André Santanchè

Claudia Bauzer-Medeiros

Genevieve Jomier

Claudia Bauzer Medeiros

Geneviève Jomier

Michel Zam

Challenges of the Anthropocene epoch -supporting multi-focus research

HAL is

Introduction

Geological societies, all over the world, are adopting the term "Anthropocene" to designate a new geological epoch whose start coincides with the impact of human activities on the Earth's ecosystems and their dynamics.

The discussion on the Anthropocene shows a trend in multidisciplinary research directly concerned with the issues raised in this paper -scientists increasingly need to integrate results of research conducted under multiple foci and scales. Anthropocenic research requires considering multiscale interactions -e.g., in climate change studies, this may vary from the small granularity (e.g., a human) to the macro one (e.g., the Earth). To exploit the evolution and interaction of such complex systems, research groups (and disciplines) must consider distinct entities of study, submitted to particular time and space dynamics. Multiscale research is not restricted to geographic phenomena; this paper, however, will consider only two kinds of scales -temporal and geographic.

For such scenarios, one can no longer consider data heterogeneity alone, but also the heterogeneity of processes that occur within and across scales.This is complicated by the following: (a) there are distinct fields of knowledge involved (hence different data collection methodologies, models and practices); and (b) the study of complex systems requires complementary ways of analyzing a problem, looking at evidence at distinct aggregation/generalization levels -a multi-focus approach. Since it is impossible to work at all scales and representations at once, each group of scientists will focus on a given (sub)problem and try to understand its complex processes. The set of analyses performed under a given focus has implications on others. From now on, this paper will use the term "multi-focus" to refer to these problems, where a "focus" is a perspective of a problem, including data (and data representations), but also modeling, analysis and dynamics of the spatio-temporal entities of interest, within and across scales. This scenario opens a wide range of new problems to be investigated [START_REF] Longo | Using the DBV model to maintain versions of multi-scale geospatial data[END_REF]. This paper has chosen to concentrate on the following challenges:

• How can GIScience researchers provide support to research that is characterized by the need to analyze data, models, processes and events at distinct space and time scales, and represented at varying levels of detail? • How to keep track of events as they percolate bottom-up, top-down and across space, time and foci of interest? • How to provide adequate management of these multi-focus multi-expertise scenarios and their evolution?

A good example of multi-focus Anthropocene research in a geographic context is multimodal transportation. At a given granularity, engineers are interested in individual vehicles, for which data are collected (e.g., itineraries). Other experts may store and query trajectories, and associate semantics to stops. At a higher level, traffic planners study trends -the individual vehicles disappear and the entities of study become clusters of vehicles and/or traffic flow -e.g., [START_REF] Medeiros | Managing sensor traffic data and forecasting unusual behaviour propagation[END_REF]. A complementary focus comes from climate research (e.g., floods cause major traffic disturbances) or political upheavals. This can be generalized to several interacting granularity levels. In spite of advances in transportation research, e.g., in moving objects, there are very few results in representation and interaction of multiple foci.

Environmental changes present a different set of challenges to multi-focus work. Studies consider a hierarchy of ecological levels, from community to ecosystem, to landscape, to a whole biome. Though ecosystems are often considered closed systems for study purposes, the same does not apply to landscapes, e.g., they can include rivers that run into (or out of) boundaries1 . A landscape contains multiple habitats, vegetation types, land uses, which are inter-related by many spatio-temporal relationships. And a study may focus on vegetation patches, or in insect-plant interactions.

In agriculture -the case study in this paper -the focus varies from sensors to satellites, analyzed under land use practices or crop strains and lifecycles. Each of the disciplines involved has its own work practices, which require analyzing data at several granularity levels; when all disciplines and data sets are put together, one is faced with a highly heterogeneous set of data and processes that vary on space and time, and for which there are no consensual storage, indexation, analysis or visualization procedures.

Previous work of ours in traffic management, agriculture and biodiversity brought to light the limitations of present research on spatio-temporal information management, when it comes to supporting multi-focus studies. As will be seen, our work combines the main solution trends found in the literature, handling both data and processes in a homogeneous way, expanding the paradigm of multiversion databases, under the model of [START_REF] Cellary | Consistency of Versions in Object-Oriented Databases[END_REF]. We have recently extended it to support multiple spatial scales [START_REF] Longo | Using the DBV model to maintain versions of multi-scale geospatial data[END_REF], and here explore multiple foci and interactions across scales.

Related work

Research on multiscale data management involves state-of-the-art work in countless fields. As pointed out in, for instance, [START_REF] Spaccapietra | GIS Databases: From Multiscale to MultiRepresentation[END_REF], multiple cartographic representations are just one example of the need for managing multiple scales. In climate change studies, or agriculture, for instance, a considerable amount of the data are geospatial -e.g., human factors.

Present research on multiscale issues has several limitations in this broader scenario. To start with, it is most frequently limited to vectorial data, whereas many domains, including agriculture, require other kinds of representation and modeling (including raster data) [START_REF] Leibovicia | Multi-scale integration for spatio-temporal ecoregioning delineation[END_REF]. Also, it is essentially concerned with the representation of geographic entities (in special at the cartographic level), while other kinds of requirements must also be considered.

The example reported in [START_REF] Benda | How to Avoid Train Wrecks When Using Science in Environmental Problem Solving[END_REF], concerning riverine ecosystems, is representative of challenges to be faced and which are not solved by research on spatiotemporal data management. It shows that such ecosystems involve, among others, analysis of spatio-temporal data and processes on human activities (e.g., urbanization, agricultural practices), on hydrologic properties (e.g., precipitation, flow routing), and on the environment (e.g., vegetation and aquatic fauna). This, in turn, requires cooperation of (at least) hydrologists, geomorphologists, social scientists and ecologists.

Literature on the management of spatio-temporal data and processes at multiple scales concentrates on two directions: (a) generalization algorithms, which are mostly geared towards handling multiple spatial scales via algorithmic processes; and (b) multirepresentation databases (MRDBs), which are geared towards data management at multiple spatial scales. These two approaches respectively correspond to Zhou and Jones' [START_REF] Zhou | A multirepresentation spatial data model[END_REF] multi-representation spatial databases and linked multi-version databases2 . Most solutions, nevertheless, concentrate on spatial "snapshots" at the same time, and frequently do not consider evolution with time or focus variation.

Generalization-based solutions rely on the construction of virtual spatial scales from a basic initial geographic scale -for instance, [START_REF] Oosterom | 5D Data Modelling: Full Integration of 2D/3D Space, Time and Scale Dimensions[END_REF] in their model mention that managing scales require "zooming in and out", operations usually associated with visualization (but not data management). Here, as pointed out by [START_REF] Zhou | A multirepresentation spatial data model[END_REF], scale and spatial resolution are usually treated as one single concept. Generalization itself is far from being a solved subject. As stressed by [START_REF] Buttenfield | Multiscale Repreentations of Water: Tailoring Generalization Sequences to Specific Physiographic Regimes[END_REF], for instance, effective multiscale representation requires that the algorithm to be applied be tuned to a given region, e.g., due to landscape differences. Generalization solutions are more flexible than MRDBs, but require more computing time.

While generalization approaches compute multiple virtual scales, approaches based on data structures rely on managing stored data. Options may vary from maintaining separate databases (one for each scale) to using MRDBs.The latter concern data structures to store and link different objects of several representation of the same entity or phenomenon [START_REF] Sarjakoski | Conceptual Models of Generalisation and Multiple Representation[END_REF]]. They have been successfully reported in, for instance, urban planning, or in the aggregation of large amounts of geospatial data and in cases that applications require data in different levels of detail [START_REF] Oosterom | Research and development in geo-information generalisation and multiple representation[END_REF][START_REF] Gao | Multi-scale features of urban planning spatial data[END_REF][START_REF] Parent | Multiple Representation Modeling[END_REF]]. The multiple representation work of [START_REF] Oosterom | 5D Data Modelling: Full Integration of 2D/3D Space, Time and Scale Dimensions[END_REF] comments on the possibility of storing the most detailed data and computing other scales via generalization. This presents the advantage of preserving consistency across scales (since all except for a basis are computed), but multiple foci cannot be considered.

The previous paragraphs discussed work that concentrates on spatial, and sometimes spatio-temporal issues3 . Several authors have considered multiscale issues from a conceptual formalization point of view, thus being able to come closer to our focus concept. An example is [START_REF] Spaccapietra | GIS Databases: From Multiscale to MultiRepresentation[END_REF], which considers classification and inheritance as useful conceptual constructs to conceive and manage multiple scales, including multiple foci. The work of [START_REF] Duce | Microtheories for Spatial Data Infrastructures -Accounting for Diversity of Local Conceptualizations at a Global Level[END_REF] is concerned with multiple (hierarchical) conceptualizations of the world, restricted to spatial administrative boundaries (e.g., the concept of rivers in Spain or in Germany). While this is related to our problem (as multi-focus studies also require multiple ontologies), it is restricted to ontology construction. We, on the other hand, though also concerned with multiple conceptualizations of geographic space, need to support many views at several scales -e.g., a given entity, for the same administrative boundary, may play distinct roles, and be present or not.

We point out that the work of [Parent et al. 2006] concerning the MADS model, though centered on conceptual issues concerning space, time and perspective (which has similar points with our focus concept), also covers implementation issues in a spatiotemporal database. Several implementation initiatives are reported. However, a perspective (focus) does not encompass several scales, and the authors do not concern themselves with performance issues. Our extension to the MVBD approach, discussed next, covers all these points, and allows managing both materialized and virtual data objects within a single framework, encompassing both vector and raster data, and letting a focus cover multiple spatial or temporal scales.

Case study

Let us briefly introduce our case study -agricultural monitoring. In this domain, phenomena within a given region must be accompanied through time. Data to be monitored include, for instance, temperature, rainfall, but also soil management practices, and even crop responses to such practices. More complex scenarios combine these factors with economic, transportation, or cultural factors. Data need to be gathered at several spatial and temporal scales -e.g., from chemical analysis on a farm's crop every year, to sensor data every 10 minutes. Analyses are conducted by distinct groups of experts, with multiple foci -agro-environmentalists will look for impact on the environment, others will think of optimizing yield, and so on.

We restrict ourselves to two data sources, satellite images (typically, one image every 10 days) and ground sensors, abstracting details on the actual data being produced. From a high level perspective, both kinds of sources give origin to time series, since they periodically produce data that are stored together with timestamps. We point out that these series are very heterogeneous. Sensor (stream) series data are being studied under distinct research perspectives, in particular data fusion and summarization e.g., [START_REF] Mcguire | Characterizing Sensor Datasets with Multi-Granular Spatio-Temporal Intervals[END_REF]]. Some of these methods are specific for comparing entire time series, while others can work with subsequences. Satellite images are seldom considered under a time series perspective: data are collected less frequently, values are not atomic, and processing algorithms are totally different -research on satellite image analysis is conducted within remote sensing literature -e.g., [START_REF] Xavier | Multitemporal analysisof MODIS data to classify sugarcane crop[END_REF]]. Our multi-focus approach, however, can treat both kinds of data source homogenously.

Satellite time series are usually adopted to provide long-term monitoring, and to predict yield; sensor time series are reserved for real time monitoring. However, data from both sources must be combined to provide adequate monitoring. Such combinations present many open problems. The standard, practical, solution is to aggregate sensor temporally (usually producing averages over a period of time), and then aggregate them spatially. In the spatial aggregation, a local sensor network becomes a point, whose value is the average of the temporal averages of each sensor in the network. Next, Voronoi polygons are constructed, in which the "content" of a polygon is this global average value. Finally, these polygons can be combined with the contents of the images. Joint time series evolution is not considered. Our solution, as will be seen, allows solving these issues within the database itself.

Solving anthropocenic issues using MVDBs

Our solution is based on the Multiversion Database (MVDB) model, which will be only introduced in an informal way. For more details the reader is referred to [START_REF] Cellary | Consistency of Versions in Object-Oriented Databases[END_REF]]. The solution is illustrated by considering the monitoring of a farm within a given region, for which time-evolving data are: (a) satellite images (database object S); (b) the farm's boundaries (database object P), and (c) weather stations at several places in the region, with several sensors each (database object G).

Introducing MVBD

Intuitively, a given real world entity can correspond to many distinct digital items expressing, for example, its alternative representations, or capturing its different states along time. Each of these "expressions" will be treated in this work as a version of the object. Consider the example illustrated in Figure 1. On the left, there are two identified database objects: a satellite image (Obj S) and a polygon to be superimposed on the image (Obj P). delimiting the boundaries of the farm to be monitored.

As illustrated by the table on the right of the figure, both objects can change along time, reflecting changes in the world, e.g., a new satellite image will be periodically provided, or the boundaries of the farm can change. For each real world entity, instead of considering that these are new database objects, such changes can be interpreted as many versions of the same object4 . This object has a single, unique, identifier -called an Object Identifier Oid5 .

A challenge when many interrelated objects have multiple versions is how to group them coherently. For example, since the satellite image and the farm polygon change along time, a given version of the satellite image from 12/05/2010 must be related with a temporally compatible version of the farm polygon. This is the central focus of the Multiversion Database (MVDB) model. It can handle multiple versions of an arbitrary number of objects, which are organized in database versions -DBVs. A DBV is a logical construct. It represents an entire, consistent database constructed from a MVDB which gathers together consistent versions of interrelated objects. Intuitively, it can be interpreted as a complex view on a MVDB. However, as shall be seen, unlike standard database views, DBVs are not constructed from queries. To handle the relation between an object and its versions, the MDBV distinguishes their identifications by using object and physical identifiers respectively. Each object has a single object identifier (Oid), which will be the same independently of its multiple versions. Each version of this object, materialized in the database by a digital item -e.g., an image, a polygon etc. -will receive a distinct physical version identifier PVid. In the example of Figure 1, there is a single Oid for each object -satellite image (Obj S) and the farm boundaries (Obj P). Every time a new image or a new polygon is stored, it will receive its own PVid.

DBVs are the means to manage the relationship between an Oid (say, S) and a given PVid (of S). Figure 2 introduces a graphical illustration of the relationship among these three elements: DBV, Oid and PVid. In the middle there are two DBVs identified by DBVids -DBV 1 and DBV 1.1 -and represented as planes containing logical slices (the "views") of the MVDB. The figure shows that each DBV has versions of P and S, but each DBV is monoversion (i.e., it cannot contain two different versions of an object). The right part of the figure shows the physical storage, in which there are two physical versions of S (identified by Ph1 and Ph9), and just one version of P.

DBV 1 relates S with a specific satellite image and P with a specific polygon, which form together a consistent version of the world. Notice that here nothing is being said about temporal or spatial scales. For instance, the two satellite images can correspond to images obtained by different sensors aboard the same satellite (e.g., heat sensor, water sensor), and thus have the same timestamp. Alternatively, they can be images taken in different days. The role of the DBV is to gather together compatible versions of its objects, under whichever perspective applies.

Since DBVs are logical constructs, each object in a DBV has its own logical identifier. Figure 2 shows on the left an alternative tabular representation, in which DBVids identify rows and Oids identify columns. Each pair (DBVid, Oid) identifies the logical version of an object and is related to a single PVid, e.g., (DBV 1, ObjS)→P h1. The asterisk in cell (DBV 1.1, Obj P) means that the state of the object did not change from DBV 1 to DBV 1.1, and therefore it will address the same physical identifier Ph 5.

DBV Evolution and Traceability

DBVs can be constructed from scratch or from other DBVs6 . The identifier of a DBV (DBVid) indicates its derivation history. This is aligned to the idea that versions are not necessarily related to time changes, affording alternative variations of the same source, as well as multiple foci -see section 5.

The distinction between logical and physical identifications is explored by an MVDB to provide storage efficiency. In most of the derivations, only a partial set of objects will change in a new derived DBV. In this case, the MVDB has a strategy in which it stores only the differences from the previous version. Returning to the example presented in Figure 2 on the left table, DBV 1.1 is derived from DBV 1, by changing the state of Obj S. Thus, a new PVid is stored for it, but the state of Obj P has not changed -no new polygon is stored, and thus there is no new PVid.

The evolution of a DBV is recorded in a derivation tree of DBVids. To retrieve the proper PVid for each (virtual) object in a DBV, the MVDB adopts two strategies: provided and inferred references7 , through navigation in the tree. This allows keeping track of real world evolution. We take advantage of these concepts in our extension of the MVDB model, implemented to support multiple spatial scales [START_REF] Longo | Using the DBV model to maintain versions of multi-scale geospatial data[END_REF]]. First, we create one tree per spatial scales, and all trees grow and shrink together. Second, the notion of object id is extended to associate the id with the scale in which that object exists - (Oid, Scaleid). This paper extends this proposal in two directions: (1) we generalize the notion of spatial scale to that of focus, where a given spatial or temporal scale can accomodate multiple foci, and the evolution of these foci within a single derivation tree;

(2) we provide a detailed case study to illustrate the internals of our solution.

From Multiversion to Multi-focus

This paper extends the MVDB model to support the several flavors of multi-focus. This implies in synthesizing the multiple foci which can be applied to objects -scales, representations etc. -as specializations of versions. Figure 3 illustrates an example of this extension. There are three perspectives within the logical view -see the Figure .   In the Physical perspective, there are three objects -two versions of satellite image S (with identifiers Ph1 and Ph2), and one version of a set of sensor data streams, corresponding to a set of weather stations G -global identifier Ph7). Satellite image and sensor data are to be combined in Applications, which can only access DBVs (and not the database). So, several DBVs are built, each of which corresponding to a distinct focus. The arrows between DBV objects and stored objects appear whenever an object is copied into a DBV, without any additional computation. In the figure, the DBV corresponding to Focus 1 makes available the satellite image version Ph1 and all data from all weather stations G. The DBV corresponding to Focus 2 makes available the satellite image version Ph2, and computes a set of Voronoi polygons from the weather station data streams -the resulting polygon is displayed in the figure with a dotted line to show that it is not directly copied from the database, but is computed from it. Finally, DBV-Focus3 contains only one image, which has been computed from DBV-Focus2.

Applications access these three DBVs in the following way. Application Scale A is built from DBV-Focus2; it corresponds to a particular spatio-temporal focus of the database, in which the image is directly extracted from the DBV, and a set of Voronoi polygons is computed from the DBV. Application Scale B is built from DBV-Focus1; it corresponds to another spatio-temporal focus of the database, in which the image and the polygons are directly copied from the DBV. The third DBV is not being used by any application. In our case study, each application corresponds to one spatial scale (scale B smaller than scale A), and sensor data are preprocessed either at the application, or by the DBMS, to allow combination of these distinct data sources. DBV-Focus 3 is an example of at least three possible scenarios: in one, S corresponds to an even smaller spatial scale, for which sensor data do no longer make sense; in another, S is the result of combination of satellite image and sensor data; in the third, the focus is in some characteristics of the satellite image, and sensor data can be ignored for the purposes of that DBV.

In order to support these kinds of DBV, the classical MVDB model was extended: (i) we added more types of relationships between DBVs; (ii) we introduced the notion of scale to be part of an OID. In the classical MVDB the only relationship between two DBVs is the derivation relationship, explained in the previous section. Our multi-focus approach requires a wider set of relationships. Therefore, now the relationship between two DBVs becomes typed: generalization, aggregation etc. This typing system is extensible, affording new types. This requires that new information be stored concerning each DBV, and that the semantics of each object be stored alongside the object, e.g., using ontologies.

Returning to our example in Figure 3 consider an application that will access the contents of S in DBV-Focus3. Since there is no explicit reference to it in the DBV-Focus2, the only information is that the state of S in the third focus has been derived in some kind of relationship with the state of S in the second DBV. Let us consider that this is a generalization relationship, i.e., the state of S in the third DBV is a cartographic generalization of the state of S in the DBV-Focus2. In order to use this logical version of S in an application, the construction of DBV-Focus3 will require an algorithm that will: (1) verify that the type of the relationship is generalization; therefore, S must be transformed to the proper scale; (2) check the semantics of S, verifying that it is a satellite image, and therefore generalization concerns image processing, and scaling.

Conclusions and ongoing work

This paper presents our approach to handling multi-focus problems, for geospatial data, based on adapting the MDBV (multiversion database) approach to handle not only multiple scales, but multiple foci at each scale. Most approaches in the geospatial field concentrate on the management of multiple spatial or temporal scales (either by computing additional scales via generalization, or keeping track of all scales within a database via link mechanisms). Our solution encompasses both kinds of approach in a single environment, where an ad hoc working scenario (the focus) can be built either by getting together consistent spatio-temporal versions of geospatial entities, or by computing the appropriate states, or a combination of both. Since a DBV can be seen as a consistent view of the multiversion database, our approach also supports construction of any kind of arbitrary work scenarios, thereby allowing cooperative work. Moreover, derivation trees allow keeping track of the evolution of objects as they are updated, appear or disappear across scales.

Our ongoing work follows several directions. One of them includes domain ontologies, to support communication among experts and interactions across levels and foci. We are also concerned with formalizing constraints across DBVs (and thus across scales and foci).

Figure 1 .

 1 Figure 1. Practical scenario of a polygon over a satellite image.

Figure 2 .

 2 Figure 2. The relationship between DBVs, logical and physical identifiers.

Figure 3 .

 3 Figure 3. Handling multiple foci.

Figure 3

 3 Figure3reflects the following facts. First, DBVs can contain just objects that are in the database, or computed objects, or a mix of both. Second, applications constructed on top of the DBVs can use exactly the same objects (the one on Scale A directly uses the same contents of DBV-Focus2), but also compute other objects (the polygon on Scale B, computed from DBV-Focus1). Third, DBVs now can be interrelated by many kinds of derivation operations.

Proceedings XIIIGEOINFO, November 25-27, 2012, Campos do Jordão, Brazil. p 1-10.

Similar to studies in traffic in and out of a region...Proceedings XIII GEOINFO, November

25-27, 2012, Campos do Jordão, Brazil. p 1-10.

We point out that our definition of version is not the same as that ofZhou and Jones Proceedings XIII GEOINFO, November 25-27, 2012, Campos do Jordão, Brazil. p 1-10.

The notion of scale, more often than not, is associated with spatial resolution, and time plays a secondary role.Proceedings XIIIGEOINFO, November 25-27, 2012, Campos do Jordão, Brazil. p 1-10.

Here, both raster and vector representations are supported. An MVDB object is a database entity

Oids are artificial constructs. The actual disambiguation of an object in the world is not an issue here Proceedings XIIIGEOINFO, November 25-27, 2012, Campos do Jordão, Brazil. p 1-10.

DBV derivation trees, part of the model, will not be presented here.

For the logical version (DBV 1.1, Obj P), the reference will be inferred by traversing the chain of derivations.Proceedings XIIIGEOINFO, November 25-27, 2012, Campos do Jordão, Brazil. p 1-10.

* Work partially financed by CAPES-COFECUB (AMIB project), FAPESP-Microsoft Research Virtual Institute (NavScales project), and CNPq


Michel Zam Karmicsoft

Dodinet Gilles

Karmicsoft

Geneviève Jomier
email: genevieve.jomier@dauphine.fr

The United States of a Meta-model build with MyDraft An agile model-driven cloud-based platform for data-oriented rich web applications

Keywords: D.2.2 [Software Engineering]: Design Tools and Techniques Design, Experimentation meta-design, model-driven, domain-specific modeling, traceability, time machine, rapid development, cloud computing

The United States of a Meta-model build with MyDraft An agile model-driven cloud-based platform for data-oriented rich web applications

Michel Zam, Gilles Dodinet, Genevieve Jomier

Speaker

Michel Zam, PhD, is co-founder and CSO of KarmicSoft, Associate Professor at Paris Dauphine University, and member of IEEE Computer Society. He holds innovation awards and patents on evolution and traceability of both data and software. He and his team build reflexive tools, flexible applications and traceable solutions. He faced design challenges, meta bugs, and knows the real story of aggressive software evolution from inside.

Description

Building data-oriented web applications is a highly demanding and well-codified specific domain. Nevertheless, delivering such applications in time and budget remains a challenging mission. The main cause is the increasing rate of business requirement evolutions that need to be impacted concurrently through data, model and even through the meta-model. Usually, final users input data minute by minute, domain experts and developers need to adapt data models and user interface hour by hour, and eventually gurus add new features to the platform itself every day.

MyDraft is a platform designed to cope simultaneously with evolution at several levels: data, model and meta-model. MyDraft manages data, models and meta-models in an unique versioned repository, embracing the executable model-driven paradigm rather than code generation techniques. Design time and runtime activities are therefore unified and the system almost never stops. In MyDraft, domain specific modeling for collaborative data-ori-ented rich web applications includes specific high level abstraction constructs as screen fragments and composition mechanisms.

The demonstration will illustrate how to model, build and run a specific data-driven rich web application from scratch in minutes, with no technical skills. As these activities are notoriously collaborative, we will also reveal the traceability support including automatic versioning and the integrated time machine. The audience will travel in space and time through the evolutionary process of an emerging application, where models and data are changed in a unpredictable order, just like in the real life. Then, we will show how to build and run a simple domain-specific model meant to orchestrate remote statistical computations, still keeping track of the state of every single running task. These adventures will inspire new features to the platform itself, so we will finally demonstrate an open-heart surgical operation. This will enhance the DNA of every single citizen of the sustainable cloud-based software environment. Instant jump back in time shows initial versions of data and earlier development states of the application and the environment itself. Trace pattern mining stimulates insight, new ideas and better ways to rebuild the system. Changing the past is tempting, but this could alter the timeline and change the course of the history, including the mindset of the audience.

The demo is relevant to the DSM community members that face evolution as a day-to-day challenge. We share the same quest for higher productivity and taste for raising the level of abstraction, but we choose to boldly eliminate the gap between problem and solution modeling. In MyDraft data and programs co-exist in a causally connected system and their interactions are traced on the fly and used to impact changes. Therefore final users, domain experts, developers and gurus can finally share a common peaceful world located in the cloud.


Marcia Caetano Da Silva

Caetano Langfeldt

Marcia Caetano

Silva Caetano

Marcia Caetano Langfeldt

Osvaldo Cruz

Durante Suas Viagens

Cezar Ferreira

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

seguinte, casa-se com Emilia da Fonseca. Ainda não foi possível reunir mais informações sobre Emilia. Na página virtual do "Projeto Memória" do Banco do Brasil lê-se apenas que "ela era mulher inteligente e espirituosa, avançada para seu tempo, gostava de vestir-se bem, de passear e de apostar nas corridas do Jockey Club do Rio de Janeiro, aonde ia sozinha, de tílburi."

Em 1896, Osvaldo Cruz muda-se para Paris, para prosseguir seus estudos em Microbiologia no Instituto Pasteur, onde permanece por dois anos. Ao regressar ao Brasil, é nomeado Diretor da Saúde Pública pelo presidente Rodrigues Alves. É nesta condição que ele viaja pela primeira vez ao Amazonas, em 1905, ao realizar uma viagem de inspeção dos portos de Norte a Sul do Brasil.

Neste período, a região amazônica passava pelo boom econômico do ciclo da borracha, quando os portos de Manaus e Belém recebiam centenas de imigrantes todas as semanas. A partir do processo de vulcanização desenvolvido por Charles Goodyear, em 1839, a borracha passou a ser um produto de alto valor. De 1840 a 1910 o preço da borracha aumentou mais de 1,000% e cerca de meio milhão de pessoas imigraram para a Amazônia, sobretudo nordestinos, fugindo da seca. A indústria de extração da borracha gerou riqueza e contribuiu para desenvolver as cidades de Manaus, Belém e Porto Velho (Daou, 2000, pp.18-23).

Osvaldo Cruz viajou acompanhado do seu secretário João Pedroso e, juntos, os médicos visitaram 24 portos em 68 dias, de 27 de setembro a 6 de dezembro de 1905 (Cruz, Chagas e Peixoto, 1972, Introdução, s.p.). Desta missão, não há relatório nos arquivos da Fiocruz.

Existe, contudo, um conjunto de cartas no acervo de Osvaldo Cruz que corresponde a esta viagem.

Entretanto, o grupo está incompleto, pois não há cartas enviadas da Amazônia, embora ele tenha chegado até Manaus. Por esta razão, a correspondência referente a esta viagem não está abordada aqui.

Em 1910, Osvaldo Cruz viajou novamente à Amazônia, acompanhado pelo médico Belisário Pena. A missão tinha o objetivo de fiscalizar as condições sanitárias dos operários e engenheiros envolvidos com a construção da ferrovia Madeira-Mamoré, cláusula importante do acordo assinado com a Bolívia em 11 de novembro de 1903, na cidade de Petrópolis, como compensação pela ocupação irregular de território boliviano por seringueiros brasileiros no alto do rio Purus.

No relatório relativo a essa viagem, Osvaldo Cruz não escondeu a sua indignação diante das péssimas condições sanitárias da região, chegando a afirmar que "as tentativas de construção dessa estrada têm sido assinaladas por verdadeiras hectacombes" (Cruz, Chagas e Peixoto, 1972, p.6). O termo não era exagero, apenas durante a terceira fase de construção da ferrovia, de 1907 a 1912, ocorreram 1.593 mortes oficialmente registradas (Hardman, 1988, p. 105). Entretanto, estima-se que o número seja muito superior, acreditando-se que ela consumiu uma vida por cada dormente instalado.

No relatório, o sanitarista lista as principais doenças que encontrou: malária, febre amarela, tuberculose, beribéri, disenteria, ancilostomíase, pneumonia, sarampo e alcoolismo, contudo, dentre todas elas, o impaludismo era o grande terror da região. Segundo o Osvaldo Cruz, a população estava de tal forma infectada pela malária, que "para ela a condição de ser enfermo constitui a normalidade" (Cruz, Chagas e Peixoto, p.32). Ele assinala também que, além de não existir nenhuma ação profilática na região, o acesso ao tratamento era caro e prejudicado pela ação criminosa de alguns comerciantes, que vendiam uma mistura de amido e bicarbonato de sódio em lugar da quinina preconizada na prevenção da doença (Ibidem, p.12).

Ao constatar as calamitosas condições sanitárias, o médico estabelece vinte determinações que deveriam ser executadas para o saneamento da área. As medidas eram tão eficazes quanto coercitivas. As medidas visavam também a prevenção de outras doenças, com a distribuição de água potável, a obrigação de uso de sapatos e o combate à venda de bebida alcóolica. A equipe médica tinha amplos poderes para demitir qualquer funcionário que não respeitasse as determinações sanitárias. Em função deste plano sistemático, a construção da ferrovia pode ser finalizada, sendo inaugurada em 1º de agosto de 1912 (Ibidem, p.42-44).

As O que chama a atenção nestes dois textos é a similaridade entre as observações do relatório e aquelas que faz na carta à esposa, apenas um dia após visitar a vila de Santo Antônio.

Fica tão impressionado que o relatório escrito semanas depois conserva o mesmo tom contundente.

É de ressaltar que procura, contudo, poupar a esposa de alguns detalhes mórbidos, como as observações presentes no relatório relativas à "crueldade" da natureza amazônica. Neste caso, as formigas ameaçadoras:

"As formigas atacam vorazmente os cadáveres, o que tive ocasião de verificar e a ação delas é tão intensa como se pode avaliar pela seguinte observação feita pelo Dr. Walcott, médico da empresa: tendo um engenheiro voltado da zona em exploração com cadáver dum trabalhador numa rede não logrou atravessar um igarapé, que encheu bruscamente após grande chuva.

Armou a rede à margem do córrego e aí passou a noite, tendo deixado no chão o cadáver envolvido em outra rede. Pela manhã encontrou o corpo quase reduzido a esqueleto e coberto por milhares de formigas." Cruz, Chagas & Peixoto, 1972, p.14. Ou sobre crocodilos, piranhas e perigosos índios:

"No rio Madeira, o jacaré constitui um perigo àqueles que caem no rio; muito mais temerosos porém são certos peixes: […] as piranhas, que em cardumes colossais atacam as pessoas e animais na água e, desde que aparece sangue, com voracidade indescritível devoram-nos." Cruz, Chagas & Peixoto, Ibidem, p.12. "Em terra, não falando dos índios Parintintins que vivem na região da margem direita do Madeira, para baixo do rio Machado e que, indomáveis, atacam todos os brancos que lhes passam ao alcance e que na região são considerados como antropófagos, não há nada a temer de animais que ataquem o homem. Na região das cachoeiras, encontra-se comumente a onça vermelha (Felis concolor), que foge do homem e, praticamente, não constituti perigo." Cruz, Chagas & Peixoto, Ibidem, p.14.

Já para Emilia, reserva comentários bucólicos sobre a natureza, como em carta de 28 de junho de 1910, dia do aniversário da esposa: "Há aqui no vale do Amazonas um pequeno pássaro que os índios denominam "uirapuru", que significa "pássaro encantado". Este animalzinho, pequeno como uma cabaxirra, é raríssimo. Vive cantando escondido nos frondes das castanheiras e de louro-rosa. O cantar desse passarinho é tão melodioso que todas as aves das circunvizinhanças acompanham-no, assim como as feras da região, que ficam todos em êxtase, ouvindo o mavioso canto da ave da fortuna e todos unidos porfiam em evitar-lhes o ataque dos abutres e outros inimigos.

É o rei dos cantores das florestas amazônicas e o portador da eterna felicidade. Segundo os assertos da pajelança, quem possuir uma pena do uirapuru gozará da eterna felicidade e será sempre acompanhado da saúde, da virtude, do amor e do bem-estar. Todos porfiam em possuir o amuleto portador da felicidade eterna, mas raros conseguem, porque o passarinho divino é raríssimo. Conheço pessoas aqui que passaram em vão a vida à procura duma pena da avezinha sagrada. Quis a sorte que travasse eu relações com um rapaz, estudante de Medicina, a quem a Mãe, no meio das lágrimas de despedida, confiara ao filho querido, como relíquia de família, um uirapuru embalsamado em carajurú e conservado numa purçanga (pequena bolsa de couro).

Este rapaz deu-me as penas do uirapuru, que junto te envio e que são as mensageiras dos mais ardentes votos que faça para que Deus transforme em realidade a crendice do gentio." Trecho de carta de Osvaldo Cruz para sua esposa, Emilia da Fonseca Cruz, Arquivo Fiocruz.

Nas cartas para Emilia há ainda algumas observações ausentes de seus relatórios oficiais, como as descrições de 2 de julho de 1910, em carta enviada de Santarém, sobre o tipo de pessoas que ele encontrava em suas viagens: « Não imaginas que péssimas companhias de viagem temos : seringueiros e aventureiros de toda a espécie, sem a mínima educação e uma leva de mulatas cearenses de vida aerada e que levam fazendo uma formidável algazarra à bordo." Trecho de carta de Osvaldo Cruz para sua esposa, Emilia da Fonseca Cruz, Arquivo Fiocruz.

Alguns detalhes do acordo para dirigir a campanha contra a febre amarela no Pará também são revelados na mesma carta: "Como te dizia em minha última carta, o governador me pediu para fazer a campanha contra a febre amarela no Pará, ao que acedi, impondo condições, sobretudo relativas ao pessoal e à não interferência da política. Depois da conferência que tivemos, ele não mais me falou no assunto e julgo que ficou desanimado com as condições que impus." Trecho de carta de Osvaldo Cruz para sua esposa, Emilia da Fonseca Cruz, Arquivo Fiocruz.

Em contraste com a realidade relatada nos textos oficiais, em que todas as crianças do vilarejo de Santo Antônio morriam ou estavam condenadas a morrer, Osvaldo descreve o conforto de que dispunha em sua viagem, como se pode ler na carta de 11 de julho de 1910: "Fui muito bem recebido em Manaus, onde o governador foi me buscar a bordo, tendo sido eu hospedado em casa de um dos empreiteiros da companhia, o senhor May, um ativo americano, moreno, com cara de brasileiro. Não imaginas como essa gente tem me tratado: como um verdadeiro príncipe. Puseram à minha disposição um navio da companhia e às minhas ordens puseram o mordomo da companhia, que, depois de indagar ao Belisário2 da minha dieta etc, pôs um cozinheiro para meu regime e, durante toda a viagem nestas paragens onde não há recursos, fui alimentado a vegetais, galinhas, ovos, doces, águas minerais, enfim, tudo quanto possa desejar." Trecho de carta de Osvaldo Cruz para sua esposa, Emilia da Fonseca Cruz, Arquivo Fiocruz.

Após lermos as cartas que Osvaldo Cruz escreveu para sua esposa Emilia quando viajava pela Amazônia, é possível ter uma visão mais ampla sobre as motivações de suas viagens e os lugares que visitou. Nelas transparece também a condição feminina na época, e o contraste que podia existir entre uma jovem pianista que estudara em Leipzig e as mulatas cearenses "de vida airosa" que viajavam no mesmo barco. A despeito de vidas muito diferentes, a pianista e as mulheres no barco lá estavam para o entretenimento dos homens.

A leitura desses textosrelatórios oficiais e cartas pessoaisatestam o impacto que teve ao conhecer duas realidades profundamente díspares, a da vida das elites das duas cidades mais ricas da região, Manaus e Belém que viviam em imensa opulência, em contraste com a precária situação daqueles que eram o esteio da economia da borracha.

As observações de Osvaldo Cruz podem ser postas em relação com as de três escritores brasileiros de peso que me 1913 já haviam publicado seus pontos de vista sobre a Amazônia: José Veríssimo (1857Veríssimo ( -1916)), sobretudo o livro de novelas Cenas da vida amazônica (1889); Alberto Rangel (1871Rangel ( -1945)), com a coletânea de contos Inferno Verde (1908) e de Euclides da Cunha (1876Cunha ( -1909)), com o conjunto de ensaios inspirados por suas visitas à região, a serviço do governo brasileiro, e publicados postumamente : À margem da história, (1909).

A despeito das fortes diferenças entre esses textos, há neles um aspecto comum: todos eles denunciam o abandono da região pelo poder central, apesar de sua então importância econômica, e ressaltam a urgência em incorporar essa região e seus habitantes ao projeto nacional e à cidadania, tanto através da instrução, como da ação política ou de medidas para um progresso social e econômico mais justo. Nesse sentido, numa fase posterior da pesquisa conto estabelecer um diálogo entre os textos destes escritores e os relatórios de Osvaldo Cruz sobre a região.

  duas últimas viagens de Osvaldo Cruz à Amazônia foram entre 1910 e 1911, quando foi contratado para promover uma campanha contra a epidemia de febre amarela no Pará. A febre amarela está extinta no Pará A comissão da profilaxia contra a febre amarela apresentou ao governo do Estado um trabalho gráfico dos seus serviços desde o início da campanha, em 12 de novembro do ano passado, e cujo resultado foi o mais brilhante, estando extinto o terrível morbus.[...]Aos esforços conjuntados do governador e do cientista dr. Osvaldo Cruz se deve tão esplêndido resultado, de pleno êxito para o renome e o crédito do Estado, os quais subirão muito, repercutindo em todo o Brasil. Esse resultado é tão mais satisfatório, porquanto no momento atual há grande necessidade da vinda de capitais e braços estrangeiros para conjurar a crise horrível que pesa sobre o Pará. Brevemente, chegará a esta capital o dr. Osvaldo Cruz, a quem será preparada condigna recepção, sendo como é, o herói da campanha de que garantiu o êxito no prazo fatal." Correio da Manhã, 4 de junho de 1911, Rio de Janeiro, p.4. Arquivo da Biblioteca Nacional. (BNDigital, Hemeroteca). . O grupo era constituído pelos médicos Carlos Chagas, João Pedroso de Albuquerque e Pacheco Leão. Em 11 de setembro de 1913, o sanitarista apresenta um relatório sobre as condições de saneamento no Amazonas ao ministro da Agricultura, Indústria e Comércio : "Condições médico-sanitárias do Vale do Amazonas". Embora não tenha ido à região, ele havia coordenado o trabalho da equipe médica à distância e assinou a primeira e a quarta partes do relatório. Neste relatório, Osvaldo Cruz confirma que o grande mal a ser combatido era a malária e propõe que o governo instale postos de quinização para os seringueiros e que ofereça prêmios em dinheiro aos seringueiros que durante um ano não apresentassem a doença. Em cada um dos rios, o governo deveria dispor de lanchas-ambulâncias para atendimento aos doentes. Realizado o plano de campanha sanitária constante das linhas acima, posso afirmar com segurança que desaparecerá o obstáculo capital que retém o progresso vertiginoso a que está destinado o vale do maior rio do mundo e ficará assim entregue à civilização uma das mais ricas, se não a mais rica zona do Brasil. Está nas mãos do governo realizar esse feito". Cruz, Chagas e Peixoto, 1972, p.155. Entretanto, com o avanço no mercado mundial da borracha cultivada nas colônias britânicas, a Superintendência de Defesa da Borracha foi extinta em menos de dois anos. Grandes buracos no centro do povoado recebem as águas das chuvas e da cheia do rio e transformam-se em pântanos perigosos, donde se levantam aluviões de anofelinas que espalham a morte por todo o povoado. Não há matadouro. O gado é abatido em plena rua, à carabina, e as porções não aproveitadas: cabeça, vísceras, couro, cascos etc., são abandonados no próprio local em que foi a rês sacrificada, jazendo num lago de sangue. Tudo apodrece junto às habitações e o fétido que se desprende é indescritível. Sobre os organismos que vivem em tal meio o impaludismo faz as maiores devastações que se conhecem. A população infantil não existe e as poucas crianças que se vêem têm vida por tempo muito curto. Não se conhecem entre os habitantes de Santo Antônio pessoas nascidas no local: essas morrem todas." Em carta de 11 de julho de 1910, ele escreveu sobre a mesma vila para Emilia: "Visitamos ontem a cidade de Santo Antônio. Não podes imaginar o que seja. Qualquer descrição, por mais pessimista, ficaria aquém da realidade. Basta que te diga que, na cidade, não há um só habitante filho do lugar. Todas as crianças que ali nascem, morrem infalivelmente e as poucas ali nascidas estão de tal modo doentes que fatalmente morrerão (em) breve. A imundície é incrível. Para dar uma idea pálida do que é ela, basta que te diga que matam os bois nas ruas e aí abandonam as vísceras, cabeça etc., que deixam apodrecer em plena rua. O mau cheiro é de tal ordem que pode-se ficar sufocado. Estou horrorizado com tanta porcaria!" Trecho de carta de Osvaldo Cruz para sua esposa, Emilia da Fonseca Cruz, Arquivo Fiocruz.

	Ao final, o sanitarista afirma:
	Ainda na ocasião da viagem à região do Madeira-Mamoré, quando Osvaldo Cruz chegou à cidade
	de Belém, capital do estado do Pará, o Governador João Coelho o contratou. Em carta à esposa
	Emilia da Fonseca Cruz, de 28 de junho de 1910, em Belém, Osvaldo Cruz comenta sobre esse
	acordo:
	"Resolvi hoje aqui uma questão que nos vai tornar a vida mais suave. O Governador do Pará
	me pediu para assumir a direção da campanha contra a febre amarela aqui, o que aceitei.
	Cruz, Chagas & Peixoto, 1972, p.10.

De volta do Madeira, irei até o Rio buscar a flor da minha gente 1 e de novo voltarei até aqui, onde passarei uns 15 dias para pôr o serviço em andamento, sob a direção de pessoa de minha confiança. Voltarei ainda no decurso de mais umas duas ou três vezes. Ainda não sei das condições que me serão oferecidas. O Governador, com grande acanhamento mandou me perguntar quanto eu desejava. Mandei-lhe dizer que deixava ao alvitre dele os valores. Mas, a julgar pelo entusiasmo em que está o homem, as nossas vantagens parecem (que) serão bem grandes. Para mim, a coisa será muito mansa e conto obter resultados seguros, prestando assim um colossal serviço ao país. Segundo me informam, só no mês passado morreram duzentas e tantas pessoas de febre amarela".

Trecho de carta de Osvaldo Cruz para sua esposa, Emilia da Fonseca Cruz, Arquivo Fiocruz. Um resumo do relatório desta campanha foi publicado pelo governador do Pará no Relatório dos Presidentes, em 7 de setembro de 1911. Os resultados da campanha foram amplamente divulgados nos jornais da época. Em 4 de junho de 1911, o jornal Correio da Manhã, do Rio de Janeiro, publicava nota sobre o fim da campanha da febre amarela no Pará: "Graças à participação em numerosas campanhas profiláticas, o nome de Osvaldo Cruz ficou definitivamente associado ao progresso tão almejado para o país. Em maio de 1912 foi eleito para a Academia Brasileira de Letras, sendo o primeiro não literato a ingressar na instituição, a partir da "tese do expoente", apoiada pelo então presidente da Academia, José Veríssimo. A chegada de "capitais e braços" mencionada por notícias de jornais, não deixa dúvidas: com o país saneado, o progresso era só uma questão de tempo. A última campanha dirigida por Osvaldo Cruz, entretanto, iria mostrar que seria necessário muito mais. Em 1910, a borracha das colônias britânicas entra no mercado mundial e acaba com o monopólio da borracha amazônica. Em 1912, o governo brasileiro tenta reverter a situação e cria a Superintendência de Defesa da Borracha. A melhoria da saúde pública entrava em linha de conta dos progressos que seriam necessários na luta contra a concorrência britânica. O governo contrata Osvaldo Cruz para organizar o saneamento do estado do Amazonas e dos então territórios do Acre e Roraima. Um grupo de médicos viaja ao Amazonas, sob sua liderança, entre outubro de 1912 e março de 1913"As cartas à esposa Emilia Fonseca, "Miloca" Ao compararmos as cartas que Osvaldo Cruz enviou à esposa durante as viagens que fez à Amazônia com os relatórios, percebe-se que o sanitarista propositadamente elabora um discurso sem meio-tons sobre os fatos que viu nos textos oficiais. No relatório de 1910, quando trabalhava para a empresa construtora da ferrovia Madeira-Mamoré, Osvaldo Cruz escreve sobre a vila de Santo Antônio do Madeira, acampamento do canteiro de obras. Lembro que a vila é hoje a cidade de Porto Velho, capital do estado de Rondônia, e que foi fundada pela empresa construtora da ferrovia. "A vila não tem esgotos, nem água canalizada, nem iluminação de qualquer natureza. O lixo e todos os produtos da vida vegetativa são atirados às ruas, se merecem este nome vielas esburacadas que cortam a infeliz povoação. Encontram-se colinas de lixo apoiadas às paredes de habitações.

Grifo do autor

Belisário Pena, médico que o acompanhava nesta viagem.


H Escamilla Núñez

H Bouadi
email: hakimbouadi@yahoo.fr

F Mora Camino

A Framework for Wind Sensitivity Analysis for Trajectory Tracking

Keywords:

In this paper a sensitivity analysis of trajectories w.r.t. wind effects is proposed. This analysis will allow to specify wind estimates properties as well as control reactiveness characteristics to ensure accurate guidance in real atmosphere. The mathematic model developed for flight dynamics is intended to take into account wind gust effects on AoA, sideslip angle and airspeed. A two layer Nonlinear Dynamic Inversion (NDI) structure has been considered to control fast and slow dynamics. In order to test the proposed approach, a full six degrees of freedom Matlab model with trained Neural Networks to emulate a Boeing 737-200 was developed.

NOMENCLATURE

α Angle of Attack, deg β Sideslip angle, deg V a Airspeed, m/s η = [φ, θ, ψ] T Euler angles, deg Ω = [p, q, r] T Angular velocities, deg/s u, v, w Groundspeed in the body frame, m/s F thr , L, D, Y Thrust/Lift/Drag/Sideforce, N F xa , F ya , F za Aerodynamic Forces in the body frame, N L , M, N Rolling/Pitching/Yawing moments, N • m C L , C D , C Y Lift/Drag/Sideforce aerodynamic coefficients C l , C m , C n Rolling/Pitching/Yawing aerodynamic coefficients µ Thrust specific fuel consumption, kg/(N • s) g Gravity, m/s 2 m Aircraft mass, kg ρ Air density, kg/m 3 S Wing area, 123.55 m 2 b Wingspan, 28.34 m c Mean chord, 4.35 m A Inertia matrix component, 1, 278, 369.56 kg • m

I. INTRODUCTION

As air traffic is predicted to increase dramatically in the upcoming years, new problems and requirements are arising, among those involving the use of 4D trajectories are of most interest. NextGen [START_REF]Next generation air transportation system[END_REF] and SESAR [START_REF]Single european sky atm research joint undertaking[END_REF] control projects, adopt the Trajectory Based Operations (TBO) paradigm, where safety and traffic capacity issues are the milestones. Knowing that TBO relies on 4D guidance, it is not surprising that automation becomes one of the important enablers, allowing aircraft to follow more accurately a desired trajectory, resulting in a fuel usage decrease and reduced CO 2 emissions per flight. It is expected that 4D guidance improves safety by decreasing the occurrence of near mid-air collisions for planned conflict free 4D trajectories and in consequence, decrease the work load for air traffic controllers .

Considering that one of the main disturbances during flight are wind gusts, it seems natural to take into account their effects while modelling aircraft dynamics. Once a mathematic model with wind contributions is obtained, a flight control structure must be assumed. In this work, a two-level Nonlinear Dynamic Inversion (NDI) has been developed to control the position and the angular velocities. The approach consists in transform algebraically a nonlinear system into a system with linear dynamics [START_REF] Slotin | Applied Nonlinear Control[END_REF], [START_REF] Khalil | Nonlinear Systems[END_REF]. Separation of slow and fast dynamics are common practice [START_REF] Snell | Nonlinear inversion flight control for a supermaneuverable aircraft[END_REF], [START_REF] Lombaerts | Pseudo control hedging and its application for safe flight envelope protection[END_REF]. Also, some machine learning algorithms and/or variations of the classical NDI approach have been tested in order to improve the performance of the method and provide robustness to uncertainties like modeling and/or measuring errors, showing good simulation results [START_REF] Rysdyk | Robust nonlinear adaptive flight control for consistent handling qualities[END_REF], [START_REF] Hameduddin | Generalized dynamic inversion control for aircraft constrained trajectory tracking applications[END_REF]. However, full knowledge of variables and parameters cannot be acquired due to possible corrupted measures or uncertainty in parameters, leading to guidance inaccuracy. Thus, this work will provide a tool to quantify the performance of the aircraft in terms of position errors due to wind gusts by performing a sensitivity analysis through simulation. Actuator dynamics for the control surfaces involving a time-constant will also be considered.

Methods to perform sensitivity analysis such as screening are common [START_REF] Schnelle | Sensitivity analysis of human driving characteristics on road and driving conditions for active vehicle control systems[END_REF], where a baseline experiment is done using nominal values of parameters, then, selecting two extreme values of these, the results of the perturbed experiment w.r.t. the baseline are observed in order to decide to which parameters the model is most sensitive to. Nevertheless, interaction between parameters is neglected and the correlation between them and outputs of the system is considered linear. Variance-based approaches show how to find which are the most relevant parameters and how much they affect the system output by computing sensitivity indices such as Sobol indices, quantifying the amount of variance in the output caused by a parameter. These methods allow interaction of different parameters and nonlinear responses between them and the outputs [START_REF] Janon | Global sensitivity analysis for the boundary control of an open channel[END_REF]. Another technique is to compute the partial derivatives of the interesting variables to analyze the local sensitivity [START_REF] Evans | Sensitivity analysis for control parameter determination for a nonlinear cable-mass system[END_REF], [START_REF] Kanno | Algebraic approach to sensitivity analysis in optimal feedback control system design[END_REF]. For our work, using an approach similar to screening analysis, wind information is used as a changing parameter to quantify the effects it has on the aircraft position.

The paper is organized as follows, Section II provides the developed mathematical model under wind conditions. Section III describes the adopted NDI control structure and Section IV shows the simulation results of this control law. Section V shows the wind sensitivity analysis trough simulation. Finally, conclusions are described in Section VI.

II. DYNAMIC MODEL IN WIND CONDITIONS

Wind gusts contributions are considered to affect directly the aircraft angle of attack (AoA), sideslip angle and airspeed, and then their effects are propagated to the angular velocities, then to the attitude, and finally to the position. Hence, when wind effects are considered to be reflected only in attitude, or only in position, it may differ from the actual phenomena.

A. Adopted Frames and Flight Variables

The earth reference frame is assumed to be Earth centered and denoted by

F E = (O E , x E , y E , z E ).
A second reference frame is considered to represent the fast dynamics of the aircraft, it is attached to the body's c.g. and is defined as F B = (C, x B , y B , z B ), referred to it as the body frame. The x B axis goes from tail to nose of the aircraft while the z B axis, perpendicular to the latter, points downwards and lies in the symmetry plane of the aircraft, to complete the triad, the direction of y B can be obtained by the cross product z B × x B . Lastly, denoted by F W = (C, x W , y W , z W ), a wind frame is defined in order to represent the aerodynamic actions on the aircraft. This frame has its x W axis aligned with the aircraft velocity vector relative to the surrounding air mass, i.e. the airspeed. The difference between x B and the projection of x W in the Cx B z B plane, gives birth to the angle of attack. Also, the angle created by the projection of V a in the Cx B y B plane and the x B axis, is known as the sideslip angle. Physical quantities from the wind frame can be mapped into the body frame by the following rotation matrix:

L BW =   c α c β -c α s β -s α s β c β 0 s α c β -s α s β c α   (1)
In the same tenor, the velocity of the aircraft (V E = [ ẋE , ẏ E , ż E ] T ), is expressed in the body frame as V B = [u, v, w] T . Also, the euler angles are used to describe the attitude of the aircraft. These angles are bounded as follows φ{-π, π}; θ{-π 2 , π 2 } ; ψ{-π, π}, although limits are never reached during normal operation. The rotation matrix from the body to the earth frame considering a rotation around the axes in the order zyx, is given by:

L EB =   c θ c ψ s φ s θ c ψ -c φ s ψ c φ s θ c ψ + s φ s ψ c θ s ψ s φ s θ s ψ + c φ c ψ c φ s θ s ψ -s φ c ψ -s θ s φ c θ c φ c θ   (2)
Moreover, defining the wind speed in the body frame as V w = [V wx , V wx , V wx ] T and from the rigid-body equations and other known relations extracted from [START_REF] Etkin | Dynamics of Flight, Stability and Control[END_REF], [START_REF] Stevens | Aircraft Control and Simulation[END_REF] it is obtained:

  u v w   =   V a c α c β + V wx V a s β + V wy V a s α c β + V wz   (3)
  u v ẇ   =   1 m (F xa + F thr ) -gs θ + rv -qw 1 m F ya + gc θ s φ + pw -ru 1 m F za + gc θ c φ + qu -pv   (4)
α = arctan w u (5a)

β = arcsin v V a (5b) V a = u 2 + v 2 + w 2 (5c)
The vector R = [α, β, V a ] T is defined for simplicity in further equations.

B. Attitude Dynamics

Concerning the attitude of the aircraft, the angular rates are produced by the deflection of ailerons, elevator and rudder, denoted by [δ ail , δ ele , δ rud ] T respectively. Thus, the rotational equations of the aircraft are given by:

Ω = I -1 M ext -I -1 Ω × (IΩ) (6)
where M ext denotes the rolling, pitching and yawing moments, and I stands for the inertia matrix, considered constant by neglecting the weight change of the aircraft:

I =   A 0 -E 0 B 0 -E 0 C   (7)
Thereby, introducing relations for the aerodynamic moments:

  L M N   = 1 2 ρSV 2 a     bC l cC m bC n   + C δ   δ ail δ ele δ rud     (8)
where

C δ =   bC l δail 0 bC l δrud 0 cC m δele 0 bC n δail 0 bC n δrud  
The rolling, pitching and yawing aerodynamic coefficients are denoted by:

  C l C m C n   =    C l β β + C lp bp 2Va + C lr br 2Va C m0 + C mα α + C mq cq 2Va C n β β + C np bp 2Va + C nr br 2Va    (9)
Then, equation ( 6) can be rewritten as in [START_REF] Lombaerts | Nonlinear reconfiguring flight control based on on-line physical model identification[END_REF] like.

  ṗ q ṙ   = 1 2 ρV 2 a SI -1     bC l cCm bCn   + C δ   δ ail δ ele δ rud     -I -1   p q r   ×   I   p q r     (10)
Subsequently, differentiating (5a), the rate of change of the angle of attack is given by:

α = u ẇ -w u u 2 + w 2 = (Vac β ) 2 [q -tan β (pcα + rsα)] + Vac β g1 -1 m (L + F thr sα) + Vw x Fz a m + gc θ c φ -Vw z Fx a m + F thr m -gs θ (Vac β ) 2 + 2Vac β (Vw x cα + Vw z sα) + V 2 wx + V 2 wz -Vw x Vw y p -Vw y Vw z r + q V 2 wx + V 2 wz + Vac β [Vw x (2qcα -ptan β ) -Vw y (pcα + rsα) + Vw z (2qsα -rtan β ) (11)
with:

g 1 = g (c α c θ c φ + s α s θ )
Similarly, differentiating (5b), the rate of change of the sideslip angle is given by:

β = Va v -v Va Va √ V 2 a -v 2 = V 2 a c β 1 m (Y -F thr cαs β ) + g2 + Va (psα -rcα) + V 2 a (Vw z p -Vw x r) + Fy a m + gc θ s φ [2Vac β (Vw x cα +Vw z sα) V 2 a + 2Va Vw y s β + c β (Vw x cα + Vw z sα) + V 2 wx + V 2 wy +V 2 wz } V 2 a c 2 β -Vw y 2Vas β + Vw y + V 2 wx + V 2 wz + [Vac β (psα -rcα) + Vw z p -Vw x r] 2Va Vw y s β +c β (Vw x cα + Vw z sα)] + V 2 wx + V 2 wy + V 2 wz - Fz a m + gc θ c φ Va Vw y sαc β + Vw z s β + Vw y Vw z - Fx a m + F thr m -gs θ Va Vw y cαc β + Vw x s β + Vw x Vw y (12)
with:

g 2 = g (c β c θ s φ + s β c α s θ -s α s β c θ c φ )
Then, from (5c), it is obtained:

Va = u u + v v + w ẇ Va = g3 + 1 m (F thr cαc β -D) + 1 mVa [Vw x (Fx a + F thr -mgs θ ) +Vw y (Fy a + mgc θ s φ ) + Vw z (Fz a + mgc θ c φ ) (13)
with:

g 3 = g (-c α c β s θ + s β c θ s φ + s α c β c θ c φ )
The expression in matrix form of relations ( 11), ( 12) and ( 13), rearranged for Ω is denoted by:

  α β Va   =   H11 1 H13 H21 0 H23 0 0 0     p q r   +   Q1 Q2 Q3   (14)
where

H11 = -(Vacαc β + Vw x ) Vas β + Vw y (Vac β ) 2 + 2Vac β (Vw x cα + Vw z sα) + V 2 wx + V 2 wz H13 = -Vas β + Vw y (Vasαc β + Vw z ) (Vac β ) 2 + 2Vac β (Vw x cα + Vw z sα) + V 2 wx + V 2 wz H21 = Vasαc β + Vw z V 2 a c 2 β -Vw y 2Vas β + Vw y H23 = -(Vacαc β + Vw x ) V 2 a c 2 β -Vw y 2Vas β + Vw y Q1 = Vac β g1 -1 m (L + F thr sα) + Vw x Fz a m + gc θ c φ -Vw z Fx a m + F thr m -gs θ (Vac β ) 2 + 2Vac β (Vw x cα + Vw z sα) + V 2 wx + V 2 wz Q2 = V 2 a c β 1 m (Y -F thr cαs β ) + g2 + Fy a m + gc θ s φ 2Vac β (Vw x cα + Vw z sα) + V 2 wx + V 2 wz V 2 a + 2Va Vw y s β + c β (Vw x cα + Vw z sα) + V 2 wx +V 2 wy + V 2 wz V 2 a c 2 β -Vw y 2Vas β + Vw y - Fx a m + F thr m -gs θ Va Vw y cαc β + Vw x s β +Vw x Vw y - Fz a m + gc θ c φ Va Vw y sαc β + Vw z s β +Vw y Vw z Q3 = g3 + 1 m (F thr cαc β -D) + 1 mVa [Vw z (Fz a + mgc θ c φ ) +Vw x (Fx a + F thr -mgs θ ) + Vw y (Fy a + mgc θ s φ )
which can be written as:

Ṙ = H (R) Ω + Q (R) (15)
It can be easily verified that if the wind components are zero, the equations ( 11), ( 12) and ( 13) take the form:

α = q -tan(β) (pcos(α) + rsin(α)) + 1 V a cos(β) g 1 - 1 m (L + F thr sin(α)) (16a) β = psin(α) -rcos(α) + 1 V a 1 m (Y -F thr cos(α)sin(β)) + g 2 (16b
)

Va = g 3 + 1 m (F thr cos(α)cos(β) -D) (16c)
The rotation speed components are related with the attitude angle rates by the Euler equations, given by:

  φ θ ψ   =   1 tg θ s φ tg θ c φ 0 c φ -s φ 0 s φ c θ c φ c θ     p q r   (17)

C. Guidance Dynamics

Considering that the thrust force has only components in x B , and knowing the relations for the aerodynamic forces in the body frame:

  F xa F ya F za   = L BW   -D Y -L   (18) and   D Y L   = 1 2 ρSV 2 a   C D C Y C L   (19)
The translational equations in the Earth frame are obtained by the 2nd Newton's law:

  ẍE ÿE zE   = L EB   F xa + F thr F ya F za   1 m +   0 0 g   (20)

D. Actuator Dynamics

Let a first-order model of the actuators be considered, assuming δ d i (i = ail, ele, rud) as the desired positions of the control surfaces, and δ i as the current positions of the control surfaces.

δi = 1 ξ i δ d i -δ i (21)
where ξ i are the time-constants. Also, the resultant thrust produced by the engines is supposed to behave as a first-order system, denoted by

Ḟthr = 1 ξ T F d thr -F thr (22)
where the F d thr is the desired thrust and F thr the current thrust. Besides, the time-constants of the actuators keep the relation: ξ T >> ξ i .

III. CONTROL A. Attitude Control

Taking the angular velocities as intermediary control variables, the necessary position of the actuators (deflection of aileron, elevator and rudder) as functions of the desired angular velocities must be determined, so the jerk vector of the angular velocities is obtained by differentiating one more time equation [START_REF] Janon | Global sensitivity analysis for the boundary control of an open channel[END_REF], leading to

  p q r   = 1 2 ρSI -1    V 2 a     b Ċl c Ċm b Ċn   + C δ ξ   δ d ail -δ ail δ d ele -δ ele δ d rud -δ rud     +2Va Va     bC l cCm bCn   + C δ   δ ail δ ele δ rud        -I -1 In   ṗ q ṙ   (23)
with

In =   -Eq (C -B)r -Ep (C -B)q (A -C)r + 2Ep 0 (A -C)p -2Er (B -A)q (B -A)p + Er Eq   and ξ =   1 ξ ail 0 0 0 1 ξ ele 0 0 0 1 ξ rud  
where the aerodynamic moment coefficients dynamics are taken into account due to their close relation with R. On the other hand, control surfaces moment coefficients dynamics are neglected. Hence, differentiating [START_REF] Schnelle | Sensitivity analysis of human driving characteristics on road and driving conditions for active vehicle control systems[END_REF], equation ( 23) can be rewritten as:

  p q r   = 1 2 ρSI -1    V 2 a C δ ξ   δ d ail -δ ail δ d ele -δ ele δ d rud -δ rud   + V 2 a Cc   α β Va   +2Va Va     bC l cCm bCn   + C δ   δ ail δ ele δ rud        + I -1 1 4 ρSVaC k -In   ṗ q ṙ   ( 24
)
where

C c =     0 bC l β -b 2 2V 2 a (C lp p + C lr r) cC mα 0 - c2 2V 2 a C mq q 0 bC n β -b 2 2V 2 a (C np p + C nr r)     C k =   b 2 C lp 0 b 2 C lr 0 c2 C mq 0 b 2 C np 0 b 2 C nr  
The vector Ṙ can be taken from [START_REF] Lombaerts | Nonlinear reconfiguring flight control based on on-line physical model identification[END_REF], and the vector Ω from [START_REF] Janon | Global sensitivity analysis for the boundary control of an open channel[END_REF]. Therefore, inverting the dynamics leads to an attitude control input denoted by:

  δ d ail δ d ele δ d rud   = 1 V 2 a ξ -1 C -1 δ    2I ρS   τp τq τr   - 2 ρS 1 4 ρSVaC k -In   ṗ q ṙ   -2Va Va     bC l cCm bCn   +C δ   δ ail δ ele δ rud     -V 2 a Cc   α β Va      +   δ ail δ ele δ rud   (25)
where the wind effects appear in the terms involving α, β and Va . Also, desired dynamics for the angular velocities are proposed:

  τ p τ q τ r   =   -k 1 (p -p d ) -k 2 ( ṗ -ṗd ) + pd -k 3 (q -q d ) -k 4 ( q -qd ) + qd -k 5 (r -r d ) -k 6 ( ṙ -ṙd ) + rd   (26)
for k i > 0 (i = 1, ...6) as gains, chosen in order to assure asymptotical convergence of the variables to their desired values. The feasibility of this approach depends on the singularity of C δ , the matrix involving the aerodynamic coefficients (assumed to be known thanks to experimental data, airflow simulations, or any other method) due to the control surfaces, aspect that can be handled.

B. Position Control

In order to assure trajectory tracking, angular velocities and thrust required to follow a reference trajectory need to be obtained, so after differentiating equation (20), the jerk vector of the position in F E is obtained.

   x (3) E y (3) E z (3) E    = LEB m   Fx a + F thr Fy a Fz a   + LEB m   Ḟxa + Ḟthr Ḟya Ḟza   + - ṁ m 2 LEB   Fx a + F thr Fy a Fz a   (27)
Considering that the mass rate of change is very small compared to the aircraft total mass, the term containing - ṁ m 2 is neglected. Also, writing the Euler property as

LEB = L EB   0 -r q r 0 -p -q p 0   = M p p + M q q + M r r (28)
where

M p =   0 c φ s θ c ψ + s φ s ψ c φ s ψ -s φ s θ c ψ 0 c φ s θ s ψ -s φ c ψ -s φ s θ s ψ -c φ c ψ 0 c φ c θ -s φ c θ   M q =   -c φ s θ c ψ -s φ s ψ 0 c θ c ψ -c φ s θ s ψ + s φ c ψ 0 c θ s ψ -c φ c θ 0 -s θ   M r =   s φ s θ c ψ -c φ s ψ -c θ c ψ 0 s φ s θ s ψ + c φ c ψ -c θ s ψ 0 s φ c θ s θ 0  
and defining the vector 27) can be rewritten as:

F ab = [F xa + F thr , F ya , F za ] T , equation (
   x (3) E y (3) E z (3) E    = 1 m   c θ c ψ MpF ab MqF ab c θ s ψ -s θ     p q Ḟthr   + 1 m MrF ab r + LEB m   Ḟxa Ḟya Ḟza   ( 29
)
where

  Ḟxa Ḟya Ḟza   =    ∂Fx a ∂α ∂Fx a ∂β ∂Fx a ∂Va 0 ∂Fy a ∂β ∂Fy a ∂Va ∂Fz a ∂α ∂Fz a ∂β ∂Fz a ∂Va    Ṙ +    ∂Fx a ∂ρ ∂Fy a ∂ρ ∂Fz a ∂ρ    ρ ( 30
)
where Ṙ is obtained from equation [START_REF] Lombaerts | Nonlinear reconfiguring flight control based on on-line physical model identification[END_REF]. Thus, taking as guidance inputs the vector [p, q, Ḟ thr ] T , the inversion of the dynamics can be proposed in the form:

  p q Ḟthr   = m   c θ c ψ MpF ab MqF ab c θ s ψ -s θ   -1     τx τy τz   - 1 m MrF ab r - LEB m   Ḟxa Ḟya Ḟza     (31)
where the wind effects are involved in the vector [ Ḟxa , Ḟya , Ḟza ] T , and desired behaviour of the position is proposed as:

  τx τy τz   =   -d1(x -x d ) -d2( ẋ -ẋd ) -d3(ẍ -ẍd ) + ... x d -d4(y -y d ) -d5( ẏ -ẏd ) -d6(ÿ -ÿd ) + ... y d -d7(z -z d ) -d8( ż -żd ) -d9(z -zd ) + ... z d   ( 32
)
for d i > 0 (i = 1, ...9) as gains chosen in order to assure asymptotical convergence of the variables to their desired values. The feasibility of this approach requires the invertibility of the matrix:

MpqT =   c θ c ψ MpF ab MqF ab c θ s ψ -s θ   (33)
which in the case in where φ ≈ ψ ≈ 0, the determinant of this matrix is given by:

| M pqT |= s θ F ya + (s θ (F xa + F thr ) -c θ F za ) (s θ F za ) + c θ (c θ (F xa + F thr ) + s θ F za ) F za (34)
and, when considered θ ≈ 0, a singularity appears for F xa +F thr = 0. This is the case when the plane is cruising at constant speed. Therefore, in order to manage this singularity, the controller can be switched for another approach, or as considered in this work, the desired angular velocities are switched to zero.

IV. SIMULATION RESULTS A six degree of freedom model for a wide body transportation aircraft has been developed in Matlab to provide simulation results with the adopted control law as well as the sensitivity analysis, the aircraft parameters were chosen close enough to emulate a Boeing 737-200 (described in the Nomenclature), flying in an International Standard Atmosphere model with uniform gravity. The time response of actuators used to move the control surfaces is 50 ms. To obtain the values of the aerodynamic coefficients, a two-layer feed-forward neural networks with sigmoid hidden neurons and linear output neurons were trained using data bases obtained from the United States Air Force (USAF) Stability and Control Digital DATCOM (Data Compendium) [16], which is a Public Domain Aeronautical Software that compute the static stability, control and dynamic derivative characteristics of fixed-wing aircrafts using the methods contained in the USAF Stability and Control DATCOM, furthermore, the data sets were compared and refined using the JSBSim open source Flight Dynamics Models (FDM) [17], used in several open source simulators and also employed to drive the motion-base research simulators of many universities worldwide. The training, validation and test sets were 70, 15 and 15 percent respectively of the available data for each aerodynamic coefficient. The training algorithm used was Bayesian Regularization and the number of hidden neurons was selected by trial and error trying to improve the performance as much as possible. The initial mass of the airplane is 50,000 kg and it is supposed to follow a dynamic as:

ṁ = -µF thr (35)
Where the thrust specific fuel consumption involves the coefficients c f 1 = 2.854x10 -5 kg/(N • m) and c f 2 = 8, 693.36 m/s, as well as the airspeed [START_REF]User Manual for the Base of Aircraft Data (BADA), European Organisation for the Safety of Air Navigation[END_REF], expressed by:

µ = c f 1 1 - V a c f 2 V a 1, 943.84 (36)
When the control surfaces are jammed at zero degrees, and enough constant thrust to hold a longitudinal flight is set, the behaviour of the aircraft is a stable, with decreasing phugoid mode with a 100 s period.

Regarding to the attitude, in figure 1 viceversa can be nullified or controlled, which plays a key roll when coordinated turns are performed.

In figure 1(b), a lateral displacement using roll is simulated, holding a fixed altitude and a constant yaw angle. In order to achieve this task, the deflection of the control surfaces of the aircraft is depicted in figure 2(a). Moreover, the behaviour of the attitude under some disturbances is examined by applying wind gusts of 30 m/s (58.3 knots) (see figure 2(b)). The first disturbance is applied around 5 s in z B direction, which produces an asymmetric disturbance in pitch. Then, a second disturbance is applied around second 10 in -y B direction, which affects roll and yaw rates, as expected. Finally, a disturbance with components in both mentioned directions is applied around the second 21. Note that for the moment, the error produced in position by these wind gusts is not examined and only a zero angular rate is desired to be kept under these disturbances. It is worth to mention that during flight, constant large variations of the Thrust are not desired, so in this work, Thrust is considered constant, resulting in a longitudinal speed of 250 m/s. In order to test de guidance controller, figure 3 Let the position errors produced by wind gusts be examined, taking into account that non-zero angular rates will allow the aircraft to reject perturbations and achieve the guidance objectives. In figure 4, wind gusts endowed with small turbulence (using a Dryden wind turbulence model) are applied, showing the effects on y and z position errors as well as the groundspeed, which has no control due to the constant Thrust. V. TOWARDS SENSITIVITY ANALYSIS THROUGH SIMULATION So far, the controller is assumed to have full knowledge of wind disturbances (by estimations, measures or forecasts available), but in reality, the use of corrupted measurements, approximated mathematical models, or uncertainty in parameters leave room for errors in the control, which can be studied through a sensitivity analysis. For our study, it is assumed that wind knowledge by the controller is the main contributor to position error improvements. Note that by wind knowledge, we refer to the accuracy of wind gust magnitude and not the direction. So, a 70% of wind knowledge when a wind gust of 10 m/s is considered, will be 7 m/s in the same direction. So that, the transport aircraft of Section IV flying at 10,000 m with a constant groundspeed of 250 m/s under some wind disturbances is used, and endowing the controller with different wind knowledge, the position errors are examined. The position errors for y and z with 0%, 50%, 75%, 90% and 100% of wind knowledge are displayed in figure 5, where the error magnitude decreases when wind knowledge increases. This means that as the components of equation ( 15) used for the control approach tend to equations (16a), (16b) and (16c), the controller will decrease its performance drastically, corroborating that the reactiveness of the control law (and hence, the position errors), is sensitive to wind knowledge. In Table I, the Mean Squared Error (MSE) and the Mean Absolute Error (MAE) in y and z axes were computed in order to provide a clear idea of the wind sensitivity w.r.t. aircraft position. The disturbances, simulation time (500 s) and sample time (1/30 s) are the same as the ones to obtain figure 5. It is worth to note that even if full wind knowledge is achieved, the control effort will always remain bounded within the typical constraints for transport aircraft.

VI. CONCLUSION Depending on each application or requirement, a maximal wind uncertainty can be allowed in order to do not exceed a desired error in position, proposed by the user. This wind uncertainty can be translated into wind sensors accuracy, wind estimations accuracy or up-to-date forecasted wind. The control law used in this work can be easily replaced by other control law to compare their sensitivity to wind. A safety envelope for a single aircraft or a group of aircrafts can be redefined, as errors will depend on wind knowledge accuracy, allowing to create compact aircraft clusters and decrease the workload for air traffic controllers. In this paper, a framework for wind sensitivity analysis is described in order to test different control laws as well as different wind uncertainties and their effects in guidance errors, quantifying its performance by computing the mean squared error and mean absolute error. A mathematical model and a NDI approach considering wind disturbances in AoA and sideslip angle, as well as in airspeed, was developed and tested in a six degrees of freedom Matlab simulation.

Fig. 1 .

 1 Fig. 1. Attitude control test.

Fig. 2 .

 2 Fig. 2. Control effort and rejection of perturbations.

  (a) shows the trajectory of the aircraft when different desired positions are commanded. An increase in altitude of 100 m and return to its original altitude, as well as a lateral displacement of 100 m and return to the original position are demanded. Next, a decrease of 10 m in altitude and a lateral displacement of 50 m in the opposite direction than the first one are commanded. Finally, the aircraft is asked to return to the original altitude and original y position. The figure3(b) displays the 3D trajectory of the described flight. The control approach also assures a climb and descent rate under 1,400 ft/min, as well as velocity in lateral displacements under 2,200 ft/min. It is a key point to remark that as control inputs for guidance are the angular velocities, if an angular velocity is commanded for a relatively long period of time, this will derive in constant and maybe undesired turning of the aircraft. In order to avoid this problem, when Euler angles reach a certain magnitude, the angular velocity is forced to become zero until an angular velocity in the opposite direction is commanded. The saturation of the Euler angles are: φ{-30 • , 30 • }; θ{-15 • , 25 • }; ψ{-π, π}.

  (a) Position response to commanded positions. (b) 3D Trajectory of guidance control test.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Guidance control test

Fig. 5 .

 5 Fig. 5. Wind knowledge effect on position errors.

TABLE I ERROR

 I

	DEPENDING ON WIND KNOWLEDGE
		y		z
	Wind Knowledge (%)	MSE	MAE	MSE	MAE
	100	10.2760	0.6731	0.7806	0.5767
	90	8.4628	0.6787	2.0858	0.6993
	80	13.8191	0.8001	5.8818	1.0335
	70	23.0642	1.0926	11.7237	1.2839
	60	35.9015	1.4416	20.3080	1.6094
	50	55.9952	1.8394	31.2249	1.9199
	40	78.7370	2.2092	44.1320	2.2091
	30	107.6038 2.6044	59.4018	2.4883
	20	140.3636 2.9848	77.5264	2.7895
	10	177.5873 3.3675	97.0740	3.0764
	0	220.3000 3.7540 118.4172 3.3786


may come

Crowdsourcing annotations for comics corpora

Mihnea Tufiș, Pierre and Marie Curie University, Paris 6, France Jean-Gabriel Ganascia, Pierre and Marie Curie University, Paris 6, France

In this proposal, we address the difficulty of creating a digitized corpus by using a crowdsourced approach for annotating comic books. The resulting XML-based encodings could assist not only researchers, but publishers and collection curators equally.

The motivation for our work is three-fold. Digital Humanities scholars will be provided with an annotated corpus for conducting research relating to comics and sequential art. Curators and collectors would be provided with a structured content, which could be more easily integrated within their collections or databases. This may assist them into enlarging public or private databases of characters or comics series and enable the creation of artefacts such as comic books dictionaries, search indices and dictionaries of onomatopoeia. From a publishing perspective, the data we are collecting will allow publishers and digital comics authors to create enhanced content for a better reading experience.

Our proposal is a complementary solution to image processing approaches for identifying page/grid structures and extracting text from narration devices (i.e. different types of bubbles) [START_REF] Rigaud | Robust text and frame extraction from comic books[END_REF]. We address the difficulty of automatically extracting complex page layouts, narration elements (characters, places, events, objects) or stylistic elements (frame shapes, onomatopoeia, movement lines), by engaging with the passionate "crowd" of comic books readers. Previous research has identified expertise sharing, belonging to a community and helping with a research project as strong motivating factors for crowdsourcing participants [START_REF] Dunn | Engaging the Crowd with Humanities Research. Crowd-Sourcing Scoping Study[END_REF]. In addition, our industrial partner will incentivize participants with product vouchers for their digital comics platform.

We aggregate the answers [START_REF] Feng | Acquiring High Quality Non-Expert Knowledge from Ondemand Workforce[END_REF] taking into account the reliability of an annotator in a given context (task difficulty, task type, annotator expertise) and the agreement between annotators [START_REF] Nowak | How reliable are annotations via crowdsourcing? A study about interannotator agreement for multi-label image annotation[END_REF]. We generate a quality score for each annotation, with the best of them being selected and compiled into a ready-to-use ComicsML encoding [START_REF] Walsh | Comic Book Markup Language: an Introduction and Rationale[END_REF].