Bruno Dato
email: bruno.dato@irit.fr

Marie-Pierre Gleizes
email: marie-pierre.gleizes@irit.fr

Frédéric Migeon
email: frederic.migeon@irit.fr

A Local Active Learning Strategy by Cooperative Multi-Agent Systems

Keywords: Multi-Agent System Learning, Local Active Learning, Context Learning

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Every learning system has advantages and drawbacks, parts of the environment where it is accurate, where it is efficient, and parts where it is not, as Wolpert stated in his "No Free Lunch Theorem" [START_REF] Wolpert | No free lunch theorems for optimization[END_REF]. Therefore, we focus on meta-learning techniques that could benefit from the composition of specific learning systems in distinct parts of the search space as well as in their borders. Dealing with sociotechnical environments of ambient systems, an intelligent application to be designed must handle properties such as openness, heterogeneity, unpredictability and dynamics [START_REF] Russell | Artificial intelligence: a modern approach[END_REF][START_REF] Abbas | Systems thinking for developing sustainable complex smart cities based on selfregulated agent systems and fog computing[END_REF]. However, as sociotechnical environments are impossible to be specified a priori, these systems must be able to adapt to their environment by learning from few experiences. They must learn throughout their lives without having any intrinsic knowledge of the tasks they will have to solve. Such systems are called agnostic systems [START_REF] Kearns | Toward efficient agnostic learning[END_REF]. To design them, it is essential to generate knowledge through processes and actions that are purely internal to the system interacting with its environment.

The proposed system enables to generate active learning requests. To deal with the previous hypotheses, we try to be agnostic regarding the learning techniques by embodying them in agents that cooperate in order to produce more knowledge. Inspired by con-structivism of Piaget [START_REF] Piaget | Piaget's theory[END_REF] and developmental learning methods applied in robotics, we define a multi-agent system that uses a local active learning strategy to enhance the results. Each agent, each learnt model, is used locally in a small part of the search space, where it is accurate. They share local information that is internal to the system to generate active requests.

This paper presents some steps of this research goal. In the next section, we provide to the reader the background information on constructivism, multiagent systems and how the context-based metalearning pattern uses data to learn from the environment. This work is intended to scale up with the number of dimensions of the search space, but to be simpler, we present it as a 2D problem. Moreover, we use a default regression model to implement the embodied model in each agent but our goal remains to be independent of the type of the learning technique.

We present in the following section the existing Context Learning which is the base of our work where each agent represents a context linked to an action or answer. Then, we detail the enhancement of the context learning with the Active Context Learning which enables the system to find in itself and alone which specific learning situations to request in order to improve its learning. In the experimentations section, we describe the metrics we use and how the experiments were conducted. Finally, a discussion, related work and conclusion are presented.

Constructivism. The work of Piaget on child development [START_REF] Piaget | Piaget's theory[END_REF] has inspired Constructivist Learning. It stated that knowledge construction cannot be separated from the subject's environment and the actions made on it. Called schema, this unit of knowledge aggregates several perceptions and several actions [START_REF] Guerin | Learning like a baby: a survey of artificial intelligence approaches[END_REF]. Robotic applications made use of the work of Drescher [START_REF] Drescher | Made-up minds: a constructivist approach to artificial intelligence[END_REF] and Holmes [START_REF] Holmes | Schema learning: Experiencebased construction of predictive action models[END_REF] to obtain self-organizing maps (SOM) [START_REF] Chaput | The constructivist learning architecture: A model of cognitive development for robust autonomous robots[END_REF][START_REF] Provost | Developing navigation behavior through self-organizing distinctive-state abstraction[END_REF]. Recently, it also served as a foundation on agentified model-based learning [START_REF] Perotto | A computational constructivist model as an anticipatory learning mechanism for coupled agent-environment systems[END_REF].

Multi-Agent Systems. In order to deal with the complexity of real world situations like in cyberphysical systems (non-linearity, dynamics, distributed information, noisy data and unpredictability), it is important to build software systems which embody as many states as the real systems do [START_REF] Ashby | Cybernetics and requisite variety. An Introduction to Cybernetics[END_REF]. For this purpose, Multi-Agent Systems [START_REF] Ferber | Multi-agent systems: an introduction to distributed artificial intelligence[END_REF], and in particular Adaptive Multi-Agent Systems (AMAS) [START_REF] Georgé | Cooperation[END_REF] provide adaptive properties to deal with these unexpected situations, which is appropriate for learning systems [START_REF] Mazac | On bootstrapping sensori-motor patterns for a constructivist learning system in continuous environments[END_REF][START_REF] Guériau | A constructivist approach for a self-adaptive decision-making system: application to road traffic control[END_REF]. AMAS are artificial complex systems with fine granularity agents enabling the emergence expected global properties. Domains like the control of biological processes, the optimal control of motors or robotics learning [START_REF] Boes | The self-adaptive context learning pattern: Overview and proposal[END_REF] have exhibited such properties.

Context Learning. The AMOEBA system (Agnostic MOdEl Builder by self-Adaptation) [START_REF] Nigon | Selfadaptive model generation for ambient systems[END_REF] 1). This is completed with a confidence c j ∈ Z that enable agents to order themselves. A Context Agent is then defined by its validity ranges, its model and its

F (P n ) = F (p 1 , . . . , p i , . . . , p n ) = O m where O m ∈ R m is
confidence C j n = {R j n , f j n , c j }. p 1 | | r j 1,start r j 1,end C j 1 (a) Dimension 1 r j 1,start r j 1,end p 1 p 2 r j 2,start

Context Learning Strategies

The implementation of AMOEBA is based on several simple rules and a default learning model (linear regression) that we briefly present after. In the following, a new local active Context Learning strategy is proposed which uses negotiation between agents neighboring the perceptions.

Former Context Learning Strategy

To define a good prediction, an error margin and an inaccuracy margin are used. The error margin defines a threshold above which a prediction is said bad. In the other case, the inaccuracy margin is used to address the precision needs, it is always less than the error margin. These two margins are calibrated by the user. In AMOEBA, agents are reactive. Their behavior is organized in execution cycles, which may be learning cycles or exploitation cycles.

Learning. During a learning cycle, each Context Agent receives the learning situation including P n .

Negotiation between them, according to the validity ranges and confidence, results in the identification of the Best Context Agent for the current execution cycle. Though cooperative analysis, they individually realize different adaptations using the labeled prediction [START_REF] Nigon | Selfadaptive model generation for ambient systems[END_REF].

Exploitation. During an exploitation cycle, only the perceptions P n are submitted to the system. The Best Context Agent is designated as the one with the higher confidence and its prediction serves as the out-

1 . A learning situation is then L n,1 = [P n , O 1 ].
Shortcomings. On a simple problem, with two models distributed in a 2D-space like represented in Fig. 2a with different colors, the presented learning rules do not allow the system to converge to an ideal representation (Fig. 2c), i.e. with the minimum of Context Agents, without any overlap or gaps. These rules do not protect against imprecise exploration (Fig. 2b). Incompetencies of the agents are not detected. Conflicts and concurrencies between the agents are not taken into account. All resolutions are made independently of the Context Agents neighbors. Exchanging information on the model between neighbors agents could improve the accuracy.

A New Local Active Context Learning Strategy

The Local Active Context Learning is an enhancement of Context Learning using internal information to requested specific learning situations. This mechanism is based on a collaboration inside the neighborhood of the Context Agents. In this section, we present the establishment of Context Agent's neighborhood, the detection and the resolution of learning inaccuracies. The resolutions are operational regardless of the number of dimensions. However, to simplify the illustrations, only two dimensions are represented in the figures.

Context Agent Neighborhood

A Context Agent is considered as a neighbor of the perceptions if its validity ranges intersect a neighborhood area surrounding the current perceptions. The size of this area results from the precision range prc Range , a parameter chosen by the user of the learning mechanism. For a perception p i , there is a default

Learning Inaccuracies Detection

With the previous definition of the neighborhood, six types of learning inaccuracies are defined. From the point of view of Adaptive Multi-Agent Systems, they are called Non Cooperative Situations (NCS):

Conflict NCS Detection (Fig. 3a). It is an overlap between Context Agents that have different models. For a learning problem with n dimensions, an overlap between two Contexts Agents is defined by n non-empty intersections of validity ranges. An overlap occurs if the intersections lengths between agents validity ranges are greater than d aed i . To differentiate models, a metric has to be defined by the user depending on the implemented learning models.

Concurrency NCS Detection (Fig. 3b). It is an overlap between two Context Agents that have similar models and give similar predictions. The geometry detection is the same as the Conflict NCS.

Range Ambiguity NCS Detection (Fig. 3c). It is a difference of model between two adjacent Context Agents. An ideal Range Ambiguity NCS is defined by n -1 non-empty intersections and a point intersection. In a continuous space, for 2 agents to be adjacent according to the perception p i , the distance between their boundaries must be less than d aed i . Overpopulation NCS Detection (Fig. 3d). It is two adjacent Context Agents that give similar predictions and can merge their common boundary without altering their other ranges. An ideal Overpopulation NCS is defined by n -1 equal ranges and a point intersection. d l pd i is used here to detect the adjacency. This NCS triggers an instantaneous fusion.

Incompetence NCS Detection (Fig. 3e). The Incompetence NCS detects empty areas (red dashed zones) within the neighborhood of the current perceptions and Context Agents. An empty area is detected if its dimensions in all perceptions p i are greater than d aed i . As few empty zones as possible are constructed.

Model Ambiguity NCS Detection. Any learning technique requires data. If the volume or quality of data is not adequate, this NCS is detected.

Once detected, learning inaccuracies (other than the Overpopulation NCS) are associated with a certain priority to be addressed. The order of priority from highest to lowest is: Model Ambiguity, Con- The diagonal crosses represent the perceptions that are used to generate active learning situations in order to solve the learning inaccuracies flict, Concurrency, Incompetence and Range Ambiguity. Each learning inaccuracy leads to a future active learning situation that is stored in a priority queue with the area of the overlap or void if there is one. Interrogating all Context Agents for learning inaccuracies is computationally expensive for large number of agents. The detection is only performed among all Context Agents in the neighborhood of the considered perceptions.

New Learning Rules

Following the introduction of the neighborhood and the learning inaccuracies, we present here the new learning rules.

The inaccuracy margin is removed and there is a dynamic error margin for each Context Agent. This error allows the agent to self-assess the accuracy of its model. For learning situations within its validity ranges, the better its predictions, the lower its error margin; the worse its predictions, the higher its error margin. A local error margin is defined as the average of the dynamic error margins of the Context Agents neighboring the perceptions.

A good prediction of the Best Context Agent is when the distance to the learning situation is below the local error margin. It results in an increase of its confidence c j and an update of its model with the learning situation. This way, the Context Agents' models are regularly updated to be robust to noise.

When the distance to the learning situation is greater than the local error margin, a Context Agent defines its prediction as bad. As it moves one of its ranges to exclude the current perception, it uses its neighborhood to destroy any overlap with another Context Agent and it decreases its confidence.

When there isn't any Valid Context Agent, the Best Closest Context Agent extends its ranges the cover the perceptions. If the creation of a new Context Agent is needed and if there are neighbors, they are used to initialize the properties of the new agent. If there aren't any neighbors, the created agent uses initialization values based on the perception limits of the search space and on the parameters chosen by the system user.

In relation to range extension, there is a limit beyond which a range can no longer be extended. The only way for a Context Agent to grow is then to merge with another Context Agent which doubles its confidence. This mechanism avoids oscillation behaviors for range modifications. d aed i is used as the critical validity range size for Context Agents subtractions.

The Active Strategy

The addition of the neighborhood allows to detect the learning inaccuracies in the learning process (section 3.1) and to define an active learning strategy that deals with the neighborhood inconsistencies. The strategy for solving the neighborhood inaccuracies is based on the availability of specific active learning situations. Learning inaccuracies are detected within the neighborhood at the end of learning cycles. Their associated priority defines their processing order. Each learning inaccuracy generates a learning situation that is requested to the oracle.

Conflict and Concurrency NCS Resolution. Conflict and concurrency learning inaccuracies generate learning situations in the overlap centers (figures 3a and 3b). This causes several Valid Context Agents. The closest Context Agent to the learning situation is the Best Context Agent. The other Context Agents reduce one of their ranges to exclude the current perceptions and destroy the overlap while minimizing volume loss.

Range Ambiguity NCS Resolution. An ambiguity learning inaccuracy generates two learning situations at a distance of d aed i from the borders of each Context Agent (Fig. 3c). These learning situations refine the borders.

Incompetence NCS Resolution. Each Incompetence learning inaccuracy generates a learning situation. It leads to a creation of a new Contest Agent. The incompetent area is filled with the dimensions of the learning inaccuracy void area (Fig. 3e).

Model Ambiguity NCS Resolution. In this case, the linear regression demands a certain quantity of learning situations to complete the model. As many learning situations as needed are generated at random positions within the validity ranges of the requesting Context Agent (Fig. 3f).

Experimentations

In this section, we compare learning without any NCS detection and resolution with the results taking into account only one NCS at a time, and then with all NCS together. Each learning experience is stopped after 1000 cycles because it is enough to explore the entire space. The learning mechanism receives a learning situation at each cycle. The metrics are averaged over 10 learning experiences. The models to be learnt are two linear models whose spatial distribution is as shown in Fig. 2a. On average, the duration of an experiment is about 3 seconds with the features 1 of the computer we are using. This work is planned to scale up with the number of dimensions of the search space, it is more demonstrative to present it as a 2D problem.

Metrics

We present here the metrics used during the experiments. For simplicity, we remove the n indices that symbolize the space dimension.

Generalization. To evaluate the ability of the mechanism to generalize, we look at the number of Context Agents n Ctxt used to represent the space.

Exploration of the search space. We are interested in different types of volumes that measure the exploration of the search space.

• V Ctxt = (∑ j V C j -V C f lt -V Conc )/V total It is the normalized volume explored by all the Context Agents. • V Inac = V C f lt + V Conc + V Inc It is the volume of learning inaccuracies. • V C f lt = (∑ ( j,k),1 j<k n Ctxt , f j = f k V C j ∩C k )/V total It is the normalized volume of conflicts. • V Conc = (∑ ( j,k),1 j<k N ctxt , f j ≈ f k V C j ∩C k )/V total It is the normalized volume of concurrencies. 1 Intel(R) Core(TM) i7-6600U CPU 2.20 GHz 2.81 GHz, RAM 32 GB • V Inc = 1-V Ctxt It is the normalized volume of the unexplored search space. V total = ∏ i (p max i -p min i )
is the volume of the search space with p min i and p max i the minimum and maximum perceptions experienced.

Learning Data. We are interested in the number of learning situations randomly supplied and actively requested.

• L Rdm are randomly generated learning situations from a uniform distribution in the interval [-100; 100] for each perception p i .

• L A represents all the active learning situations.

• L Model A , L C f lt A , L Conc A , L Inc A and L Rge
A are all the different kinds of active learning situations (Model Ambiguity, Conflict, Concurrency, Incompetence and Range Ambiguity).

Prediction. To evaluate the proposals of the learning mechanism, we calculate the normalized prediction error E O according to the oracle predictions:

E O = |O -O |/|O|.
The prediction metric is calculated over 250 exploitation random cycles.

Results

In this section, we present the results obtained by comparing the resolutions of the different learning inaccuracies. The metric values we give here are the averages available on T. 1.

Results without NCS Resolution

When no NCS is taken into account, it is visually noticeable (Fig. 4a) that the volume of learning inaccuracies is significant (42.28%). 159 Context Agents cover only 80.23% of the space and there is an error of 55.4% on the predictions.

Results with NCS Resolution Alone

For each of the following cases, we compare the metric values obtained with the previous case as a reference.

Conflict NCS. The treatment of conflicts does not bring any obvious visual difference (blue/green intersections Fig. 4b). 15 active learning situations are requested to reduces the volume of conflicts from 0.7% to 0.12%.

Concurrency NCS. The treatment of concurrencies brings an exploration almost without any overlap (blue/blue and green/green intersections Fig. 4c). 136 active learning situations are required to reduce the volume of concurrency from 21.81% to 1.38%. Incompetence NCS. Incompetency processing results in an exploration with almost no gaps (white areas Fig. 4d). 378 active learning situations allow to decrease the void volume (2.03%), the concurrency volume (9.85%), and the Model Ambiguity NCS (41). 53 Context Agents cover 97.97% of the search space and the prediction error is reduced to 2.68%.

L C f lt A (#) 0 ± 0 15 ± 3 0 ± 0 0 ± 0 0 ± 0 15 ± 6 26 ± 9 L Conc A (#) 0 ± 0 0 ± 0 136 ± 4 0 ± 0 0 ± 0 71 ± 11 58 ± 15 L Inc A (#) 0 ± 0 0 ± 0 0 ± 0 378 ± 50 0 ± 0 415 ± 38 185 ± 31 L Rge A (#) 0 ± 0 0 ± 0 0 ± 0 0 ± 0 132 ± 17
Range Ambiguities NCS. The treatment of ambiguities alone gives a similar exploration if not worse to the case without NCS treatment (Fig. 4e).

Results with All NCS Resolutions

When all NCS are processed during training Fig. 4f, exploration is close to the expected ideal Fig. 2c. 31 Context Agents cover 97.23% of the space. The volume of all learning inaccuracies drops from 42.28% to 3.67%, the lowest of all cases. Prediction error is the lowest with 1.81%.

Dynamic Model

Fig. 4g experiment tests the ability of the learning mechanism to reuse its knowledge and to adapt to a variation. From an experiment of 1000 cycles with all NCS (Fig. 4f), a second experiment is conducted with 1000 learning cycles on a new model. T. 1 shows that the exploration performances are slightly worse but the quantity of model learning situations L Model A is much lower.

Discussion

When none of the learning inaccuracies are addressed, the metric results are far from ideal. The prediction error is very bad, which is explained by the very large amount of non-exploitable space. Processing NCS alone allows to validate the expected behaviors but the associated explorations do not converge towards the ideal exploration. When all NCS are treated, the number of Context Agents and the prediction error are the lowest of all the encountered cases, but there are still minute learning inaccuracies. The number of Context Agents still does not reach the optimum. To reach it, an additional treatment is missing that would allow the Context Agents to reorganize their validity ranges, i.e. to split if it allows a merge. The dynamic experiment shows the capacity of the learning mechanism to adapt its exploration and to reuse already known models to accelerate learning. The learning case that we present here is a simplified case to validate our approach. Further evaluations will focus on exploring more complex search spaces with non-linear models to be learnt which are closer to real complex systems.

Related work

The approach of integrating a local model within each Context Agent differs from classical regression and classification approaches. Piecewise learning, agentified and distributed, online and dynamic, allows adding internal mechanisms that guide learning by making it active, independently of the learning technique. In this section, we present similar methods and highlight their similarities and differences.

Data Selection. The approach presented in this paper is comparable to active learning, which consists of deciding which data should be labeled from a set of unlabeled data [START_REF] Settles | Active learning literature survey[END_REF]. It also reminds semi-supervised learning, which seeks to achieve better performance by combining unlabeled and labeled data [START_REF] Li | Learning safe prediction for semi-supervised regression[END_REF]. Our work focuses on how multiagent systems allow to actively request labeled data online with a generic approach independent of the learning models.

Domain, dimension and distribution/locality.

Transfer learning uses related domains or tasks to enhance learning [START_REF] Pan | A survey on transfer learning[END_REF]. Unsupervised learning uses only unlabeled data for data aggregation or dimensional reduction problems [START_REF] Hastie | Unsupervised learning[END_REF]. Distributed learning divides the training data into subsets before processing them [START_REF] Lin | Distributed learning with regularized least squares[END_REF]. We find local learning work for classification based on generalization, continuity in prediction and scalability [START_REF] Zantedeschi | A Unified View of Local Learning: Theory and Algorithms for Enhancing Linear Models[END_REF]. Our approach is intended for different online learning problems of classification or regression depending on the implemented models with fixed dimensions. The dynamic experience shows that transfer learning is effectuated when Context Agents reorganize themselves to match the new geography.

Intrinsic Motivation. Beyond inverse reinforcement learning and learning by intention, in the fields of robotics, intrinsic motivation [START_REF] Oudeyer | Intrinsic motivation systems for autonomous mental development[END_REF][START_REF] Bondu | Active learning using adaptive curiosity[END_REF] is a way to guide exploration by focusing on the learning process itself. Intrinsic motivation is independent of the task, it promotes hierarchical learning of knowledge and the reuse of skills [START_REF] Mirolli | Functions and mechanisms of intrinsic motivations[END_REF]. It is particularly found in the field of developmental robotics and focuses on the development of robots with infantile mental capacities [START_REF] Cangelosi | Developmental robotics: From babies to robots[END_REF]. This approach is intended for blank systems that learn from scratch. In the literature, there are mostly architectures that use different learning mechanisms [START_REF] Bellas | Multilevel darwinist brain (mdb): Artificial evolution in a cognitive architecture for real robots[END_REF][START_REF] Vernon | A roadmap for cognitive development in humanoid robots[END_REF]. We take inspiration from this work but we are not yet experimenting on blank robotic systems.

Among these learning methods, our work falls within the framework of several learning domains. Our interest here is in adding internal mechanisms to our context-based meta-learning approach and not in comparing with other isolated learning methods that do not match all of our concerns.

Conclusion and Perspectives

As multi-agent systems are well suited to cope with the constraints of the sociotechnical world, we have proposed a learning paradigm based on the extension of the contextual learning pattern. This extension is based on the use of information shared in the neighborhood of a learning situation. We proposed a taxonomy of these situations and a solution based on agents cooperation. Self-observation of self-adaptive multi-agent systems allows to detect learning inaccuracies in the local models. The local active learning situations bring improved prediction performance by anticipating ambiguous situations and solving them. All the behaviors of the cooperative agents are designed generic in order to be agnostic from the application domain, the learning technique and the number of dimensions. We are currently working in the field of robotics on multi-articulated robotic arms in order to learn their inverse kinematics model. Further work will also focus on the comparison with other learning techniques.

  a labeled prediction vector. Perceptions denote the vector of inputs P n = [p 1 , . . . , p n ] ∈ R n and a learning situation is defined by the vector L n,m = [P n , O m ]. The goal of the Context Learning System is to give as output a prediction vector O m ∈ R m where O m = O m . Each Context Agent C j n is in charge of managing the learning model for the j th pavement in dimension n which represents a part of the schema. The global function F is approximated by a local function f j n (p 1 , . . . , p i , . . . , p n ) = o j m with o j m ∈ R m . The n-dimension space is reduced to a n-parallelotope for every Context Agent in the form of validity ranges R j n ] for each perception p i (Fig.

  Simple learning problem of 2 linear models symbolized by different colors put of the system. If no Valid Context Agent can be identified, Closest Context Agent to the perceptions is designated as the Best Context Agent. Implemented Model. In this study, each Context Agent C j n has a local linear regression model f j n . In this case, the prediction vectors and the oracle predictions are a real values O 1 and O

  minimum experienced values during the learning phase on the perception p i . From this, it results the learning precision distance d l pd i = 0.5 * r creation i and an approximation error distance d aed i = 0.25.r creation i . The neighborhood radius is r N i = 2.r creation i .

  learning inaccuracies with 1D projections.

  Model Figure 4: Screen shots of learning experiences after 1000 training cycles with different NCS resolution. Each color is a different linear model.

Table 1 :

 1 Metrics of exploration, learning data, generalization and prediction averaged over 10 episodes of 1000 learning cycles for different NCS resolutions (presented section 4.1). Red values represent worse results than reference case (No NCS), green values represent better results than the reference case and bold values represent the impacted learning data for each case. The dynamic column represents an additional experiment made with 1000 more learning cycles on a different disposition of the models after a classical learning episode with all the NCS

  is based on Context Learning. To implement Piaget's schema in a n-dimension space, Context Agents are used to approximate local models. Models are based on any machine learning technique (neural networks, linear regression, SVMs, decision trees, k-means...). The global model can be described as a hidden function


Andy Combey
email: andy.combey@univ-grenoble-alpes.fr

Agnès Tricoche

Laurence Audin

David Gandreau

Carlos Benavente Escóbar

José Bastante Abuhadba

Hernando Tavera

Miguel Ángel Rodríguez-Pascua

Andy Combeya

Agnès Tricocheb

Laurence Audina

David Gandreauc

Carlos Benavente Escóbard

José Bastante Abuhadbae

Hernando Taveraf

Miguel Ángel Rodríguez-Pascuag

Monumental Inca remains and past seismic disasters: A relational database to support archaeoseismological investigations and cultural heritage preservation in the Andes

Keywords: Archaeoseismology, Database, Seismic Hazard, Cultural heritage, DRR, Cusco

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

relevant support for disaster risk reduction plans in archaeological sites conservation. We stress the necessity of adopting cost-effective and easy-to-implement tools for cultural heritage monitoring in emerging countries through this case study. Our database may represent a relevant methodological background and template for further initiatives in both fields of archaeoseismology and cultural heritage protection.

Introduction

As a social, cultural and symbolic act, architecture and, more specifically, the built heritage is an integral part of the collective memories and traditions [START_REF] Caimi | Cultures constructives vernaculaires et résilience: entre savoir, pratique et technique: appréhender le vernaculaire en tant que génie du lieu et génie parasinistre[END_REF][START_REF] Garnier | Natural hazards, disasters and local development[END_REF][START_REF] Ortega | Traditional earthquake resistant techniques for vernacular architecture and local seismic cultures: A literature review[END_REF]. In 1972, during the General Conference of the UNESCO, State parties agreed on the necessity of "ensuring the identification, protection, conservation, presentation and transmission to future generations of the cultural and natural heritage" (UNESCO, 1972, Art.4). To do so, the international organization proposed several guidelines related to seismic hazard mitigation (UNESCO, 2007, p. 173): "reducing risk through ensuring maintenance," "strengthening buildings," "improving earthquake warning systems" as well as "developing comprehensive earthquake plans." The creation and development of monitoring systems thus represent a prerequisite to follow those preparedness guidelines correctly.

Identifying earthquake evidence and damage in archaeological remains has long been seen as a re-active investigation. Archaeoseismologists intervened "after" a seismic event with the objective to improve the seismic catalog and thus better assess the regional seismic hazard.

Hence, ancient human settlements and monuments have turned out to be valuable markers of past seismic activity, providing complementary information to the traditional geomorphological and paleoseismological studies and filling the gap between prehistorical and instrumental seismology [START_REF] Karakhanyan | Archaeoseismological studies at the temple of Amenhotep III, Luxor, Egypt[END_REF][START_REF] Noller | Archaeoseismology. Shaking Out the History of Humans and Earthquakes[END_REF][START_REF] Silva | Archaeoseismic record at the ancient Roman City of Baelo Claudia (Cádiz, south Spain)[END_REF][START_REF] Similox-Tohon | The identification of an active fault by a multidisciplinary study at the archaeological site of Sagalassos (SW Turkey)[END_REF]. The recent shift from qualitative to (semi)quantitative methods not only strengthens the archaeoseismological methodology and its scientific basis [START_REF] Ambraseys | Earthquakes and archaeology[END_REF][START_REF] Galadini | Archaeoseismology: Methodological issues and procedure[END_REF][START_REF] Sintubin | Archaeoseismology[END_REF] but also provides a great opportunity to connect the research field to proactive strategies such as risk management and disaster risk reduction (DRR) programs in the context of cultural heritage protection [START_REF] Jusseret | Earthquake Archaeology: A Future in Ruins?[END_REF][START_REF] Sintubin | Archaeoseismology: Past, present and future[END_REF]. Indeed, the large-scale registration of Earthquake Archaeological Effects (EAE -Rodríguez-Pascua et al., 2011), the use of remote sensing tools (Lidar, photogrammetry -Forlin et al., 2018;[START_REF] Yerli | Assessment of seismically induced damage using LIDAR: The ancient city of Pınara (SW Turkey) as a case study[END_REF] as well as the construction of seismic deformation simulation thanks to 3D models [START_REF] Hinzen | Rotation of Objects during the 2009 L'Aquila Earthquake Analyzed with 3D Laser Scans and Discrete-Element Models[END_REF][START_REF] Hinzen | Rectangular Blocks vs Polygonal Walls in Archaeoseismology[END_REF][START_REF] Pecchioli | Evidence of seismic damages on ancient Roman buildings at Ostia: An arch mechanics approach[END_REF] constitute important steps towards monitoring strategies of archaeological remains. Addressing the impact of past earthquakes on cultural heritage has turned into an emerging priority, particularly in the Mediterranean area [START_REF] Marchetti | The Archaeoseismology of Historical Buildings: A Model Study from the L'Aquila Area in Italy[END_REF][START_REF] Montabert | Tracing the seismic history of Sant'Agata del Mugello (Italy, Tuscany) through a crossdisciplinary approach[END_REF][START_REF] Remondino | Reality-based 3D documentation of natural and cultural heritage sites-techniques, problems, and examples[END_REF]. However, in South America and across the High Andes, research is still at its early stage [START_REF] Aguilar | Investigations on the structural behaviour of archaeological heritage in Peru: From survey to seismic assessment[END_REF][START_REF] Briceño | Seismic Vulnerability Assessment of a 17th Century Adobe Church in the Peruvian Andes[END_REF][START_REF] Noel | Seismic Assessment of the Church of San Sebastian in Cusco, Peru by Means of Pushover Nonlinear Analysis[END_REF]. In Peru, considered as the most vulnerable country of the continent in terms of seismic hazard [START_REF] Stillwell | Natural hazards and disasters in Latin America[END_REF]World Bank, 2012), increasing the risk preparedness and resilience of built heritage requires innovative and multipurpose approaches. To fill this gap in the Cusco region, we propose the implementation of a new database designed to characterize the level of damage of the cultural heritage facing earthquake threats (or even broader natural disastrous events).

Research aim

The Cusco area stands out for its rich pre-Columbian and colonial heritage. While the area and its monuments were severely affected by past ground shaking episodes, the current seismic hazard remains poorly assessed and its implications in terms of heritage vulnerability sometimes even overlooked [START_REF] Carlotto | La Geología en la conservación de Machupicchu, serie I Patrimonio y Geoturismo N o 1[END_REF][START_REF] Noel | Seismic Assessment of the Church of San Sebastian in Cusco, Peru by Means of Pushover Nonlinear Analysis[END_REF]. In the framework of the archaeoseismological project RISC ("Risque sismique, Incas et Société à Cusco"), we developed a user-friendly database, whose aim was to keep a record of potential seismic effects observed in Inca remains (ca.1300-1532 AD). Initially designed as an ephemeral data collection tool, the RISC database has turned into a permanent platform for data mining. Taking into account the main challenges that South America has to face in terms of cultural heritage preservation [START_REF] Gamboa | Archaeological Heritage at Risk: Preservation, Destruction and Perspectives for Pre-Columbian Sites from the Periphery of Trujillo, Peru[END_REF]ICCROM, 2004), we consider the use of large and organized datasets in archaeoseismological studies as a particular promising resource to improve the seismic vulnerability assessment and management of numerous touristic archaeological sites.

Through this case study, we hope to offer a valuable database template, easy to use and adapt for future research.

Theory

Seismic risk in the Andes

Social vulnerability to earthquakes is a crucial challenge in the coming years, exacerbated by the constant and rapid urbanization processes [START_REF] Jackson | Fatal attraction: living with earthquakes, the growth of villages into megacities, and earthquake vulnerability in the modern world[END_REF]. The increasing exposure is probably even more acute in South America and especially all along the Andes.

Actually, the mountain range that borders the western part of the continent concentrates an overwhelming majority of the current seismic strain and deformation rate [START_REF] Costa | An overview of the Main Quaternary Deformation of South America[END_REF][START_REF] Dewey | Active tectonics of the Andes[END_REF]. The Andean region is also marked by a high density of population compared to the rest of South America, hosting mega-cities like Santiago, Lima, Quito or Bogota. Recent seismic risk assessment evaluates that more than one-third of the total population of the continent "may experience strong ground shaking in a 50-yr period (2% probability of exceedance in 50 yrs)" and 30 millions of people "reside in areas of high hazard where earthquakes are quite likely (50% in 50 yrs)" [START_REF] Petersen | Seismic Hazard, Risk, and Design for South America[END_REF]. Anarchic urban sprawl, informal settlements and deficient building standards are aggravating factors that alter the capacity of Andean societies to cope with violent ground motion episodes.

Unfortunately, little is still known on the quaternary deformation and associated seismic activity [START_REF] Costa | An overview of the Main Quaternary Deformation of South America[END_REF]. Suffering from huge discrepancies between inter-plate and intra-plate seismicity [START_REF] England | Uncharted seismic risk[END_REF], the current global seismic risk assessment remains heterogeneous and too poor in many regions distant from the active tectonic margins. Unlike the well-monitored subduction seismicity, scattered active crustal faults in continental interiors are not sufficiently mapped and characterized (motion type, return period, strain rates… - [START_REF] Petersen | Seismic Hazard, Risk, and Design for South America[END_REF]. Local and regional models for seismic hazard assessment, first attempt to set up a scientific basis for political decision-making, are still in their infancy [START_REF] Das | A probabilistic seismic hazard assessment of southern Peru and Northern Chile[END_REF][START_REF] Leyton | Preliminary re-evaluation of probabilistic seismic hazard assessment in Chile: from Arica to Taitao Peninsula[END_REF] and few are the ones that consider shallow crustal seismicity [START_REF] Aguilar | Probabilistic Seismic Hazard Assessment in the Peruvian Territory[END_REF]Asociación Colombiana de Ingeniería Sísmica, 2010;[START_REF] Beauval | A New Seismic Hazard Model for Ecuador[END_REF][START_REF] Yepes Arostegui | Probabilistic seismic hazard assessment in Ecuador: inputs, practical applications and communication[END_REF].

In such active tectonic areas, traditional approaches (e.g., instrumental seismology, tectonic geomorphology and paleoseismology) appear to be insufficient to assess properly the seismic hazard and risk. The lack of intelligible written sources before the Spanish Conquest (midsixteenth century) diminishes the potential of historical seismic studies substantially. Crossand multi-disciplinary approaches are therefore needed to improve the regional seismic catalog and get an appropriate resolution to the moderate-low return period associated with crustal faulting [START_REF] Blumetti | Quaternary earthquakes: Geology and palaeoseismology for seismic hazard assessment[END_REF][START_REF] Liu | Mid-continental earthquakes: Spatiotemporal occurrences, causes, and hazards[END_REF]. Archaeoseismology has demonstrated to be particularly well suited to address this issue and link accurate instrumental data from the last century with long-time sedimentological/limnological records [START_REF] Caputo | Archaeo-and palaeoseismological investigations in Northern Thessaly (Greece): Insights for the seismic potential of the region[END_REF][START_REF] Meghraoui | The Contribution of Paleoseismology to Earthquake Hazard Evaluations[END_REF][START_REF] Sintubin | Archaeoseismology[END_REF][START_REF] Stiros | Identification of earthquakes from archaeological data: methodology, criteria and limitations[END_REF]. The built archaeological heritage of South America, whose history spans at least the two last millennia, represents a promising marker of past seismic activity. Results may complement scanty colonial accounts and improve the dating of poorly constrained seismic events evidenced in paleoseismological trenches.

As the result of centuries of building experiments, the cultural heritage reflects a long empirical learning process with regard to seismic hazard. However, given its complex history and our inability to manage it properly, this legacy constitutes one of the most vulnerable sectors with respect to earthquakes and thus requires special attention. Unfortunately, it remains too often a second-ranking priority for emerging economies.

Challenges of the conservation of the cultural heritage

While cultural heritage and particularly archaeological sites play a crucial part in the identity construction process of southern American countries (national symbol, self-esteem, touristic income), the lack of financial resources hampers ambitious conservation plans (ICCROM, 2004;[START_REF] Sevieri | A multi-hazard risk prioritization framework for cultural heritage assets[END_REF]. Governments dedicate most of their funding legitimately to reduce poverty and support the productive economy and are thus not able to preserve adequately their Cultural assets [START_REF] Heras | A value-based monitoring system to support heritage conservation planning[END_REF]ICCROM, 2004). A lack of institutional memory in public institutions and authorities as well as issues in terms of formation of the persons in charge of the Conservation work are two supplementary factors that explain dysfunctions in the cultural heritage preservation policies [START_REF] Jokilehto | Training as an essential part of risk preparedness[END_REF]. Despite the recent effort to overcome those problems, a report requested by the World Heritage Committee in 2006 stated that "most world heritage properties, particularly in developing areas of the world, do not have established policies, plans and processes for managing risk associated with potential disasters" (World Heritage Committee, 2006, p. 1). However, cultural heritage buildings are even more at risk because of their great age as well as the several constructive phases and the inadequate human interventions that may have affected them [START_REF] Despotaki | Evaluation of Seismic Risk on UNESCO Cultural Heritage sites in Europe[END_REF][START_REF] Fuentes | Seismic Vulnerability and Risk Assessment of Historic Constructions: The Case of Masonry and Adobe Churches in Italy and Chile[END_REF][START_REF] Ferrigni | ATLAS of local seismic cultures (supplement in Stop Disasters)[END_REF]The Getty Conservation Institute, 2015).

Regarding the seismic risk, one main interrogation is nonetheless raising: how do we protect the cultural heritage from a natural hazard that is intrinsically unpredictable and uncontainable?

In case of an earthquake, it is impossible to remove the causative factor of damage, but it is possible to mitigate it [START_REF] Feilden | Between Two Earthquakes. Cultural Property in Seismic Zones[END_REF]. The main organizations and institutions involved in the conservation field advocate for preferring a pro-active (preventive) approach to a re-active (curative) one [START_REF] Feilden | Management Guidelines for World Cultural Heritage Sites[END_REF][START_REF] Jokilehto | ICCROM's Involvement in Risk Preparedness[END_REF]UNESCO, 2010;[START_REF] Van Balen | Challenges that Preventive Conservation poses to the Cultural Heritage documentation field[END_REF]. Considered as the best-cost-effective strategy, the preventive approach aims to maintain authenticity by reducing the building's vulnerability and limiting the potential destruction. That results in expensive retrofitting works but also in more modest monitoring devices and condition assessment surveys to assess the seismic vulnerability of the buildings (UNESCO, 2010). Monitoring is based on the concept of time and change and supposes the existence of constantly updated documentation about the heritage of interest and the potential vulnerability factors [START_REF] Gandreau | Inventory of earthen architecture[END_REF][START_REF] Paolini | Risk management at heritage sites: a case study of the Petra world heritage site[END_REF][START_REF] Van Balen | Challenges that Preventive Conservation poses to the Cultural Heritage documentation field[END_REF]. Archaeological and historical buildings need, therefore, to be considered in a long-term perspective [START_REF] Stovel | Risk preparedness: a Management Manual for World Cultural Heritage[END_REF]. Earthquakes experienced by the buildings in the past as well as their consequences, are particularly helpful in making the best diagnosis. Prerequisite to any conservation decision (ICCROM, 2004), monitoring has to rely on a multi-sectoral and collaborative approach (UNISDR, 2015).

Databases appear to be well-suited to organize large sets of data and ensure standardized and harmonized methodologies. As it has been previously demonstrated, they are particularly helpful for supervising cultural heritage [START_REF] Berg | Using a GIS-based Database as a Platform for Cultural Heritage Management of Sites and Monuments in Norway[END_REF][START_REF] Zerbini | Developing a Heritage Database for the Middle East and North Africa[END_REF] and supporting systematic processes of damage assessment (UNESCO, 2010). How can the system be nevertheless more useful for safeguarding the heritage? An archaeoseismological database may provide relevant input data for future risk reduction.

Material and methods

Overview of the RISC project

Famous worldwide for its cultural heritage, including notably the Cusco city and the Machu Picchu archaeological site inscribed both on the World Heritage List (https://whc.unesco.org/fr/list/, last accessed July 25, 2021), the Cusco region (Peru) is less known for its recurrent and potentially destructive seismicity. As various Andean regions distant from the subduction trench and as explained in 3.1, the Cusco area suffers from a poor understanding of its crustal seismicity. The concise historical catalog (Silgado Ferro, 1978;[START_REF] Tavera | Catálogo General de Isosistas para sismos peruanos[END_REF] available, coupled with still scarce paleoseismological studies (Benavente [START_REF] Escobar | Neotectónica y Peligro Sísmico en la Región Cusco[END_REF][START_REF] Cabrera | Surface Rupture Associated with a 5.3-mb Earthquake: The 5 April 1986 Cuzco Earthquake and Kinematics of the Chincheros-Qoricocha Faults of the High Andes, Peru[END_REF][START_REF] Palomino Tacuri | Caracterización Morfo-tectónica y paleo-sismológica del Sistema de Fallas Pachatusan -Cusco (Tésis de Licenciatura)[END_REF][START_REF] Guevara | Estudio Morfotectónico y Paleosísmico de las fallas Tambomachay y Qoriqocha, Implicancia en el peligro sísmico de la región Cusco[END_REF], does not allow to assess properly the return period of the numerous active faults of the region, which triggered damaging earthquakes in historical (1650,1950,1986) and pre-historical times [START_REF] Combey | Evidence of a large "prehistorical" earthquake during Inca times? New insights from an indigenous chronicle (Cusco, Peru)[END_REF]. We decided thus to develop the RISC project, whose objective is to improve the seismic hazard assessment by implementing the first large archaeoseismological survey in South America. Due to their particular and massive megalithic architecture, monumental Inca settlements of the Cusco and Sacred Valley constitute well-suited "seismoscopes" [START_REF] Sintubin | Archaeoseismology[END_REF] that may have recorded large ground motion events since the fourteenth century [START_REF] Rodríguez-Pascua | Did earthquakes strike Machupicchu?[END_REF]. The location of numerous Inca sites in seismically active areas during the instrumental period (since 1960) as well as their distribution near active normal faults, emphasize their archaeoseismological potential (Fig. 1a). We surveyed 17 monumental archaeological sites of the region (Fig. 1a) with the objective to identify and register EAE, i.e., architectural damage, direct consequences of seismic activity (Fig. 2). on [START_REF] Ericksen | The Cusco, Peru, Earthquake of May 21, 1950[END_REF]Silgado Ferro, 1978;[START_REF] Tavera | Catálogo General de Isosistas para sismos peruanos[END_REF]b) Proportion of High, Medium, and Low levels of confidence of EAE records for each archaeological site. The chart displays the results of the previous database version, i.e., the level of confidence is only based on the assessment of the seismic origin. Sites with an insufficient dataset are reported in grey.

The management of a large amount of observations was soon understood as the main challenge of the archaeoseismological fieldwork leading to several issues in terms of methodology and data analysis. Therefore, we decided to build a database that would allow storing the data in an orderly manner. A database speeds up indeed considerably the real-time data acquisition, facilitates its management and processing, guarantees the homogeneity of all of those input values [START_REF] Anichini | A database for archaeological data recording and analysis[END_REF][START_REF] Gattiglia | Databases in Archaeology[END_REF] 4.2 A field-designed database with a single front-end user interface We used the proprietary FileMaker Pro 16 software, which has the advantage of providing both the data storage and the user interface. Easy-of-use and ergonomic, thanks to its customizable interface, this Database Management System (DBMS) provides a particularly well targeted solution to meet investigation needs. Thanks to the FileMaker Go extension, freely available in any iOS device, database models are easily transferable and adaptable to the two main types of mobile devices (smartphone or tablet). The main advantage of those devices is to provide an interface wide enough to allow a direct digital entry during the fieldwork [START_REF] Gattiglia | Databases in Archaeology[END_REF]. The use of a mobile device as the main tool for data collection required rethinking deeply the design of the user interface to address the specific fieldwork requirements (accuracy, simplicity, rapidity). We built, therefore, a straightforward database organized around one main table, the "Damage" table (Supplementary 2), and characterized by a sober and intuitive display.

"Damage" gathers the main information relative to the core of the investigation topic, i.e., the EAE registered on the archaeological heritage (Fig. 2). Moreover, we integrated basic information relative to the geographical and architectural context of the EAE.

The most suitable and easiest way to make RISC operative for users was to create one form composed of three distinct tabs (Fig. 3). The first one, entitled "Context" includes basic data on the geographical and architectural environment of the EAE (Fig. 4). The second tab focuses on the EAE description and characterization. Finally, the third one is dedicated to the illustration of the registered EAE (any type of visual representation). By means of those three tabs, the present form reproduces and supports the three main steps of the EAE record. It has turned into a single front-end user interface, simplifying the data entry. We made some other adjustments to make the interface as user-friendly as possible:

-A widespread use of thesauri and dynamic lists of values reduce the risk of data heterogeneity and the entry time. Four interdependent values lists, which feed into each other as data is entered, were inserted in the "Context tab", enabling the database user to fill the tab according to a hierarchical tree (Fig. 4 -Supplementary 2). Standardizing the dataset avoid creating future accidental discrepancies and speeds up hence the data analysis thanks to efficient queries.

-The automatized data entry for some metadata fields. Among others, that is the case for the dates of creation and modification of each record. They are directly managed by FileMaker and do not need any supervision.

-Script-writing dedicated to task automation such as the taking of picture or the GPS coordinates acquisition (Supplementary 2).

The current structure and design of the RISC database do not prohibit or impede future evolutions or extensions. The flexible nature of the database opens the door to substantial adjustments, providing solutions to other scientific needs and questioning.

An adaptable and customisable tool enhancing the archaeoseismological methodology

Fieldwork procedures and methodologies are still too often unreported in the archaeoseismological literature, and it is therefore difficult for the reader to understand how the EAE and evidence were identified, ranked and interpreted [START_REF] Galadini | Archaeoseismology: Methodological issues and procedure[END_REF]. The development and design of a database in the framework of the project RISC came with an automation of the data recording and enabled, thus the creation of additional fields that may improve substantially the data quality and its assessment.

Recording architectural damage referred to as "Earthquake Archaeological Effects" does not mean in any way that the potential non-seismic causes are completely ruled out from the scientific discussion. That is the global quality of the dataset and level of confidence in the archaeoseismological observations, as a statistic assessed through metadata fields, that allows discussing the potential impact of past earthquakes at the scale of an archaeological site or even a region (Giner Robles et al., in press;Giner-Robles et al., 2011 -Fig.1b). That is why such a database would be an important first step towards studies on paleo-or historical earthquakes on a peculiar architecture such as the Inca monuments.

To meet the requirements of both data assessment and fieldwork, we considered a qualitative assessment based on clear and simple criteria as the most adapted and effective solution. We created two metadata fields (Fig. 3) based on a list of values and containing four probability and confidence levels ("Low", "Medium", "High" and "Certain"). We originally created one metadata field, whose objective was to assess the level of confidence in the seismic cause of the damage (Fig. 1b -1 in Table 1). We introduced then a new one related to the difficulty of characterizing the recorded EAE. This field addresses the different measurement biases and gives the reader a qualitative estimation of the uncertainty of the measurements and observations.

The filling of the second metadata field (2 in Table 1) is based on a limited number of criteria (accessibility to the architectural feature, presence of vegetation cover as well as alterations, posterior to the damage that makes difficult the observation and characterization). On the other hand, the interpretation of the seismic cause of the damage (1 in Table 1) depends on several indicators:

-The masonry type (rustic, cellular, cyclopean, polygonal and sedimentary -Agurto [START_REF] Agurto Calvo | Estudios acerca de la construcción, arquitectura y planeamiento incas[END_REF]. Those different categories are directly related to different rock types (calcareous/andesite/granite) and distinct layouts (forms and types of courses). They have therefore different vulnerabilities to slow deterioration processes. For instance, the rustic masonry type in Inca architecture is highly vulnerable to a large spectrum of deterioration processes (dissolution, vegetation growth, physical weathering and alteration) that makes it more difficult to distinguish effects related to climatic processes from damage induced by seismic shaking; -the damage aspect and dimension; -the petrological and geological contexts (water ingress in the architecture, slope instability, soil and rock properties and structural weaknesses); -the management of the archaeological site (site history and large restoration works).

Based on the presence or absence of "positive" criteria, it is possible to assign a specific level of confidence for each recorded EAE. This method allows assessing quickly the quality of the archaeoseismological data at the site and regional scale.

Due to the unpredictable and changing nature of the fieldwork, the database has to be adjusted and improved frequently following an iterative process. Those improvements originate principally from the trial and error process (back and forth between field and laboratory).

However, the DBMS offers great flexibility making it possible to cope easily with superficial and structural changes. Database extensions do not alter the current functioning and do not necessarily induce large modifications of the front-end user interface. The particularity of FileMaker databases, able to run on both fixed and mobile devices, constitutes a great opportunity to imagine and test new database versions on a computer without modifying the operative version available on tablets during the survey work (Endnote 1). As an example, we developed the first extension to indicate a potential causal relationship between one particular seismic event and the recorded EAE. This add-on takes form through an additional and optional button in the bottom part of the main interface. Clicking on this button will lead the user to select one existing seismic event related to the architectural damage recorded if or when known or will guide him to create a "new" event responsible for the damage (Fig. 3). Besides its utility in distinguishing EAE produced by distinct past earthquakes (the chronological assumption will require bibliographical and/or historical sources - [START_REF] Rajendran | Archeological and Historical Database on the Medieval Earthquakes of the Central Himalaya: Ambiguities and Inferences[END_REF], the extension may prove to be particularly relevant during a survey carried out immediately after a future destructive seismic event [START_REF] Cancino | Damage Assessment of Historic Earthen Buildings after the August 15[END_REF][START_REF] Davis | Identifying archaeological evidence of past earthquakes in a contemporary disaster scenario: case studies of damage, resilience and risk reduction from the 2015 Gorkha Earthquake and past seismic events within the Kathmandu Valley UNESCO World Heritage Property (Nepal)[END_REF]. This particular case demonstrates how much the current RISC database might be enlarged and upgraded in the near future to address new scientific issues.

Regarding RISC perspectives, we should consider several shortcomings and feasible improvements. The creation of a well-organized dataset of earthquake-induced damage on archaeological sites of the Cusco region has one fundamental implication: the reproducibility of the archaeoseismological investigation enabling the periodical update of the information while keeping track of previous recordings as an indicator of potential changes [START_REF] Van Balen | Challenges that Preventive Conservation poses to the Cultural Heritage documentation field[END_REF]. Taking into account this change in outlook induces a substantial widening of the database scope and opens the door to interesting adjustments. We could only mention some of them: new fields dedicated to the qualitative estimation of the global state of conservation of the architectural feature and indices assessing the level of structural risk caused by the EAE. Furthermore, we may consider enhancing the temporal dimension of the EAE recording as a means to make the database even more suitable for periodic archaeoseismological surveys.

We developed RISC as a user-friendly program to support and strengthen our archaeoseismological project. Table 1. Two metadata fields, providing a level of confidence in 1-the seismic origin of the damage and 2-the measurement precision and difficulty, were added to the database interface. This table summarizes the main criteria used for the most common EAE types registered during our survey. Those criteria determine the level of confidence based on a qualitative scale ranging from "Low" to "Certain". '//' : the criterion does not apply to this EAE type 'X' : no « positive » criterion 'Row in grey': confidence level not registered.

Results and discussion

Facilitating archaeoseismological survey

The archaeoseismological survey carried out within the Cusco area involved nine persons during two field campaigns. Those two campaigns of three months in total led to the inventory of more than 5000 architectural features in 17 archaeological sites (Fig. 1a). The implementation of a tailor-made database contributed to improving significantly the speed and efficiency of the fieldwork. Three semi-automatized and multifunctional entry processes were particularly useful: the creation of several dynamic lists of values, the connection between several tablet functions and the database (GPS, camera…), and the possibility to duplicate the DBMS on several tablets without affecting the data homogeneity. Working in pairs was particularly well-suited and productive. As an illustration, one pair was able to register more than 100 EAE in only a half day of work in Pisaq settlement. Even if it depends obviously on the density of seismic damage in Inca buildings, it shows how RISC brought powerful support to the data acquisition (detailed and accurate).

The database not only fastens the entry time it also allows a standardized data quality assessment. Although qualitative, both metadata fields we imagined to assess the data quality enable evaluating the archaeoseismological potential for each site visited as well as the precision for each single EAE record (measurements and observations). At the time of the archaeoseismological survey, the database included only one metadata field (See 4.3). The results of the data quality provide interesting results about the relevancy of the archaeological sites datasets. In three of the 17 archaeological examined, the sample was too small (n<20)

and/or involved an insufficient proportion of medium and high-quality indices (<50% -in grey in Fig. 1b). Although we considered, in the frame of our study, those three sites as irrelevant for the archaeoseismological interpretation, all the data will be stored and will remain available for future purposes. The confidence indexes represent valuable feedback for future investigations in the same area, necessary to carry out better-targeted surveys.

Archaeoseismological methodologies are particularly dependent on the type of architecture and thus EAE that professionals may encounter. The typologies as well as the identification criteria have to fit the geographical and cultural context and the research needs, influencing the database content and interface. While the database conception needs to be tailor-based, we consider that the structure of our database may be a helpful template for other researchers in South America and an off-the-shelf system in case of an earthquake.

Re-assessing the seismic hazard in the Cusco region

The archaeoseismological approach carried out in Cusco highlighted numerous seismic damage on Inca architecture along the Sacred and Cusco valleys. Through statistical and qualitative analysis detailed in 5.1, survey records stored in RISC were quickly processed. We concluded on the undeniable presence of EAE in 14 archaeological sites of the area (Fig. 1).

Although further research is required to date the EAE registered and assesses earthquake recurrence; preliminary results demonstrate an unexpectedly large impact of ground motions.

The wide distribution and common occurrence of EAE argue for a drastic reappraisal of the (pre)historical seismicity in that region, seismicity that was underappreciated before. Several Inca remains located in the Sacred valley display seismic damage (e.g., Machu Picchu, Ollantaytambo, Huchuy Qosqo and Pisaq), contrasting indeed with the low level of seismic activity during the instrumental era (Fig. 1a -Supplementary 1) and contradicting past statements on the seismic vulnerability of Machu Picchu [START_REF] Carlotto | La Geología en la conservación de Machupicchu, serie I Patrimonio y Geoturismo N o 1[END_REF].

The dating of EAE is still a critical point when dealing with poorly contextualized remains. It requires crossing approaches to complement the archaeoseismological data. That is why we develop additional detailed tables, including architectural, archaeological and seismological information. Those linked tables do not only contextualize EAE in their build environment, they also foster the multidisciplinary collaborative effort around this specific topic.

Immediately after the archaeoseismological survey or during the post-processing, the user has the possibility to add data about the dating and characteristics of archaeological buildings or past seismic events found in the scientific literature. This accretionary process of data input/storing increases substantially the cross-disciplinary potential and leads to a better involvement of archaeological, architectural, and paleoseismological results into the final interpretation.

Finally, the RISC database contributed substantially to the reassessment of the seismic hazard in the area thanks to its spatial dimension. The GIS compatibility of the database outputs (spreadsheet files) enables quick visualization of the EAE distribution at a regional scale and within a studied site. Looking at the global distribution and density of EAE exhibits a clear pattern: a stronger seismic impact in the Eastern part of the Sacred Valley and the core of the Cusco valley (Fig. 1a). Refining this data will allow maybe to identify a common seismic source responsible for the damage. Similarly, the precise maps derived both from the geolocation (Fig. 5a) and the detailed architectural context available for each record are the starting point for will open the door to the identification of vulnerability factors and local site effects [START_REF] Brando | Structural Survey and Empirical Seismic Vulnerability Assessment of Dwellings in the Historical Centre of Cusco, Peru[END_REF]. The organized and comprehensive dataset gathered by the database enables, even, a precise mapping of the EAE at the building scale (Fig. 5b). This multi-scale analysis enhances considerably the archaeoseismological interpretation and constitutes a prerequisite for periodic inspections.

As we demonstrated in 5.1 and 5.2, RISC was designed as a powerful tool to support two main phases of the seismic hazard assessment: the data collection and the past earthquake characterization. Bearing in mind that the most profitable way to assess the vulnerability of a historic building is the analysis of the consequences induced by the previous earthquake in its fabric [START_REF] Cancino | Damage Assessment of Historic Earthen Buildings after the August 15[END_REF][START_REF] Feilden | Between Two Earthquakes. Cultural Property in Seismic Zones[END_REF], the database may have a crucial role in strengthening the risk preparedness in archaeological heritage programs.

Monitoring the archaeological heritage

Initially, our archaeoseismological survey was conceived as an ad hoc data acquisition, i.e.

responding to an academic project completely disconnected from current heritage vulnerability issues. Archaeoseismologists have developed though a specific expertise in architecture that can benefit considerably to heritage stakeholders and curators.

Considering converting the "casual" survey into a systematic and periodic inspection requires taking into account preservation concerns and rethinking completely the whole potential of our approach. Although the current objective of RISC is to record and inventory seismic damage only, this type of structural alteration may constitute important weaknesses in the building fabric, sensitive to other destructive processes (erosion, landslides, human actions …). The dataset obtained in the framework of an archaeoseismological research project turns out, therefore, to be an ad hoc condition assessment of the archaeological heritage (Fig. 6). It brings valuable information on the state of conservation of the buildings and calls for a regular implementation of such analysis. The database is, in that sense, a promising tool for monitoring the state of conservation of the building and preventing potential deterioration of the structure.

As previously mentioned in 4.3, the database structure might be easily improved to take into account this temporal dimension in the data acquisition. According to previous studies, some 50 percent of the damage during an earthquake is directly related to the lack of maintenance [START_REF] Feilden | Between Two Earthquakes. Cultural Property in Seismic Zones[END_REF]. If this figure does not address the situation for the cultural heritage, in particular, the incidence of too scarce and/or inappropriate conservative works was yet emphasized as a major vulnerability factor [START_REF] Brando | Structural Survey and Empirical Seismic Vulnerability Assessment of Dwellings in the Historical Centre of Cusco, Peru[END_REF][START_REF] Cancino | Damage Assessment of Historic Earthen Buildings after the August 15[END_REF]. Based on the frame of reference that constitutes the ad hoc inspection and based on the seismic hazard data provided by the archaeoseismological approach, two critical DRR phases may benefit from the present methodological tool: the monitoring pre-and postintervention (Fig. 7). Once a large dataset has been collected and has been made available, it converts into relevant support for assessing the evolution of the archaeological remains state and for proposing new conservation plans. Similarly, the inspections conducted with the database will contribute to evaluate the positive or negative impact of potential retrofitting works. We are thus convinced that an archaeoseismological database like RISC has a role to play in helping to quantify the threats, scaling the prevention measures and controlling their effects (Fig. 7).

In heritage conservation, vulnerability analysis results too often in complex and resourceconsuming procedures [START_REF] Canuti | Preliminary Remarks on Monitoring, Geomorphological Evolution and Slope Stability of Inca Citadel of Machu Picchu (C101-1)[END_REF][START_REF] Ravankhah | Integrated Assessment of Natural Hazards, Including Climate Change's Influences, for Cultural Heritage Sites: The Case of the Historic Centre of Rethymno in Greece[END_REF], leading to an everwidening gap between academics and heritage curators/decision-makers. In emerging economies like Andean countries, for which cultural expenditure may represent a low priority investment, it is even more essential to select the most appropriate and frugal mitigation option, resulting from a subtle balance between implementation/maintenance costs and benefits (ICCROM, 2004;[START_REF] Paolini | Risk management at heritage sites: a case study of the Petra world heritage site[END_REF]. Minimally invasive, easily and quickly implementable, low-cost strategies and low-tech devices represent a pragmatic way to cope with immediate and urgent conservation threats, as yet acknowledged for photogrammetry [START_REF] Abed | Architectural and Cultural Heritage Conservation using Low-Cost Cameras[END_REF][START_REF] Dhonju | Feasibility study of Low-Cost Image-Based Heritage Documentation in Nepal[END_REF][START_REF] Remondino | Reality-based 3D documentation of natural and cultural heritage sites-techniques, problems, and examples[END_REF]. The good cost-benefit ratio that generally characterized those methods contributes thus to reopen a fruitful dialogue and collaboration between parties with divergent concerns. We believe that RISC database is one relevant example of a multifunctional, flexible and easily replicable assessment strategy that could be implemented in archaeological sites throughout the Andes. The great amount of information accumulated during the monitoring process facilitates the prioritization of the interventions [START_REF] Sevieri | A multi-hazard risk prioritization framework for cultural heritage assets[END_REF] and serves as comprehensive support for decision-making. The international community now considers risk preparedness and DRR as a priority (UNISDR, 2015). Hence, databases like RISC have to play a role in transforming heritage conservation into a day-to-day effort, financially sustainable.

As Feilden (1987, p. 19) pointed legitimately: "after an earthquake, a precise knowledge of every historic building and its contents is one of the most crucial factors in making an accurate assessment of the damage and conservation work required". We strongly support that archaeoseismological databases represent a relevant tool to acquire, store and process this type of architectural and structural knowledge. RISC established that organized datasets might be particularly helpful during three specific steps of the Seismic Risk Management cycle: condition assessment, past seismicity characterization and heritage supervision.

Conclusions

Despite the challenges and difficulties, there is an absolute necessity to involve more deeply science in risk assessment topics and better communicate results to the public and decisionmakers [START_REF] Stewart | Communicating Seismic Risk: the Geoethical Challenges of a People-Centred, Participatory Approach[END_REF]. Research methodologies and approaches may contribute notably to raise awareness about the seismic threat on cultural heritage and support adapted DRR programs. Monitoring archaeological site has turned to be a key stage in implementing proactive measures to face the seismic hazard. It also constitutes a meeting ground for a wide spectrum of specialists and an excellent opportunity to carry out integrative and multidisciplinary analysis (ICCROM, 2004;[START_REF] Stovel | Risk preparedness: a Management Manual for World Cultural Heritage[END_REF]UNISDR, 2015).

We are convinced that archaeoseismology, situated at the crossroads between seismic and vulnerability studies, has to take part in this multi-sectoral approach in heritage preservation.

By providing all the necessary information about the RISC database, we hope to share a relevant template for future archaeoseismological investigations in the Andes, and more broadly, in all emerging countries. This user-friendly way of storing and organizing data improves the data entry and processing and considerably facilitates data sharing [START_REF] Labrador | Ontologies of the Future and Interfaces for All: Archaeological Databases for the Twenty-First Century[END_REF].

RISC database does not represent only advancement in implementing large semi-quantitative approach in the Andes. It also demonstrates how a basic data collection system might become a relevant interface for a systematic and periodic condition assessment. A properly selected and organized dataset may play a central role during archaeological remains supervision and may serve as a basis for disaster risk management [START_REF] Heras | A value-based monitoring system to support heritage conservation planning[END_REF][START_REF] Paolini | Risk management at heritage sites: a case study of the Petra world heritage site[END_REF]The Getty Conservation Institute, 2015). Given the humanitarian stakes during a seismic crisis, in-depth assessments of built heritage integrity are usually carried out at the end of the emergency phase.

However, quick on-site damage analysis allows the identification of risks posed to both cultural heritage and the populations in the aftermath of a disaster. Easy to deploy after a seismic crisis, such a database would constitute a unique asset that would benefit any immediate action undertaken to inventory damage in endangered cultural heritage and evaluate the effects of those emergency measures prior to retrofitting works. Hence, easy to implement and customize, our database prototype seems to be a promising complementary tool to monitor archaeological sites, especially in emerging countries where low-tech devices constitute the most appropriate and cost-effective solution (The Getty Conservation Institute, 2015).

Endnote 1) We are aware that the usability of proprietary software such as FileMaker Pro may represent a limit to the promotion of the RISC database, especially in developing countries. However, only one license is needed to design the database that may be then replicated freely in as many iOS portable devices as necessary (FileMaker Go is a free app). Furthermore, based on the conceptual and physical models of the database presented in detail in this work (Supplementary 2), any reader interested in building a similar database will be able to do it as an open-source option.

Fig. 1 .

 1 Fig.1. a) Cusco regional map displaying the main active seismic areas during the last 60 years (instrumental seismicity) and the location of the 17 archaeological sites surveyed during the RISC project. The size of the buffer zones depends on the estimated rupture length for each seismic event (see Supplementary 1). Information on historical earthquakes (blue stars) is based

  , and reduces the risk of loss. The structure of the database itself enables faster researches and data mining. We based our program on the pioneer initiatives of the ACoR (Atlas des techniques de la Construction Romaine, https://acor.humanum.fr/, last accessed July 25, 2021 -Dessales, 2020) and OPUR (Outil Pour Unités de Réparation) databases (ANR Recap: http://recap.huma-num.fr/webpublic/#recap, last accessed July 25, 2021), which aimed to register and characterize roman building techniques and ancient post-seismic repairs in Pompeii site[START_REF] Dessales | Un database per studiare le riparazioni post-sismiche[END_REF]. While adopting a starkly different approach by focusing on damage, RISC benefited considerably from those previous projects, especially in terms of data structuration and data entry. The main objective was to conceive a database structure that would closely fit fieldwork requirements.

Fig. 2 .

 2 Fig.2. EAE chart adapted to Inca megalithic architecture (modified from Rodríguez-Pascua et al., 2011). Our fieldwork focused on the EAE affecting the building fabric, and due to off-fault effects.

Fig. 3 .

 3 Fig.3. The RISC front-end user is organized around three tabs: "Context", "Damage" and "Picture". Those three sections reproduce the three main steps during the data acquisition. In blue: the two metadata fields to assess the data quality. In red: the database extension, which allows relating one EAE with a particular seismic event.

Fig. 4 .

 4 Fig.4. "Context" tab of the RISC front-end user interface. You may note the user-friendly structure based on interdependent values lists.

  in-depth inspection of damage. Including complementary data on the previous restoration works as well as indications on surveyed/non surveyed areas, we might consider identifying sectorial patterns. Understanding what buildings were the most affected and for what reason

Fig. 5 .

 5 Fig.5. a) Spatial distribution of the EAE (red dots) in the archaeological settlements of Cusco and Saqsaywaman. Credits DEM and Inca walls: Instituto Nacional de Cultura, Center for Advanced Spatial Technologies (Univ. of Arkansas) & Cotsen Institute for Archaeology (UCLA); b) Distribution of the EAE on the Sun Temple of Ollantaytambo. The color indicates the probability of the seismic origin (beige: Low; orange: Medium; red: High).

Fig. 6 .

 6 Fig.6. Diagram summarizing the theoretical disconnection existing between two worlds: heritage conservators and academic scientists. From our point of view, archaeoseismology can provide an interesting tool to engage collaboration and dialogue.

Fig. 7 .

 7 Fig.7. Graphical representation of the Disaster Risk Reduction program applied to heritage conservation and inspired on the Preventive Conservation Cycle (principles formulated by the ICOMOS Charter (ICOMOS, 2003). RISC project demonstrates the role that may play database systems during four stages of this cycle.

  The intrinsic properties of databases, coupled with the results of the archaeological survey, suggest a broader interest covering several DRR stages in the cultural heritage conservation program.

	EAE	Level of conf.	Masonry Type	EAE characteristics	1 -SEISMIC ORIGIN Aspect	Geological Context	Human Context	2 -MEASUREMENT BIAS
	Dipping Broken Corner	Low Medium	Rustic Cellular Cyclopean Polygonal Sedimentary Cellular Cyclopean Polygonal	Plane < cm Dip angle <25° Ultimate course of masonry Plane > cm Dip angle >25°	Plane hardly definable Clean Plane	Pre-existing rock fractures within the block X	Cleaning work Cleaning work	Difficult to access Irregular plane Low dip angle Vegetation Irregular plane
			Sedimentary
		High	Polygonal Sedimentary	Plane > cm Dip angle >25°	Clean Plane	X	X	X
		CERTAIN			DOCUMENTED DISORDERS (pictures or scientific literature)
	Displaced masonry block	Low Medium High	// // //	Small and unique Ultimate course of masonry Non constant displacement Non constant displacement X	Mortar masonry Dry joint masonry Dry joint masonry	Slope instability Water ingress Water ingress X	Restoration work Unfinished Structure Restoration work X	Heterogeneous displacement Heterogeneous displacement X
		CERTAIN			DOCUMENTED DISORDERS (pictures or scientific literature)
			Rustic
			Cellular					Non-apparent fracture plane
		Low	Cyclopean	Affecting 1 rock	//	Slope instability	Large-scale repairs	Irregular plane
			Polygonal					Vegetation
	Fracture -Crack	Medium	Sedimentary Cellular Cyclopean Polygonal	Affecting more than 1 rock	//	X	X	X
			Sedimentary
		High
		CERTAIN			DOCUMENTED DISORDERS (pictures or scientific literature)
		Low	//	Ultimate course of masonry	//	Slope instability	Unfinished Structure	Small movement (<2°)
	Block	Medium	//	X	//	X	X	X
	Rotation	High
		CERTAIN			DOCUMENTED DISORDERS (pictures or scientific literature)

Acknowledgements

This work would not have been possible without the cooperation of the Decentralized Department of the Ministry of Culture from Cusco and the Geopark of Machu Picchu. We also thank Léo Marconato, Lorena Rosell, Peter Molnar, Sara Neustadt, Fabrizio Delgado and Xavier Robert for their precious assistance during the field campaigns. The authors would like to express their gratitude to Hélène Dessales for her enthusiasm in sharing her feedbacks on the ACoR database as well as to Philippe Garnier for his constructive proofreading. This work was part of the CuscoPATA project (006-2016-FONDECYT) and of the inter-institutional agreement between IRD (Institut de Recherche pour le Développement) and INGEMMET (Instituto Geológico, Minero y Metalúrgico del Perú). This work has been realised in the framework of the IDEX CDP Risk@Univ. Grenoble Alpes as part of the program ''Investissements d'Avenir" overseen by the French National Research Agency (ANR-15-IDEX-02). The project has received, as well, financial support from the CNRS through the MITI interdisciplinary programs and from the IRD.

Appendix Supplementary data to this article can be found online at https://doi.org/10.1016/j.jsames.2021.103447.