. But it is also important to consider the role of linear effects in extreme wave localization, because the initial stage of wave propagation will generally always begin in the linear regime, and nonlinear effects will become important only as the wave amplitude increases to an appropriate level. In the case of the Great Wave, a particular clue of how linear effects may play a role is seen by noting the Great Wave's localization both along its direction of travel and transversally -we see the wave rising from the foreground and ending in the middle ground of the print [START_REF] Cartwright | What kind of a wave is Hokusai's Great wave off Kanagawa?[END_REF]. Whilst such localization has been studied in the framework of nonlinear effects [START_REF] Onorato | Modulational instability in crossing sea states: a possible mechanism for the formation of freak waves[END_REF][START_REF] Tamura | Freakish sea state and swell-windsea coupling: Numerical study of the Suwa-Maru incident[END_REF], we discuss below how it can also arise from linear propagation.

Before our discussion of this mechanism, however, we first make the important observation that such two-dimensionally localized waves do in fact occur in nature, and can assume large amplitudes and undergo wave breaking as illustrated in the woodcut. In this context, we remark that although breaking waves are often associated with the laterally extended surf waves arriving on a beach, any water wave can break when the wave crest steepens sufficiently [START_REF] Banner | Wave Breaking in Deep Water[END_REF]. There is nothing unphysical about a localized wave undergoing breaking at high steepness.

To confirm this explicitly, we show a photograph in Figure 1 the known height of the Astrolabe's helipad deck which was the point of observation. The waves on the background sea were estimated to have much lower heights in the 1-3 m range, consistent with the interpretation of the isolated higher amplitude wave as a rogue wave. We also note that the difference in absolute heights between this sub-Antarctic wave and the Great Wave is unimportant for our discussion here because the essential physics of ocean wave breaking remains the same for waves over a large range of amplitudes [START_REF] Banner | Wave Breaking in Deep Water[END_REF].

We now consider how such dramatic localization as seen in both this photograph and the Great Wave woodcut may arise from linear propagation effects. Specifically, we examine the process of directional focusing, which arises whereby periodic wave trains with different directions and phases interfere together at a particular point in space and time to create an extreme rogue wave at their focus. Typical results of numerical modeling are shown in Figure 2 [START_REF] Fochesato | Numerical modeling of extreme rogue waves generated by directional energy focusing[END_REF]. In fact, the modeling is based on fully realistic propagation equations that include both linear and nonlinear effects, but the essential concentration of energy at the point of focus arises from linear convergence to a focus. Nonlinearity plays a dominant role only as the wave approaches the linear focus where it increases the wave steepness to the point of breaking. The visual similarity of the numerical modeling of directional focusing with the localization properties seen in the woodcut is immediately apparent, and thus directional focusing is clearly also a mechanism that could underlie the formation of the Great Wave.

At this point we can note another feature of the Great Wave that suggests the presence of several surrounding waves of large amplitude. Although these other waves appear outside the frame of the image, it is natural to consider whether the fishermen are actually experiencing a "wave packet" of several large rogue waves. This is in fact perfectly plausible. Although each single rogue wave crest is localized in space and time, numerical studies and observation have also reported that several (typically between 2-3) consecutive rogue waves can be generated [START_REF] Kharif | Rogue Waves in the Ocean[END_REF][START_REF] Clauss | Dramas of the sea: episodic waves and their impact on offshore structures[END_REF][START_REF] Nikolkina | Rogue waves in 2006-2010[END_REF]. The occurrence of multiple rogue waves in this way can arise from nonlinear effects, but is also possible with directional focusing [START_REF] Fochesato | Numerical modeling of extreme rogue waves generated by directional energy focusing[END_REF].

Our conclusions concerning the Great Wave off Kanagawa can be easily stated. When discussing the Great Wave, considering its transverse localization is essential to any attempts to understand its origin and to propose plausible underlying physical mechanisms. It is also important to realize that the process of wave breaking itself is not confined to the simple case of extended surf waves on a beach, but occurs with all high amplitude waves. The photographic evidence provided here of a breaking wave in the Southern Ocean is a striking example. Although it is not possible to make any unambiguous conclusions about the particular wave or waves that may have been seen by Hokusai to inspire his celebrated woodcut, we believe that directional focusing is a plausible mechanism that predicts wave characteristics highly similar to the Great Wave off Kanagawa. In terms of the artwork of the woodcut itself, highlighting the physics of the transverse localization of the Great Wave provides room for unexpected optimism when interpreting the scene that is depicted. Transverse localization due to an effect such as directional focusing might suggest that the boats may not be in as much danger as usually believed. Is Hokusai really trying to highlight the skillful way that the Japanese crews are navigating around the wave to avoid it breaking over them?

Our discussion also highlights the generality of wave localization phenomena in nature that can arise from both linear and nonlinear processes, although it is clearly difficult to differentiate which process may be dominant based on field observation alone. Interestingly, this brings to mind a particular problem in the interpretation of water wave phenomena that dates back to the 19 th century, and whose resolution in the 20 th century is linked to the very beginning of the field of nonlinear science itself. The 19 th century event of relevance here is John Scott Russell's 1834 observation of the Great Wave of Translation on the Union Canal in Scotland [START_REF] Scott Russell | Report on Waves[END_REF]. Although Scott Russell himself was convinced that what he had seen was a fundamentally new class of wave, this interpretation was contentious, and authorities at the time such as Stokes and Airy preferred not to accept the need for any new theoretical ideas beyond the notions of water wave theory at the time [START_REF] Darrigol | The Spirited Horse, the Engineer, and the Mathematician: Water Waves in Nineteenth-Century Hydrodynamics[END_REF][START_REF] Craik | The origins of water wave theory[END_REF]. It was only much later in the 1960s with the development of techniques such as inverse scattering and numerical methods for solving nonlinear differential equations, that the full nonlinear theory of solitons provided the context with which to understand Scott Russell's observation completely [START_REF] Scott | The Nonlinear Universe: Chaos, Emergence, Life[END_REF].

Ongoing research in the hydrodynamics community concerning the role of linear and nonlinear effects in rogue wave emergence continues this tradition of debate as to whether observations of novel waves in nature really require new theoretical descriptions [START_REF]Special Issue on Rogue Waves -Towards a unifying concept[END_REF]. The field of rogue wave study today is of course in a much better position than Scott Russell was, in that the tools of advanced mathematics allow detailed simulations of a wide range of water wave propagation behavior. But even now, we are very often in the situation where we must compare our numerical modeling with the laboratory of the ocean itself where not all parameters are known or controlled. This serves to highlight the central role of observation above all, and the tremendous importance of talented observers (such as Hokusai) to capture the physics of the natural world.

  Figure 1(b) are smaller than that of the great wave in the woodcut, with the wave height in the

Acknowledgements

We acknowledge support from the European Research Council Advanced Grant MULTIWAVE and essential discussions with F. Sarano.


Bojan Marinković
email: bojanm@mi.sanu.ac.rs

Luigiliquori
email: luigi.liquori@sophia.inria.fr

A Distributed Catalog for Digitized Cultural Heritage

Keywords: Peer-to-peer, Distributed databases, DHT-based Overlay networks, Information retrieval, Digitized cultural heritage

Peer-to-peer networks have emerged recently as a flexible decentralized solution to handle large amount of data without the use of high-end servers. In this paper we present a distributed catalog built up on an overlay network called "Synapse". The Synapse protocol allows interconnection of different overlay networks each of them being an abstraction of a "community" of virtual providers. Data storage and data retrieval from different kind of content providers (i.e. libraries, archives, museums, universities, research centers, etc.) can be stored inside one catalog. We illustrate the concept based on the Synapse protocol: a catalog for digitized cultural heritage of Serbia.

1I n t r o d u c t i o n 1.1 Context

Digitization is an important step towards preservation and promotion of heritage. It safeguards cultural diversity in the global environment and offers a rich treasure to the world-wide public of the Web. Usually, digitization can be seen as a collection of activities, including digital capture, transformation from analogue to digital form, description and representation of heritage objects and documentation about them, processing, presentation and long-term preservation of digitized content, etc.

The document [START_REF]Recommendations for coordination of digitization of cultural heritage in South-Eastern Europe, Conclusions of the Regional Meeting on Digitization of Cultural Heritage[END_REF] states that current digitization practice in SEE is still not matching the priorities communicated on the EU-level and that the rich cultural content of the region is still underrepresented in the electronic space. One of the main principles accepted by the participants states that "It isrecognizedthatknowledgeofthecultural and scientific heritage is essential for taking decisions concerning its digitization and for interpreting the digitized resources. For this reason, inventorying and cataloging should precede or accompany the digitization of cultural and scientific assets."

At the moment, there is no widespread meta-data standard for describing digitized heritage in Serbia. Actually, although most of the institutions caring about national heritage have started the digitization process, there is no meta-data standard formally accepted at the state level. Because of that we are faced with something that can be called the meta-data problem.Differentprovidersofheritageresources(libraries,museums, archives, some research institutions) use international standards appropriate for M. Gusev and P. Mitrevski (Eds.): ICT Innovations 2010, CCIS 83, pp. 176-186, 2011. c Springer-Verlag Berlin Heidelberg 2011 their specific fields, or ad-hoc methods, or old procedures for describing cultural assets in classical format (formulated in 1980s or early 1990s). In fact, some providers are still waiting for some solution of the meta-data problem and do not do anything related to digital cataloging. This means that digital catalogs in Serbia, if they exist at all, cannot help in communication between different kinds of providers and users.

On the other hand, at the international level, there are plenty of meta-data standards for describing heritage resources, for example: Dublin Core [START_REF]The Dublin Core Metadata Initiative[END_REF], EAD [10], MARC [START_REF]MARC Standards[END_REF], TEL AP [START_REF]The European Library[END_REF], FRBR [START_REF]A weblog about FRBR: Functional Requirements for Bibliographic Records[END_REF][START_REF]IFLA Study Group, Functional Requirements for Bibliographic Records[END_REF], etc.

Given all of the aforementioned, the Committee for digitization of the UNESCO commission of Serbia has recognized the meta-data problem as the most sophisticated one in the cataloging phase of digitization. During the past years, some efforts were made in the field of standardization, which resulted in the development of the recommendation for the meta-data format described in [START_REF] Ognjanović | NCD Recommendation for the National Standard for Describing Digitized Heritage in Serbia[END_REF], but this recommendation has not, still, been accepted as a formal national standard.

There were also some efforts directed towards developing technology for storing these meta-data documents, but there is still no widespread application. Recent attempts to create digital repositories, such as, for example, Europeana [16], are mostly based on centralized architectures. Here we consider an alternative, decentralized approach, based on overlay networks.

Overlay networks have recently been identified as a promising model to cope with the Internet issues of today, such as scalability, resource discovery, failure recovery, routing efficiency, and, in particular in the context of information retrieval. Many disparate overlay networks may not only simultaneously co-exist in the Internet, but can also compete for the same resources on shared nodes and underlying network links. This can provide an opportunity to collect data on various kind of digitized documents which are, by their nature, highly distributed resources, while keeping backward compatibility, efficient searching, failure resistance, etc. One of the problems of the overlay networking area is how different overlay networks may interact and cooperate with each other. Overlay networks are heterogeneous, and basically unable to cooperate with each other in an effortless way, without merging, an operation which is very costly since it is not scalable and not suitable in many cases forsecurityreasons.Ho we ver ,inmanysituations, distinct overlay networks can take advantage of cooperating for many purposes: collective performance enhancement, larger shared information, better resistance to loss of connectivity (network partitions), improved routing performance in terms of delay, throughput and packets loss, by, for instance, cooperative forwarding of flows.

In the context of large scale information retrieval, several overlays may want to offer an aggregation of their resources to their potential common users without losing control of them. Imagine two companies wishing to share or aggregate information contained in their distributed databases, obviously while keeping their proprietary routing and their exclusive right to update it. In terms of fault-tolerance, cooperation can increase the availability of the system -if one overlay becomes unavailable the global network will only undergo partial failure as other distinct resources will be usable. The solution could be found in using a meta-protocol which allows a request to be routed through multiple overlays, where one overlay contains one kind of institutions, even using different routing algorithms, thus increasing the success rate of every request.

The ready-to-market DHT(Distributed Hash Tables)-based technology of structured overlay networks is enriched with the new capability of crossing different overlays through co-located nodes, i.e. by peers who are, by user's choice, member of several overlays [START_REF] Liquori | Synapse: A Scalable Protocol for Interconnecting Heterogeneous Overlay Networks[END_REF]. Such nodes are themselves able not only to query multiple overlays in order to find a match, but also to replicate requests passing through them from one network to another and to collect the multiple results.

Problem Overview

In the digitization of catalog services, using an Information System (IS) has been shown to be essential in matching the offers, the requests, and the resources. The IS is, in most cases, a front-end web site connected to aback-enddatabase.Aclassicalclientserver architecture is usually sufficient to manage those services. In presence of multiple services, for technical and/or commercial reasons, it is not possible to share contents across different providers, despite the evident advantage. In most cases, ISs are not suitable to communicate in any of their features (lookup, search, etc.). Although, in general, this does not affect the correct behavior of an IS, it is clear that interoperability would increase the overall quality of the service. Moreover, the classical shortcomings of client-server architectures make both services unavailable in case both servers are down. Any attempt to make different and disconnected institutional, client-server based architectures, does not foresee any form of service interconnection, with the unpleasant consequence of losing potential matches between offers and requests between users of different communities on the same subject.

As a basic example, let us consider two cultural institutions which contain digital documents inside their databases. One node of the first database stores one volume which is searched for by a node of the second one. Without "inter-network" cooperation, these two databases would never communicate together. But, if these ISs do co-operate with each other, the results can be far more precise and accurate.

As we said above, the digitized documents are, by their nature, highly distributed resources. Because of this, we decided to develop a catalog based on Synapse protocol as a real-life proof-of-concept. Here we analyze how the Synapse protocol [START_REF] Liquori | Synapse: A Scalable Protocol for Interconnecting Heterogeneous Overlay Networks[END_REF] can be used as a tool to connect a huge number of content providers.

Outline

The rest of paper is organized as follows: In Section 2 we summarize some mechanisms proposed in the literature related to distributed systems and describes briefly the interconnection of different distributed catalogs by means of our Synapse protocol. In Section 3 we introduce an idea of a distributed catalog service and show how it is mapped onto a DHT. In Section 4 we show a running example with a proof-of-concept which we have implemented on the base of a real case of study. Section 5 describes the results of the deployment of a client prototype tested over a distributed platform at Mathematical Insitute. In Section 6 we present our conclusions and ideas for further work.1

2R e l a t e d W o r k a n d C o n t r i b u t i o n s 2.1 Related Work

The classical viewpoint on distributed databases, as it is described in [START_REF] Ramakrishnan | Database Management Systems[END_REF], defines desirable properties for distributed database management systems (DBMS). These properties are: distributed data independence,anopportunitytosendquerieswithoutspecifying where the referenced relations are located, and distributed transaction atomicity,a n opportunity to access and update data at several sites just as they would write transactions over purely local data. Depending on whether the data is distributed over the same DBMS software or not, we distinguish homogeneous and heterogeneous distributed database systems. In situations where these systems are heterogeneous, we have to establish gateway protocols.

In these systems, data is usually distributed by fragmentation,w h e nf r a g m e n t so f data are divided over several sites. This fragmentation can be horizontal,w h e ne a c h fragment consists of a subset of rows of original relation, and vertical,wheneachfragment consists of a subset of columns of the original relation. Fragmentation is followed with replication of data and several copies of one fragment are stored in the system. We must keep track of how the relations are fragmented and replicated, which can be be complicated. The catalog of this track-keeping can be centralized, in which case the entire system would be vulnerable to failure of the site which contains the catalog, or also distributed, in which case the biggest issue is maintaining data consistency.

In [START_REF] Antonopoulos | Amulti-ringmethodforefficient multi-dimensional data lookup in p2p networks[END_REF], the authors have developed a multi-ring model based on Chord, in which each shared resource is described by one or more keywords. Nodes are organized in multiple keyword rings, and each node in a keyword ring contains the list of nodes that host resources matching a certain keyword/value pair. A new keyword ring is created only when the number of queries or registered resources for the keyword rises above a certain threshold. To enable keyword rings to be found, a Super Ring is used to host a ring of nodes which contain pointers to other rings. One major drawback of the model is that it heavily depends on the bootstrap node.

ML-Chord, presented in [START_REF] Lu | ML-Chord: A multi-layered P2P resource sharing model[END_REF], is a multi-layered P2P resource sharing model which introduces overlay layers of categories. The number of these categories depends on the number of categories for a specific domain or ontology. Also, two types of nodes are introduced : normal peers,whichcanbeassociatedwithoneorseverallayersandbridge peers, which are peers with better capabilities, linked to all categories and themselves form a category as well. The problem with this approach is that it is not possible to simply encapsulate a new system into an existing one because all of the Chord layers share the same hash function. Although this system is scalable and efficient, it is not possible to easly introduce a new category during the system lifetime. The developers suggest that one node should be linked to only one layer for better performance. So, if anodewithgoodcapabilities has not become a bridge peer at the start of the lifecycle of the system, it will remain a normal node, and its beneficial capabilities will be lost.

Interconnecting Different Overlay Networks

As said in the introduction, co-operation of different ISs implemented via overlay networks is a challenging problem which make pragmatical benefit in the context of this paper, namely catalog digitization. In the context of large scale information retrieval, several overlays may want to offer an aggregation of their information/data to their potential common users without losing control of it. One may perceive that having a single global overlay has many obvious advantages and is the de facto most natural solution: unfortunately it appears unrealistic in many real cases. In some optimistic case, different overlays are suitable for co-operation by opening their proprietary protocols in order to build an open standard; in many other pessimistic cases, this opening is simply unrealistic for many different reasons (backward compatibility, security, commercial, practical, etc.).

The catalog we present in this paper is based on Synapse [START_REF] Liquori | Synapse: A Scalable Protocol for Interconnecting Heterogeneous Overlay Networks[END_REF], a scalable protocol for information retrieval over the inter-connection of heterogeneous overlay networks. The protocol is based on co-located nodes, also called synapses,servingaslow-costnatural candidates for inter-overlay bridges. In the simplest case, where overlays to be interconnected are ready to adapt their protocols to the requirements of interconnection, every message received by a co-located node can be forwarded to other overlays that node belongs to. In other words, upon receipt of a search query, in addition to its forwarding to the next hop in the current overlay, according to their routing policy, the node can possibly start a new search, according to some given strategy, in some or all other overlay networks it belongs to. This obviously implies that a Time-To-Live value has to be provided and detection ofalreadyprocessedqueriesimplemented,soastoavoid infinite looping in the networks, as it is the case in unstructured peer-to-peer systems. Applications of top of Synapse see those inter-overlays as a unique overlay.

Experiments and simulations, we run, showed that a small number of well-connected synapses is sufficient in order to achieve almost exhaustive searches in a "synapsed" network of structured overlay networks. We believe that Synapse can give an answer to circumventing network partitions; the key points being that:

several logical links for one node lead to many alternative physical routes through these overlay, and as y n a p s ec a nr e t r i e v ek e y sf r o mo v e r l a y st h a ti td o e sn o te v e nk n o w ,s i m p l yb y forwarding the query to another synapse that, in turn, is better connected.

For more details on the Synapse protocol, see [START_REF] Liquori | Synapse: A Scalable Protocol for Interconnecting Heterogeneous Overlay Networks[END_REF].

Contribution

Our intention is not to give a final solution for a new concept of DBMS, but to show an idea that it is possible to establish a DBMS with desirable properties, which can connect heterogenous DHTs in a homogenous way and which can be easily expanded, without real fragmentation of data, while keeping the property of load balance and good performance of a whole system. Also, we will show that this system is applicable to real-life situations.

3A p p l i c a t i o n P r i n c i p l e s

One of the main features of a distributed catalog is to assist researchers and members of the wider community in retrieving information concerning some fact of interest, information which can be provided from different kinds of sources. As mentioned before, digitized documents, by their nature, are highly distributed resources. By connecting different kinds of data providers into one system, the quality of the resulting information can be increased.

In this paper, we consider a distributed catalog which contains only meta-data on digital documents which follows a part of the Recommendation for the meta-data format for describing digitized heritage, described in [START_REF] Ognjanović | NCD Recommendation for the National Standard for Describing Digitized Heritage in Serbia[END_REF]. One of the main reasons for this is the intellectual property rights issue. Simply, some institutions do not wish to outsource control over their digital repositories, and, instead, choose only to publish the information that they are in possession of a certain document. The digital documents themselves can be retrieved with one of the meta-data fields which contains information on their actual remote location.

Au s e rc a nc o n n e c tt oo n eo rm o r ec o m m u n i t i e sw h i c hh ei sm e m b e ro f( i .e .h e has been invited to or his request has been accepted). Two operations are then available, namely: (i) storing a new record and( i i )fi n d i n gar e c o r dw h i c hc o n t a i n ss o m e information.

Suppose we wish to store the following information on a digital object: If we were to decide to make the catalog searchable for the values in the fields: title, creator, relatedAsset, mimeFormat and digitalObjectOwner,thenwewouldstore segments in accordance with Table 1.

<digitalObject>
More precisely:

1. For every field of a meta-data record which we choose to be searchable, the hashed value for the current overlay of the entire meta-data record as value with the key which contains information about the field and its value is stored (rows 1 to 5 in table 1). 2. The entire meta-data record as a value with the corresponding key that contains its hashed value for the current overlay is stored (row 6 in table 1).

Note that all of the keys are stored with theirhashedvalues.Withthisinplace,thesearch mechanism has two phases. During the first phase, we attempt to find the hashed value of the meta-data record (the first kind of entries) and then, during the second phase, to find the entire meta-data record (the second kind of entries) only in the overlays which contain the first kind of entries. Although we have multiple copies of data, so as to accomplish failure resistance of the system, the storage space is of the same complexity as for a standard DBMS with indices. If N and M are the number of overlays and the number of nodes per overlay, respectively, then the time complexity of a search, in the worst case, is O((N +1) * (time to search an overlay with M nodes)).

4C a s e S t u d y

Institutions which are interested in sharing meta-data information on their digital documents can be connected in different overlaysbytheirnature.So,allarchivesmaybe ap a r to fo n eo v e r l a y ,a l ll i b r a r i e so ft h eo t h e r ,a n ds i m i l a r l yw i t hm u s e u m s ,r e s e a r c h centers, universities, etc. These overlays can be connected by institutions which contain various kind of content, like research centers with important libraries or research centers which are part of the universities, etc. All of these institutions would run the same application.

The following proof-of-concept is a simple application to store and retrieve records from one or multiple overlays. It offers the following three functionalities, arranged in a Graphical User Interface developed in Java, for cross-platform compatibility:

-J o i n i n gof a new network, -S t o r i n gof a new record, -S e a r c h i n gfor records.

The application is designed using a tabbed organization of different forms. This is to allow the user to easily perform multiple operations at the same time (e.g. doing multiple queries and comparing the results). Furthermore, it constitutes a familiar usage environment, resembling, in the approach, most of modern Internet browsers (multiple tabs, address/search on a top bar). Basic editing features, like saving and loading a record to and from an XML file, copying/pasting and printing the XML raw data, are provided. Network join. As shown in Figure 1a, upon starting, the program will propose to the user a list of known DHTs to connect to. These represent existing overlays put in place using the same system, which are, therefore, compatible with our software. It is important to notice that, after having connected to a first overlay, a user can choose to further join other available networks. This can be done via the menu entry Network → Join, which will propose the same dialog box as in Figure 1a.

Once being a member of multiple overlays, not only it becomes possible to query all of the overlays simultaneously, but, thanks to the capabilities of the synapse protocol described in Section 2.2, it will also be possible to act as a relay, replicating requests from one overlay to another.

Storing a new record. Figure 1b shows the insertion form for a new record in the DHT.

In this catalog we store the records which follow a part of the mentioned recommendation of the meta-data format:

-T i t l eof the digital document (i.e. electronic book) -N a m eo ft h ea u t h o rwho made electronic version -L i n kof the remote location of the digital document -R e l a t e do b j e c t(i.e. hard copy book) -N o t eor a short description -D a t ewhen electronic copy was made -M i m et y p e(i.e. pdf) -O w n e rof the digital object While some of the fields may be optional, the ones used as search criteria have to be filled before the record can be saved. Therefore, the "Save" button remains disabled until all of the appropriate text boxes are filled.

Record searching.

Looking for a record takes place in a way resembling the behavior of most modern Internet browsers: as one can see in Figure 2a, the search type and field are in the upper toolbar. Here the user can choose the type of search to perform (title, author, owner, related object, mime type) and fill the search key. By pressing the "Search" button, a query for the corresponding key is performed in the overlay (or overlays, if synapses are present or the software is connected to multiple networks). A To display the details of a record the user can double-click on the corresponding row in the table. This (showed in Figure 2b) will open a new tab containing record details.

The details tab is similar to the new record form, except that the text fields cannot be edited (although it is still possible to select and copy the text inside).

The button "Display raw XML" will open a new dialog showing the actual XML data.

5E x p e r i m e n t s

In order to test our inter-overlay protocol, as a ground base of our catalog, we have developed open-synapse software. It is based on the open-chord v. 1.0.5 implementation, developed by Distributed and Mobile Systems Group Lehrstuhl fuer Praktische Informatik Universitaet Bamberg, which is, essentialy, a Java implementation of the Chord protocol. This platform fully implements a Chord-based inter-overlay network, but to achieve the goal of connecting heterogenous overlay networks, we have decided that in our implementation every Chord ring has its own hash function. The experiments were realized on an IBM Beowulf Cluster 1350. During the tests we have started 5 logical nodes at each of up to 12 working nodes. The nodes have been uniformly dispatched over 3 or 6 overlays, and during deployment, the overlays were progressively bridged by synapses (the degree of each logical node wasnevergreaterthan2).So,wedidtests with 15, 30 and 60 nodes uniformly dispatched over 3 overlays and 60 nodes uniformly dispatched over 6 overlays.

Figure (3a) shows the satisfaction ratio when increasing the number of synapses. By the satisfaction ratio we mean the percentige of the succesfull answers for the vaules that are, already, inserted into the system. It can be seen that a quasi-exhaustiveness has been achieved when the synapses are members of only 2 overlays. Note that the satisfaction ratio confirms the simulation results, which are available in [START_REF] Liquori | Synapse: A Scalable Protocol for Interconnecting Heterogeneous Overlay Networks[END_REF]. Figure (3b) shows the average elapsed time from the moment a query is sent to some node in the system until the moment when the answer is received. This time was not so short, but this is due to the configuration of the cluster. We suppose that these results could be illustration of the performance in a real-life situation, in which the nodes would not be members of networks which arewithinthesameinfrastructure.

6C o n c l u s i o n

In this paper we have shown that the Synapse protocol has good potential as a new concept of DBMS. With this concept, it is possible to connect heterogenous DHTs in a homogenous way. We have proven the scalability of this protocol and its applicability to a real-life situation.

Since we cannot guarantee full exhaustiveness of information retrieval, we have decided that the procedure of removing/updating items should currently be out of scope of our research. The reason for this is that the only one who may remove or update items inside the catalog should be the one who inserted them in the first place, thus guaranteeing the highest probability of data consistency. For this, we would first need to implement a User Management System, for instance, by implementing cryptographic technics into our system, as described in [START_REF] Avramidis | Chord-PKI: Embedding a Public Key Infrastructure into the Chord Overlay Network Public Key Infrastructure[END_REF].

As mentioned before, within this system we can also store the digital documents themselves. We have also decided that in the current phase, this should be out of scope of this paper, but we consider this to be a possible continuation of our research.

As a positive side-effect, we believe that our catalog can lay promising groundwork for a low-cost solution to cultural interconnection of the institutions inside the region.

Fig. 1 .

 1 Fig. 1. Connecting and Inserting

Fig. 2 .

 2 Fig. 2. Searching and Retrieving

Fig. 3 .

 3 Fig. 3. Deploying Synapse

Table 1 .

 1 Different data structures stored in the distributed catalog DHT for each entry

	<title>Title</title>
	<creator>Name</creator>
	<location>link</location>
	<relatedAsset>
	Realife object</relatedAsset> <note>	No.	Key	Value
	<src lang ="	1	title♯Title	hash( )
	language of the value">value</src> </note>	2	creator♯Name	hash( )
	<archivalDate>date</archivalDate>	3 relatedAsset♯realifeObject hash( )
	<mimeFormat>mime type</mimeFormat> <digitalObjectOwner> Owner</digitalObjectOwner>	4 mimeF ormat♯mimeT ype hash( ) 5 hash( )
	</digitalObject>	6	hash( )
	XML metadata record	where represents the full meta-data record on one digital document

The developed software and all of the results of the tests are available at the web-page http://www.mi.sanu.ac.rs/ ˜bojanm/synapse.

Acknowledgment. The authors warmly thank Petar MaksimovićandCédric Tedeschi for their precious suggestions during the writing of this paper.