Anke M Brock
email: anke.brock@irit.fr

Bernard Oriola
email: bernard.oriola@irit.fr

Philippe Truillet
email: philippe.truillet@irit.fr

Christophe Jouffrais
email: christophe.jouffrais@irit.fr

Delphine Picard
email: delphine.picard@univ-amu.fr

Map design for visually impaired people: past, present, and future research

Keywords: Cartes Interactives, Interaction Homme-Machine, Accessibilité, Design de cartes, Déficience visuelle, Technologies interactives, Multi-touch Interactive Maps, HCI, Accessibility, Map design, Visual Impairment, Multi-touch

come

Introduction

Imagine moving to an unknown city. What would you do to obtain accurate knowledge of the environment? Read a map? Go out and explore the streets in your neighborhood? Both activities are easy to perform if you are sighted. However, for visually impaired (VI) people, orientation and mobility are challenging. Yet, different studies proved that VI people can achieve spatial cognition [START_REF] Ungar | Cognitive Mapping without Visual Experience[END_REF]. Mental mapping is usually performed through the integration of information perceived by the senses. When vision is lacking, spatial information perceived through external (auditory, olfactory, somatosensory) and internal (perception of own posture and movement) cues provides only a partial perception of space and events. Therefore, exploring an unknown environment is stressful and sometimes dangerous for VI people [START_REF] Gaunet | Exploring the Functional Specifications of a Localized Wayfinding Verbal Aid for Blind Pedestrians: Simple and Structured Urban Areas[END_REF]. Mental mapping can be achieved more safely using indirect sources of information, such as verbal descriptions or tactile representations of an environment (maps or small-scale models) [START_REF] Jacobson | Talking tactile maps and environmental audio beacons: An orientation and mobility development tool for visually impaired people[END_REF][START_REF] Picard | Does Knowledge of Spatial Configuration in Adults with Visual Impairments Improve with Tactile Exposure to Small-Scale Model of their Urban Environment[END_REF]. The latter are miniaturized symbolic representations of a real space. Tactile maps allow for the absolute and relative localization of spatial objects such as streets or buildings, the estimation of distances and directions, as well as finding an itinerary between two points [START_REF] Hatwell | The tactile reading of maps and drawings, and the access of blind people to works of art[END_REF].

From paper to interactive maps

Tactile paper maps (also called raised-line maps) have long been used to present spatial information to VI people. They were used both as a learning device during education and as a wayfinding aid for navigation [START_REF] Jacobson | Talking tactile maps and environmental audio beacons: An orientation and mobility development tool for visually impaired people[END_REF]. Despite their common usage by VI people, these maps have important limitations. First, due to the specificities of the tactile sense, raised-line maps must be scanned sequentially, placing great demands on memory. Second, tactile maps include a large amount of information, often resulting in perceptual overload for readers [START_REF] Jacobson | Talking tactile maps and environmental audio beacons: An orientation and mobility development tool for visually impaired people[END_REF]. Third, the usage of Braille in tactile maps is critical. However, Braille text requires a lot of space, and does not adapt to changes in orientation, inter-cell spacing and font properties [START_REF] Tatham | The design of tactile maps: theoretical and practical considerations[END_REF]. Many VI people do not read Braille: in France, only 15% of the Blind are Braille readers (C2RP, 2005). Using a separate legend in Braille potentially introduces interpretation problems as referencing is disrupted during map reading [START_REF] Jacobson | Talking tactile maps and environmental audio beacons: An orientation and mobility development tool for visually impaired people[END_REF]. Last, once maps are printed on swell paper, the information they contain cannot be modified or updated and can therefore become quickly invalid [START_REF] Yatani | SpaceSense: representing geographical information to visually impaired people using spatial tactile feedback[END_REF].

The introduction of new technologies in recent years has opened up possibilities for designing accessible maps. As argued by [START_REF] Oviatt | Multi modal Interactive Maps: Designing for Human Performance[END_REF], maps that are based on the use of interactive technology have the potential to provide a substantially broader spectrum of the population with spatial knowledge, irrespective of age, sensory impairment, skill level, or other considerations. Looking at the literature concerning existing concepts of accessible interactive maps has indicated that several research projects have been devoted to the design of interactive maps for VI people within the 25 last years (from 1988 to today). All of these projects involved interactive geographic maps (including mostly streets and buildings). Within this corpus, the underlying concepts for map designing differ in various noticeable aspects. In Table 1, we propose a classification of 25 map prototypes, based on the following three criteria: 1) type of input and output modalities (regarding to the device, not the user), 2) number of modalities used (unimodal versus multimodal), 3) the possibility to use the device in mobility (immobile versus mobile). 1 shows that most interactive map prototypes in recent research are immobile and assist the preparation of itineraries at home, before travelling. Some of these devices involve unimodal input through touch sensitive screens, and unimodal auditory output, providing, for instance, the name of geographic elements or sounds when the user touches the screen [START_REF] Heuten | Interactive 3D sonification for the exploration of city maps[END_REF][START_REF] Jacobson | Navigating maps with little or no sight: An audio-tactile approach[END_REF][START_REF] Kane | Access Overlays: Improving Non-Visual Access to Large Touch Screens for Blind Users[END_REF]. Several map projects are based on a similar system, but with a raised-line paper map placed on top of the screen (Brock, Truillet et al., 2012;[START_REF] Miele | Talking TMAP: Automated generation of audio-tactile maps using Smith-Kettlewell's TMAP software[END_REF][START_REF] Minatani | Tactile Map Automated Creation System to Enhance the Mobility of Blind Persons -It's Design Concept and Evaluation through Experiment[END_REF][START_REF] Paladugu | On presenting audio-tactile maps to visually impaired users for getting directions[END_REF][START_REF] Parkes | NOMAD": An audio-tactile tool for the acquisition, use and management of spatially distributed information by partially sighted and blind persons[END_REF][START_REF] Wang | Instant tactile-audio map: enabling access to digital maps for people with visual impairment[END_REF]. The output is then multimodal as it is composed of tactile (the map's raised design) and auditory feedback. In certain dedicated devices, the raised-line map may be replaced by a field of actuated pins and input is perceived via a touch sensor integrated in the display [START_REF] Shimada | Development of Directly Manipulable Tactile Graphic System with Audio Support Function[END_REF][START_REF] Zeng | Audio-Haptic Browser for a Geographical Information System[END_REF].

Finally, alternative input modalities exist, including image recognition [START_REF] Seisenbacher | 3D-Finger -System for Auditory Support of Haptic Exploration in the Education of Blind and Visually Impaired Students -Idea and Feasibility Study[END_REF], haptic mice [START_REF] Kaklanis | HapticRiaMaps: Towards Interactive exploration of web world maps for the visually impaired[END_REF][START_REF] Rice | Design considerations for haptic and auditory map interfaces[END_REF], keyboards [START_REF] Zhao | Data Sonification for Users with Visual Impairment[END_REF], tangibles [START_REF] Pielot | Tangible User Interface for the Exploration of Auditory City Map[END_REF] and gamepads [START_REF] Schmitz | Making Digital Maps accessible using vibrations[END_REF]. Multimodal input devices are usually based on touch input in combination with other input techniques such as speech recognition [START_REF] Kane | Access Overlays: Improving Non-Visual Access to Large Touch Screens for Blind Users[END_REF], keyboard input [START_REF] Weir | Development and Evaluation of Sonified Weather Maps for Blind Users[END_REF] or a computer mouse [START_REF] Campin | SVG Maps for People with Visual Impairment[END_REF]. Different approaches were proposed by [START_REF] Milne | Tangible and body-based interaction with auditory maps[END_REF] who used a pen and the body's orientation as input, as well as [START_REF] Simonnet | SeaTouch: a haptic and auditory maritime environment for non visual cognitive mapping of blind sailors[END_REF] who combined usage of a haptic device with keyboard and speech input. In the BATS project [START_REF] Parente | BATS : The Blind Audio Tactile Mapping System[END_REF] a generic prototype was produced with the possibility to switch between several input devices, such as a mouse, a keyboard, a joystick, a touch pad or a gamepad, and to produce auditory output optionally combined with haptic feedback.

Recently, mobile applications were designed. They are based on the use of mobile phones with audio output [START_REF] Su | Timbremap: : Enabling the Visually-Impaired to Use Maps on Touch-Enabled Devices[END_REF] or audio output combined with vibration [START_REF] Poppinga | TouchOver map: Audio-Tactile Exploration of Interactive Maps[END_REF][START_REF] Yatani | SpaceSense: representing geographical information to visually impaired people using spatial tactile feedback[END_REF].

The different types of interactive maps summarized in Table 1 show both advantages and disadvantages. [START_REF] Zhao | Data Sonification for Users with Visual Impairment[END_REF] demonstrated that navigating a map with a keyboard was more difficult for VI users than with a touch screen. Also, the recollection of objects in space improved when using a touch screen as compared to the same task with a computer mouse [START_REF] Tan | Kinesthetic cues aid spatial memory[END_REF].

Given that most blind users have learned how to explore raised-line maps in school, using an interactive prototype based on a raised-line map relies on previously acquired skills and is thus probably easier to manage. Besides, tactile and audio modalities have complementary functions when presenting spatial information [START_REF] Rice | Design considerations for haptic and auditory map interfaces[END_REF]. For example, Braille labels can be removed when using speech output. The map can then be designed without overcrowding, including essential (spatial) tactile information only. The audio information can also facilitate the recognition of tactile shapes (Golledge, Rice, & Jacobson, 2005). As a whole, these research projects show that the combined use of audio and tactile feedback is especially helpful when presenting geographic information. Hence, they argue in favor of the design of interactive devices made of raised-line maps placed over a touchscreen.

Design of our interactive map

In our own research projects, we developed an interactive map prototype that could be used as an experimental platform to study the usability of accessible maps and advanced non-visual interaction.

We relied on a participatory design process adapted to VI users [START_REF] Brock | Méthodes et outils de conception participative avec des utilisateurs non-voyants[END_REF] to ensure that users' needs were closely considered. In the following sections, we detail the different steps of the design process (analysis, creating ideas for the design, prototyping and evaluation) of the interactive map prototype.

Analysis of the context of use

A first step in the participatory design process was devoted to the analysis of the context of use (users' characteristics and users' tasks) as well as the technical environment (ISO -International Organization for Standardization, 2010). The context of use included aspects such as the characteristics and needs of blind users, the specificities of their spatial cognition, their inclination towards new technologies, and the influence of strategies during haptic exploration. The technical context included aspects such as the production of raised-line maps and the choice of hardware and software environments as described in Brock, Truillet, et al. (2010) and Brock, Truillet, et al. (2012). Both analyses allowed us to make choices regarding interaction techniques, map content and layout selected for our prototype in the next steps of the design process.

Generating ideas

Brainstorming is one of the standard methods used in participatory design for generating ideas. It is usually based on the extensive use of the visual sense (i.e. written notes on a blackboard), and is therefore not feasible with VI users. Nonetheless, it is possible to adapt brainstorming to VI people, with some remaining challenges [START_REF] Brock | Méthodes et outils de conception participative avec des utilisateurs non-voyants[END_REF]. We conducted several brainstorming sessions, with VI users and orientation and mobility instructors, which focused on the topic of mobility and orientation without sight. We specifically selected ideas that related to either the type of geographic information that would be dispensed (public transportation, tourist attractions, etc.) or the different levels of information accessible on a single map (for instance a first level on the name of the geographic element -i.e. "museum" -, and a second level on a set of practical information pertaining to the geographic element -i.e. opening hours-).

Figure 1. Photograph of our interactive map prototype

Prototype

Prototype design was based upon the previous analysis of context and generation of ideas. We developed successive versions of the prototype, taking into consideration users' needs and recommendations (see Brock, Truillet, et al., 2012). The first prototyping step was a low-fidelity prototype based on the method of "Wizard of Oz". This method usually involves visual representations, but can be adapted to VI people [START_REF] Brock | Méthodes et outils de conception participative avec des utilisateurs non-voyants[END_REF]. Concretely, we adapted it by using raised-line maps and simulated speech output. Based on the pre-tests with the low-fidelity prototype, we confirmed the users' appreciation for the interactive map concept. The final prototype consisted of a raised-line map placed over a multi-touch screen (see Figure 1). Output interaction was both tactile (the map's raised design) and auditory (text-to-speech associated with touch events). We implemented a double tap as input interaction for a first version of the prototype. Details of the implementation and design are described in Brock, Truillet, et al. (2012).

Assessing prototype usability

Assessing the usability of any interactive device is central to participatory design. Usability is defined by three components, they are: efficiency, effectiveness and satisfaction (ISO -International Organization for Standardization, 2010). In a first study (Brock, Truillet, et al. 2012), we assessed user satisfaction for our prototype using a SUS questionnaire [START_REF] Brooke | SUS: A "quick and dirty" usability scale[END_REF]. A high level of user satisfaction was obtained regardless of users' age, previous visual experience or Braille experience.

Interestingly, our prototype made spatial information accessible to poor Braille readers who would have had serious difficulties with a classic raised-line map that included a Braille legend. In a second study (to be published), we compared satisfaction, efficiency (measured by exploration time) and effectiveness (measured by spatial learning) with our interactive map versus that of a classical raisedline paper map. Results indicated significantly higher efficiency and satisfaction with the interactive map than with the raised-line map, but showed no significant differences between the two types of maps in terms of spatial cognition (effectiveness). These findings allowed us to pursue the development of interactive maps for VI people with confidence.

Further development

Participatory design is an iterative process (ISO -International Organization for Standardization, 2010) and users' assessment of a prototype provides the keys to revising the design of the interactive map prototype in order to improve usability. One aspect worth considering relates to strategies used by blind users to read maps. Despite several studies in experimental psychology, the specific nature of these exploratory modes and their relations to performance level in spatial cognition remain obscure [START_REF] Thinus-Blanc | Representation of space in blind persons: Vision as a spatial sense?[END_REF]. Addressing these issues would be important for the design of accessible user interfaces. In this perspective, we developed Kintouch, a prototype that tracks finger movements by integrating data from the Microsoft Kinect camera and a multi-touch table (Brock, or image and can thus help analyzing haptic exploration strategies much more easily than with classical video observation. Our short-term objective is to use these observations in order to adapt interaction techniques and thus to make the prototype even more accessible and usable.

Conclusion

In this paper, we reviewed different concepts of accessible maps for VI people, starting with the classical raised-line paper maps and moving on to more recent interactive maps, including our own interactive map prototype. We have shown that new technologies can help overcome the limitations of traditional solutions. Touch screens and raised-line printers are nowadays relatively cheap, especially when compared to the specific equipment required by VI people. Therefore VI people could make use of interactive map prototypes in associations and schools, or even at home. However, as we have pointed it out, the development of interactive maps for VI people is a dynamic ongoing process, and the future will most likely offer blind users a variety of new and functional assistive technologies.

Namely, in the near future, new touch screen technologies are likely to remarkably improve accessible map design. Several current projects aim to develop tactile devices with haptic feedback (see for example [START_REF] Bau | REVEL: Tactile Feedback Technology for Augmented Reality[END_REF]. Interestingly, such devices will promote the design of interactive maps, without the need to superimpose raised-line paper maps. Thus, the future of maps may even forego paper. The challenges would then be on advanced interaction that efficiently serves spatial cognition.

Table 1 .

 1 A classification of interactive map projects

				OUTPUT
				Unimodal	Multimodal
							Audio + haptic	Audio
					Audio	Audio	mouse	+ tactile reference
				Auditory feedback	+ haptic device	+ display with pins Audio + raised-line map	+ raised-line map	frame	Audio + vibration
							Brock et al. 2012;
							Miele et al. 2006;
							Minatani et al. 2010;
				Heuten et al. 2006;		Shimada et al.	Paladugu et al. 2010;
			Touch screen or	Jacobson 1998;		2010;	Parkes 1988;
			sensor	Kane et al. 2011		Zeng et al. 2010	Wang et al. 2009
			Touch through				Seisenbacher et al.
			image recognition				2005
					Kaklanis et al.
			Mouse or haptic		2011;
			device		Rice et al. 2005
			Keyboard	Zhao et al. 2008
		Unimodal	Tangible Gamepad Generic haptic input device		Parente et al. 2003		Pielot et al. 2007	Schmitz et al. 2010
			Touch + keyboard				Weir et al. 2012
			Touch + speech
			recognition	Kane et al. 2011
							Campin et al.
			Touch + mouse				2003
			Haptic device,
			keybord + speech		Simonnet et al.
			recognition		2009
	INPUT	Multimodal	Tangible + body orientation Generic + keyboard	Milne et al. 2011 Parente et al. 2003
	Mobile	Unimodal	Touch screen	Su et al. 2010			Poppinga et al. 2011; Yatani et al. 2012

Immobile

Inspection of Table

Acknowledgments

This work was partially supported by the French National Research Agency (ANR) through TecSan program (project NAVIG ANR-08TECS-011) and the Midi-Pyrénées region through APRRTT program. We also thank the Institut des Jeunes Aveugles, Toulouse, for great help during the different steps of the participatory design.


Anke M Brock
email: anke.brock@irit.fr

Slim Kammoun
email: slim.kammoun@irit.fr

Hugo Nicolau

Tiago Guerreiro

Shaun K Kane
email: skane@umbc.edu

Christophe Jouffrais
email: christophe.jouffrais@irit.fr

Keywords: NVI (Non-Visual Interaction) Non-visual interaction, eyes-free interaction, visual impairment, situational impairment, accessibility, haptic, audio, thermal, gestural interaction. ACM Classification H.5.2. [Information Interfaces and Presentation]: User Interfaces, K.4.2. [Computers and Society]: Social

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

Introduction

In a recent fact sheet, the WHO reports that 285 million people are visually impaired worldwide [START_REF] Who | Visual Impairment and blindness Fact Sheet N° 282[END_REF]. Improving access to information and technology for visually impaired people is thus a significant challenge for HCI researchers and practitioners. While non-visual interfaces have traditionally targeted blind users, eyesfree interaction is increasingly becoming common across a wide range of contexts, such as for situationally impaired mobile device users [START_REF] Goel | WalkType: using accelerometer data to accomodate situational impairments in mobile touch screen text entry[END_REF][START_REF] Heuten | Tactile wayfinder: A non-visual support system for wayfinding[END_REF]. Motivations for eyes-free interaction include environmental, social, device related and personal factors [START_REF] Yi | Exploring user motivations for eyes-free interaction on mobile devices[END_REF]. We believe that it would be beneficial for all researchers in the field to work together more tightly, as challenges for non-visual interaction (NVI) seem to overlap regardless of users' abilities.

Non-visual interaction techniques typically leverage modalities such as haptics [START_REF] Kammoun | Guiding Blind People with Haptic Feedback[END_REF] and audio [START_REF] Mynatt | Transforming Graphical Interfaces Into Auditory Interfaces for Blind Users[END_REF][START_REF] Zhao | Data Sonification for Users with Visual Impairment[END_REF], and feature applications such as internet browsing [START_REF] Asakawa | What's the web like if you can't see it?[END_REF], text entry [START_REF] Oliveira | Blind people and mobile touch-based text-entry[END_REF], indoor and outdoor navigation [START_REF] Azenkot | Smartphone haptic feedback for nonvisual wayfinding[END_REF][START_REF] Kammoun | Guiding Blind People with Haptic Feedback[END_REF], maps exploration [START_REF] Brock | Design and User Satisfaction of Interactive Maps for Visually Impaired People[END_REF][START_REF] Jacobson | Navigating maps with little or no sight: An audio-tactile approach[END_REF], games [START_REF] Trewin | Exploring Visual and Motor Accessibility in Navigating a Virtual World[END_REF], crowd-based Q&A [START_REF] Bigham | Nearly real-time answers to visual questions[END_REF], and even photography [START_REF] Jayant | Supporting blind photography[END_REF]. This SIG aims to discuss the challenges of NVI as a whole; that is, connecting the accessibility community with other NVI researchers. In fact, one of the current research challenges is in finding out whether the problems encountered by visually-impaired people are similar to those of sighted users whilst situationally impaired. Other challenges are related to the paradigm shift from visual interfaces: when to provide NV interfaces? How to seemingly shift between modalities? How to perform traditional computational tasks without visual feedback in an efficient and effective way? How to keep the cognitive load to a minimum? Examples of tasks comprise menu navigation, text-input, exploration of large datasets (e.g. social network feeds), understanding visual representations (e.g. graphics, maps), and so forth. Other challenges may arise when using specific modalities such as eyes-free gestural interaction on touch screens [START_REF] Kane | Access Overlays: Improving Non-Visual Access to Large Touch Screens for Blind Users[END_REF][START_REF] Mcgookin | Investigating touchscreen accessibility for people with visual impairments[END_REF], which can be improved by haptic feedback [START_REF] Bau | Tactile Feedback Technology for Augmented Reality[END_REF].

Much work on non-visual HCI has come from the accessibility community. Several international conferences address accessibility issues (e.g., the ACM SIGACCESS Conference on Computers and Accessibility, the International Conference on Computers Helping People with Special Needs, and the International Cross-Disciplinary Conference on Web Accessibility). However, these conferences focus broadly on accessibility issues, and do not specifically focus on non-visual interaction or HCI. The IEEE World Haptics and Eurohaptics Conferences specifically focus on haptic interaction. Other conferences, such as MobileHCI, address NVI in mobile contexts, but only feature a subset of the broader community.

We believe that CHI is the ideal venue for bringing together the community exploring NVI, for the following reasons. First, NVI for visually impaired and sighted users is of interest to the CHI community. CHI 2012 comprised a paper session entitled "Supporting visually impaired users," and has featured papers on NVI for both visually impaired and sighted users. Second, CHI is a regularly-occurring and global event. Third, CHI is a multidisciplinary conference that attracts practitioners with a variety of backgrounds, which may play an important role in this transversal field. Finally, since CHI is not focused exclusively on accessibility, it provides the opportunity to connect accessibility researchers with other NVI researchers. Given the prevalence of visual interaction and the relative obscurity of NVI, technical disruption may be required to improve NVI, and a CHI SIG provides a rich environment for creating such disruption.

Invited Participants

Our aim is to bring together and reinforce the community of researchers and practitioners working on non-visual interaction for people of all abilities. This includes interaction for visually impaired people, as well as NVI for sighted people. We hope to create new synergies and identify future challenges.

We plan to invite known members of the community personally by mail, including visually impaired researchers. Furthermore, we will create a Facebook event and website for advertising the SIG. The SIG event will be open to all. Those who wish to present during the session will be asked to send in a short description of their main research areas before the conference.

Schedule of this SIG CHI Meeting

The aim of this SIG is to discuss how to create and maintain the community of NVI, and to identify future research challenges and directions. The SIG will be most relevant to researchers, practitioners or people interested in the field of NVI. We think that by working together we can connect technologies and ideas to identify the opportunities and challenges towards more accessible and usable interactions.

The organization and schedule of this SIG will be as follows:

 5 minutes: introduction to the SIG, presentation of the objectives and schedule.



10 minutes: moderators will give a brief presentation in order to give an overview of the field and introduce the discussion topics



Brainstorming session (50 min): if less than 20 participants, attendees present themselves. Groups of participants based on a selection of shared interests will be created. Moderators will structure the ideas according to different discussion topics (sensory modalities, specific user groups, type of application, etc.). Groups will be encouraged (but not required) to discuss three primary questions, developed by the organizers:

1. Do we want to create an official community and how can we keep this community alive? Do we want to create sub communities (e.g., for projects addressing visually impaired people, or haptic interaction) or do we want to unite the whole NVI community? (15 minutes) 2. Which are the future challenges that we expect in our field and how can we face them? (20 minutes)

3. Do we want to organize a workshop for CHI 2014? (15 minutes)  15 minutes: Working groups report back; summary of the event and next steps.

Post-CHI Activities

After CHI, we will sum up the discussion and share the results with the broader community via publication (e.g., on the SIGACCESS newsletter or ACM Interactions). We will also follow up on a discussion board, which will be used to plan activities for this community in 2014 and beyond. Our aim is to implement a regular meeting of community members at venues such as CHI and ASSETS. An additional objective is the organization of a workshop on NVI for CHI 2014.


Hafiz Ahmed
email: hafiz.ahmed@inria.fr.

Rosane Ushirobira
email: rosane.ushirobira@inria.fr.

Denis Efimov
email: de-nis.efimov@inria.fr.

Damien Tran
email: d.tran@epoc.u-bordeaux1.fr

Mohamedou Sow

Pierre Ciret

Jean-Charles Massabuau
email: jc.massabuau@epoc.u-bordeaux1.fr

Monitoring biological rhythms through the dynamic model identification of an oyster population

Keywords: Dynamic Model, Ecological Monitoring, Oyster Population, System Identification, Circadian Rhythm Modeling, Bioindicator

The measurements of valve activity in a population of bivalves under natural environmental conditions (16 oysters in the Bay of Arcachon, France) are used for a physiological model identification. A nonlinear auto-regressive exogenous (NARX) model is designed and tested. The method to design the model has two parts. 1) Structure of the model: The model takes into account the influence of environmental conditions using measurements of the sunlight intensity, the moonlight, tide levels, precipitation and water salinity levels. A possible influence of the internal circadian/circatidal clocks is also analyzed. 2) Least square calculation of the model parameters. Through this study, it is demonstrated that the developed dynamical model of the oyster valve movement can be used for estimating normal physiological rhythms of permanently immersed oysters and can be considered for detecting perturbations of these rhythms due to changes in the water quality, i.e. for ecological monitoring.

I. INTRODUCTION

Since last century, the quality of our world's environment is changing swiftly causing significant changes in the marine water quality. For this reason, nowadays, local, regional and international legislation has strict laws and recommendations on the protection of aquatic environment against the disposal of harmful and dangerous substances 1 . In order to abide by these laws and recommendations for the protection of aquatic environment, a large scale monitoring of water quality is essential [START_REF] Mimendia | A review of the use of the potentiometric electronic tongue in the monitoring of environmental systems[END_REF]. However, the realization of such an extensive network of aquatic monitoring is very costly and technically challenging from an engineering point of view. Researchers and engineers are then working on an indirect monitoring of the aquatic environment from behavioral and physiological responses of representatives of the marine fauna [START_REF] Pandey | Morphological abnormalities in periphytic diatoms as a tool for biomonitoring of heavy metal pollution in a river[END_REF], [START_REF] Rose | Development and monte carlo analysis of an oyster bioaccumulation model applied to biomonitoring data[END_REF], [START_REF] Cabecinha | Performance of a stochasticdynamic modelling methodology for running waters ecological assessment[END_REF], [START_REF] Cabecinha | Applying a stochastic-dynamic methodology (stdm) to facilitate ecological monitoring of running waters, using selected trophic and taxonomic metrics as state variables[END_REF], [START_REF] Jorgensen | A general model for the heavy metal pollution of aquatic ecosystems: Model development[END_REF], [START_REF] James | Modelling pollution dispersion, the ecosystem and water quality in coastal waters: a review[END_REF]. Bio-indicators demonstrate high efficiency, for instance through bio-accumulation of contaminants/pollutants in their tissues 2 . Nevertheless, until now, large scale extensive aquatic monitoring does not seem viable and realistic as it involves intensive exploitation of human resources for the collection of samples, complex chemical analysis and so on [START_REF] Telfer | Review of environmental impact assessment and monitoring in aquaculture in europe and north america[END_REF]. A solution of the aforementioned problem is to develop unmanned autonomous systems using biosensors, able to work round the clock, at high frequency by remote control. As of today, networks of such online sensors, operating at large scale do not exist and are still a matter of research. To fulfill the objective just mentioned before, an installation of numerous online remote sensors is required, working at high frequency for instant collection of information on a daily basis in marine environment [START_REF] Kröger | Sensing the sea[END_REF]. Behavioral and physiological responses of wildlife to contamination are very sensitive and these responses can be used for an indirect monitoring of the aquatic environment [START_REF] Tlili | Assessment of the health status of donax trunculus from the gulf of tunis using integrative biomarker indices[END_REF]. However, a limiting factor today is that it requires high volumes of data , whose analysis needs appropriate mathematical analysis, running near real-time [START_REF] Galang | Real-time detection of water pollution using biosensors and live animal behaviour models[END_REF]. Other difficulties lie in the fact that animals may be heavily influenced by surrounding environment, group interactions and internal rhythms (e.g. feeding, breathing, spawning) [START_REF] Ahmed | Dynamical model identification of population of oysters for water quality monitoring[END_REF].

Observation of the opening and closing activities of bivalves is a possible way to evaluate their physiological behavior in reaction to their nearby water. The deviations from a considered normal behavior can be used for detection of a contaminant in surrounding water. Thus, our aim was to gain more insights into these reference natural conditions by focusing on biological rhythms of their valve activity in situ. The pioneer work that analyzes bivalve's activities through the record of their valve movements (e.g., valvometry) was realized by Marceau [START_REF] Marceau | Contraction of molluscan muscle[END_REF] with smoked glazed paper. Today, valvometers are commercially available 3 and are mainly based on the principle of electromagnetic induction, like the Mossel Monitor [START_REF] Kramer | The valve movement response of mussels: A tool in biological monitoring[END_REF] or the Dreissena Monitor [START_REF] Borcherding | The Zebra Mussel Dreissena Polymorpha: Ecology, Biological Monitoring and First Applications in the Water Quality Management[END_REF], [START_REF]Ten years of practical experience with the dreissena-monitor, a biological early warning system for continuous water quality monitoring[END_REF]. In recent years, the interest for modeling and estimation of behavior of marine animals directly in real marine conditions has intensively increased [START_REF] Robson | Mussels flexing their muscles: A new method for quantifying bivalve behavior[END_REF], [START_REF] Garcia-March | Shell gaping behavior of pinna nobilis l., 1758: Circadian and circalunar rhythms revealed by in situ monitoring[END_REF], [START_REF] Beyene | Validation of a quantitative method for estimating the indicator power of, diatoms for ecoregional river water quality assessment[END_REF].

A distinctive and remarkable monitoring solution has been realized in the EPOC CNRS UMR laboratory in Arcachon, France [START_REF] Tran | Estimation of potential and limits of bivalve closure response to detect contaminants: Application to cadmium[END_REF], [START_REF] Sow | Water quality assessment by means of hfni valvometry and high-frequency data modeling[END_REF], [START_REF] Schmitt | Statistical study of bivalve high frequency microclosing behavior: Scaling properties and shot noise analysis[END_REF], where a new framework for noninvasive valvometry has been developed and implemented successfully since 2006. The system can work under field condition for long period of time without in situ human intervention (> 1-2 years). No other system according to the best knowledge of the authors has operated for several years like this one even in the laboratory environment. The monitoring solution was tested in the laboratory environment several years before deploying it into the sea. The designed method is strongly based on bivalve's respiratory physiology and ethology. The developed platform for valvometry was built using lightweight electrodes (approximately 100 mg each) linked by thin flexible wires to high-performance electronic units. The electrodes are capable to estimate the distance of opening of shell (see Fig. 1) for a mollusc with an accuracy of a few µm. Moreover, in the field, the energy consumption is very low, only 1 watt. One data point is generated every 0.1 sec (24 hours per day), for a bivalve, the electronic unit supports connection with 16 animals. Next, the results of measurements are transmitted by a wireless connection to the laboratory, the obtained data is publicly available online on the site of the project4 . This system allows the bivalves to be studied in their natural environment with minimal experimental constraints. The obtained arrays of data of opening and closing activities of bivalves were used for analysis from different points of view using statistical approaches (estimation of probability density functions for time and amplitude of opening) [START_REF] Tran | Estimation of potential and limits of bivalve closure response to detect contaminants: Application to cadmium[END_REF], [START_REF] Sow | Water quality assessment by means of hfni valvometry and high-frequency data modeling[END_REF], [START_REF] Schmitt | Statistical study of bivalve high frequency microclosing behavior: Scaling properties and shot noise analysis[END_REF].

Many researchers have studied the behavior of bivalves using valvometry and also through chemical analysis of the tissues of oysters. In [START_REF] Luna-Acosta | Persistent organic pollutants in a marine bivalve on the marennes-oléron bay and the gironde estuary (french atlantic coast)part 2: Potential biological effects[END_REF], [START_REF] Luna-Acosta | Persistent organic pollutants in a marine bivalve on the marennes-oleron bay and the gironde estuary (french atlantic coast)-part 1: Bioaccumulation[END_REF], authors have studied the impact of persistent organic pollutants on juvenile oysters through chemical analysis. They have shown that active biomonitoring is possible with juvenile oysters. In [START_REF] Palmer | Using oyster tissue toxicity as an indicator of disturbed environments[END_REF], authors have studied the tissues of oysters collected from various locations of southern Texas. They have concluded through chemical analysis that toxicity in the tissue can be used as an indicator for disturbed environment. Similar approach of using oysters as a biomonitoring tool through chemical analysis can also be found in [START_REF] Aguilar | American oyster (crassostrea virginica) and sediments as a coastal zone pollution monitor by heavy metals[END_REF]. However, chemical analysis is essential in all these cases.

In [START_REF] Englund | Valve movement of anodonta anatina and unio tumidus (bivalvia, unionidae) in a eutrophic lake[END_REF], authors have studied the valve activity behavior of two unionid mussel species in a eutrophic lake in southern Finland. Long term fluctuations in valve movements were observed and authors suggested that this fluctuations may be the reflection of the enrichment of pollutants in the mussels. In [START_REF] Ham | Effect of fluctuating low-level chlorine concentrations on valve-movement behavior of the asiatic clam (corbicula fluminea)[END_REF], Asiatic clams were exposed to waters receiving chlorine containing industrial discharges. It was shown that valves of the clams exposed to pollutants opened more often and for longer period than clams not exposed to pollutants. Comparison of valve movement activity of fresh water mussel between lake and river was done in [START_REF] Englund | Valve movement of the freshwater mussel anodonta anatina: a reciprocal transplant experiment between lake and river[END_REF]. It was shown that variability in valve opening is much higher in river than lake. So, it can be concluded from this whole dataset that valve opening activity may have a relation with the habitat of the bivalves.

Recently, the effect of a specific pollutant (i.e. Arsenic) on the valve opening activity in fresh water clam in laboratory environment was done in [START_REF] Chen | A real-time biomonitoring system to detect arsenic toxicity by valve movement in freshwater clam corbicula fluminea[END_REF], [START_REF] Jou | Synthesis and measurement of valve activities by an improved online clambased behavioral monitoring system[END_REF]. In this paper, authors have used statistical modeling approach (hill based dose response model [START_REF] Clayton | Statistical models in epidemiology[END_REF]) to see the effect of Arsenic on the valve opening activity by exposing the freshwater clams Corbicula fluminea to Arsenic contaminated water. In [START_REF] Englund | Valve movement of anodonta anatina and unio tumidus (bivalvia, unionidae) in a eutrophic lake[END_REF], it was shown that valve opening behavior is significantly different in their natural habitat than laboratory environment. This limits the scope of the results obtained in [START_REF] Chen | A real-time biomonitoring system to detect arsenic toxicity by valve movement in freshwater clam corbicula fluminea[END_REF]. We propose here to develop an indirect monitoring system which is pollutants independent and also deals with natural habitat (i.e. the sea) through rhythmicity identification of an oyster population.

For that purpose, the goal of the present study is the identification of a physiological dynamical model of nonlinear autoregressive exogenous (NARX) type for bivalves using a high volume of data (12.63 Gigabytes). The data came from a population of 16 oysters living in the Bay of Arcachon, France. The model takes into account the influence of external forces (like the sunlight and the moonlight, the tide level, precipitation, water salinity level). Since the behavior of oysters is also guided by internal circadian/circatidal rhythms, their influence is also incorporated in the developed NARX model. The type and the origin of internal circadian/circatidal rhythms of bivalves is rather uncertain, that is why a side result of the present study consists in verifying different hypotheses for modeling of circadian/circatidal rhythms for oysters. The proposed model is of Grey-box type [START_REF] Wu | A gray model with a time varying weighted generating operator[END_REF].

The outline of the paper is as follows. A brief description of the measurement scheme and experiments is given in Section 2 (a more detailed information can be found in [START_REF] Tran | Estimation of potential and limits of bivalve closure response to detect contaminants: Application to cadmium[END_REF], [START_REF] Sow | Water quality assessment by means of hfni valvometry and high-frequency data modeling[END_REF], [START_REF] Schmitt | Statistical study of bivalve high frequency microclosing behavior: Scaling properties and shot noise analysis[END_REF]). The model identification procedure is presented in Section 3. The verification of the model and its utility for an ecological monitoring of water quality are discussed in Section 4.

II. MEASUREMENT SYSTEM DESCRIPTION

The monitoring site is situated in the Bay of Arcachon, France, at the Eyrac pier (Latitude: 44 • 40 N, Longitude: 1 • 10 W). The map of the location can be seen in Fig. 2. Sixteen Pacific oysters, Crassostrea gigas, measuring from 8 cm to 10 cm in length were permanently installed on this site. These oysters were all from the same age group (1.5 years old) and came from the same local supplier. They also all grew in the Bay of Arcachon. They were submerged on the sea bottom (at 3 m to 7 m deep in the water, depending on the tide activity).

The principle of the total measurement process including electronic equipment has been first described in [START_REF] Tran | Estimation of potential and limits of bivalve closure response to detect contaminants: Application to cadmium[END_REF]. The measurement system was further modified (adjusted to severe open ocean conditions and mainly mechanical not electronic) later on in [START_REF] Chambon | Influence of the parasite worm polydora sp. on the behaviour of the oyster crassostrea gigas: A study of the respiratory impact and associated oxidative stress[END_REF], [START_REF] Tran | Field chronobiology in molluscan bivalves: How moon and sun cycles interactions deeply drive oyster activity rhythms[END_REF]. A significant advantage of the developed monitoring system (slave unit in the field) is that it is completely autonomous without in situ human interference for one full year. Each animal is equipped with two lightweight coils (sensors), ≈ 100 mg each, attached on the edge of each valve. These coils measure 2.5 × 2.5 × 2 mm and were coated with a resin sealing before attaching them on the valves. One of the coils sends a highfrequency sinusoidal signal, that is received by another coil. Measurements are performed every 0.1 sec successively (with the frequency 10 Hz) for each of the sixteen animals. This means that the behavior of a particular oyster is measured every 1.6 sec. Every day, 54000 triplets (1 distance, 1 stamped time value, 1 animal number) are collected for each oyster. The strength of the electric field produced between the two coils can be written as [START_REF] Sow | Water quality assessment by means of hfni valvometry and high-frequency data modeling[END_REF]:

E ∝ 1 y ( 1
)
where E is the strength of the electric field and y is distance between the point of measurement and the center of the transmitting coil. Equation (1) leads to estimation of the distance between coils. The measured signal (D mv in millivolts) is converted into distance in millimeters (D mm ) using the following calibration model [START_REF] Sow | Water quality assessment by means of hfni valvometry and high-frequency data modeling[END_REF] Dmv = 151

Dmm 0.35 -1.48 (2)
The distance being estimated can be seen in Fig. 1.

On the shore, a second electronic unit takes care the data acquisition and transmission. This unit is equipped with a GSM/GPRS modem and uses Linux operating system for driving the first control unit submerged in the water, managing the data storage with a time stamp, accessing the Internet, and transferring the data. An original self-developed software module runs on mobile phone technology. At the end of a working day, the collected data is transmitted to a central workstation server (the master unit) located in the Marine Station at Arcachon, France. The valve activity data is stored in a central database and the access to this database is provided via an Internet connection (under some restrictions on the amount of data). A schematic description of the monitoring system is presented in Fig. 3. The collected tidal data includes a measurement of the height of the water column every hour, while the times and levels of low and high tides are provided by the hydrographic and oceanographic service of the marine 5 . To take into account the nycthemeral rhythm of the bivalve, the sun and the moon positions at the sampling site have been used [START_REF] Ahmed | Velocity estimation of valve movement in oysters for water quality surveillance[END_REF], [START_REF] Ahmed | Automatic spawning detection in oysters: a fault detection approach[END_REF].

It is worth to note that data losses in transmission were sometimes observed due to impairment of data transfer.

III. MODEL IDENTIFICATION

Summarizing the description given in the previous section, after a specified duration of the experiment, the electronic system provides a matrix of values of opening of valves for each oyster P i,j for 1 ≤ i ≤ N, 1 ≤ j ≤ n, where n = 16 is the number of oysters in the experiment and N is the number of measured points, N = 54000 * N days with N days > 0 is the number of days used for the identification of the model. The actual valve distance is given in millimeters (mm) and the range is between 0 to 12 mm. In our case, the data of 2007 collected at the Eyrac pier in Arcachon has been used. So, N days = 365. For the population i.e. for 16 oysters, the measurement system gave us total 315.36 million data points. In addition to the valve distance, the values S i , M i , W i are also provided for 1 ≤ i ≤ N , they characterize the sun and moon positions with respect to the horizon in degrees and the tide levels in meters respectively. The signals S i and M i take negative values for the corresponding positions below the horizon line. Besides the three periodic signals (i.e. S i , M i , W i ), information regarding rain profile (i.e. precipitation) and water salinity level were also provided on a hourly basis and denoted as r i and i respectively for 1 ≤ i ≤ 24 * N days . The valve opening data P i,j being used in our current work differs from that of our previous work [START_REF] Ahmed | Dynamical model identification of population of oysters for water quality monitoring[END_REF]. In [START_REF] Ahmed | Dynamical model identification of population of oysters for water quality monitoring[END_REF], we considered the opening/closing of valve based on threshold. Based on a selected threshold, the opening of the valve (in percentage) during one hour was calculated for our previous work. This clearly distinguishes our current work with that of previous one since here we consider the actual distance instead of using any threshold to determine the relative activity of an oyster. Moreover, precipitation and water salinity level information are also being considered in our current work for the model identification which were not used in our previous work [START_REF] Ahmed | Dynamical model identification of population of oysters for water quality monitoring[END_REF].

The first problem that arises while dealing with the valve distance data is that its length is not uniform all through the year. Like almost every other animal, the size of oysters also changes as time passes by. We need to normalize the data between certain bound so that the effect of change of length of distance can be compensated. The normalization was done considering a 6 days window and with a bound [0, 1], where 0 represents complete closing of the valve while 1 represents complete opening of the valve. The formula to calculate the normalized value is:

pi,j = Pi,j -mina=i-N t ,••• ,i(Pa,j ) maxa=i-N t ,••• ,i(Pa,j ) -mina=i-N t ,••• ,i(Pa,j ) (3)
where Nt is the total number of data points in last 6 days, Pi,j is the actual valve distance and pi,j is the normalized valve distance [START_REF] Ahmed | A fault detection method for automatic detection of spawning in oysters[END_REF]. The next question that arises is how to use the data of 16 different oysters for the model identification of the population. The normalized valve distance of three different oysters can be seen in Fig. 4. From this figure, it can be observed that although the behavior of all these oysters are not exactly the same but the correlation between the behaviors is also not that weak 6 . So, averaging the behavior of all oysters can be a good way to capture the dynamics of the population. Since N ≈ 2 × 10 7 , to simplify the computation and the presentation in this study, the measurements have been averaged on hourly basis i.e. define δN = 3600[sec] 1.6[sec] = 2250 and L = N δN , then for all 1 ≤ j ≤ n:

p k,j = δN -1 kδN q=(k-1)δN +1 P q,j , s k = δN -1 kδN q=(k-1)δN +1 S q , (4)
m k = δN -1 kδN q=(k-1)δN +1 M q , w k = δN -1 kδN q=(k-1)δN +1 W q ,
corresponds to hourly averaged opening of the valves, the sun and moon positions, the water level respectively. The examples of obtained signal s k , m k and w k are shown in Fig. 5a. In Fig. 5b, the frequency spectrum of these periodic/quasi periodic 6 The correlation coefficient of oyster 1 with respect to oyster 2,3,..., [START_REF]Ten years of practical experience with the dreissena-monitor, a biological early warning system for continuous water quality monitoring[END_REF] signals can be seen. Finally, precipitation and water salinity level information are shown in Fig. 6.

The averaged opening position of valves, on an hourly basis, for the investigated population of oysters can be defined as:

h k = n -1 n j=1 p k,j (5)
The averaged valve opening of the population h k can be seen in Fig. 7.

From the plot, it can be easily inferred that the opening average of valves on hourly basis for the population h k has a more regular and smoother behavior than individual ones. This behavior leads us to consider the signal h k as a suitable choice for forthcoming analysis and model identification. Thus an averaged physiological population dynamics has to be modeled and identified for oysters. An additional motivation for this choice is standard in modeling biological systems: each individual exhibits a proper variability according to stochastic exogenous and endogenous forces, which are hard to predict or measure, while averaged signal h k is less sensitive to these perturbations and represents mainly the regular physiological behavior of the animals. Naturally, this is especially true if the population size n is big (this is not the case in the considered application due to various experimental complexities forcing us to limit the population size to 16). Another alternative to averaging can be using population models similar to what is developed to characterize the effect of drug treatments [START_REF] Zhusubaliyev | Nonlinear dynamics in closed-loop anesthesia: Pharmacokinetic/pharmacodynamic model under pid-feedback[END_REF], [START_REF]Bifurcation analysis of pid-controlled neuromuscular blockade in closed-loop anesthesia[END_REF]. However, those models require larger population size and heterogeneity among the animals. In our case, the population size is very small. Moreover, the oysters are not very heterogeneous. They all are of same age group (1.5 years), collected from the same local supplier and were raised in the same place (bay of Arcachon). Also, the correlation among the oysters is not weak as well. All the inputs of our model (water salinity, water level etc.) were also available on an hourly basis. Thus, hourly averaging is natural in our case.

It is known [START_REF] Tran | Field chronobiology in molluscan bivalves: How moon and sun cycles interactions deeply drive oyster activity rhythms[END_REF] that the opening activity of oysters h k is externally governed by the sunlight, moon oscillations and the tide activity, denoted here by s k , m k and w k respectively. Moreover, precipitation (r k ) and the salinity level in the water ( k ) may also have an external impact on the opening activity of oysters. Other sources of rhythmicity are internal (feeding, breathing etc.) and supervised by internal clocks. The reference signal generated by circadian rhythm genetics, which is directly influencing h k , will be denoted by c k . The generic structure of a dynamical physiological model for population of oysters can be presented as follows [START_REF] Ahmed | Dynamical model identification of population of oysters for water quality monitoring[END_REF] :

h k = F (h k-1 , . . . , h k-ν , s k , . . . s k-µ , (6)
m k , . . . m k-µ , w k , . . . w k-µ , r k , . . . r k-µ , k , . . . k-µ , c k , . . . c k-µ , θ) + k , c k = D(ξ k ), (7)
ξ k = G(ξ k-1 , s k , . . . s k-µ , m k , . . . m k-µ , w k , . . . w k-µ ),
where ν ≥ 0 represents the number of past events taken into account by the animals in order to determine the opening distance at the next time instant k (i.e. in this model k -1 is the current time instant and h k-1 is the current valve state); µ ≥ 0 is the number of previous values for the positions of sun/moon, tide levels, precipitation and water salinity levels that are used in the decision on the value of h k (the model ( 6) assumes that the instant values of s k , m k , r k , k and w k can be used for this decision); k ∈ R is the disturbance representing additional uncertain influencing forces and approximation errors (it is assumed that this term is sufficiently small if the model has been well identified); θ ∈ R q , q > 0 is the vector of constant parameters of the model ( 6), and F : R ν+6µ+6+q + → R + is a function defining the physiological model structure; ξ k ∈ R p is the state of the circadian oscillator [START_REF] James | Modelling pollution dispersion, the ecosystem and water quality in coastal waters: a review[END_REF]; the functions G : R p+3µ+3 → R p and D : R p → R define the structure of the circadian rhythm model [START_REF] James | Modelling pollution dispersion, the ecosystem and water quality in coastal waters: a review[END_REF]. The model [START_REF] James | Modelling pollution dispersion, the ecosystem and water quality in coastal waters: a review[END_REF] assumes that circadian oscillations are entrained by the external cues s k , m k and w k (some of them depending on the type of the rhythm under consideration, see below). The structure scheme of the model is given in Fig. 8.

The identification procedure consists in selecting an appropriate structure for the physiological model F (•) and the circadian model G(•), D(•), with posterior calculation of the corresponding vector of parameters θ.

Further in this section two problems are considered. First, the issue of circadian rhythms modeling is discussed and a solution 6), [START_REF] James | Modelling pollution dispersion, the ecosystem and water quality in coastal waters: a review[END_REF] is proposed. Second, an ARMAX structure is selected for F (•) and the corresponding model is designed.

A. Models of circadian clocks

A rhythm in chronobiology is a biological process that displays an endogenous and self-sustained oscillation with a period of about 24 hours, for instance the circadian rhythm. These rhythms are driven by an internal clock, i.e. by a biochemical embedded mechanism. Their main properties are the generation of periodic rhythms, endogeneity, adaptability to a local environment by external forces called zeitgebers (the most important one being daylight for terrestrial animals), and robustness over a range of physiological temperatures. Rhythms have been observed in almost all forms of living organisms, from cyanobacteria and plants to mammals. The science of biological temporal rhythms, such as solar and lunar related rhythms, is called chronobiology [START_REF] Naylor | Chronobiology of marine organisms[END_REF] [START_REF] Dunlap | Chronobiology: biological timekeeping[END_REF].

1) Hypothesis on clocks: There exist many mathematical models of clocks mechanisms [START_REF] Klerman | On mathematical modeling of circadian rhythms, performance, and alertness[END_REF], [START_REF] Smolen | A reduced model clarifies the role of feedback loops and time delays in the drosophila circadian oscillator[END_REF], [START_REF] Goldbeter | Computational approaches to cellular rhythms[END_REF], [START_REF] Ahmed | On robustness of phase resetting to cell division under entrainment[END_REF]. Different hypothesis on the nature of clocks presented in oysters [START_REF] Tran | Field chronobiology in molluscan bivalves: How moon and sun cycles interactions deeply drive oyster activity rhythms[END_REF] have been issued, but not yet supported by a mathematical model. First, as many animals, the oysters may have circadian oscillations with the period of 24 hours synchronized by sunlight (i.e. circadian clock). Second, as animals living in a tidal ecosystem, they may also have a second rhythm with the period 12.4 hours and entrained by tides, which may be driven by a circatidal clock. Third, the oyster rhythms may be regulated by the moon with the period 24.8 hours under the control of circalunidian clocks. The diversity of hypothesis follows the variety of habitation areas of bivalves, e.g. arctic zones (where the sunlight may have approximately constant intensity during several months), open ocean conditions with strong tides or Mediterranean bays, where tides are almost negligible. Finally, this motivates the fourth hypothesis: a unique "circadian/circatidal" clock, synchronized by sunlight and tides, generating a bimodal rhythm running from 12.4 to 24.8 hours depending on the local biotope conditions. Among several different cases regarding the nature of the circadian clock, we have considered two hypothesis in our current work, namely:

1) Hypothesis 1 (H1): The rhythm of the oysters is governed mostly by a circadian clock in response to sunlight. 2) Hypothesis 2 (H2): The rhythm of the oysters is governed mostly by a circatidal clock and a circadian clock in response to the tide level and sunlight simultaneously.

The structure scheme of the model for the two different hypothesis is given in Fig. 9. Based on these two hypothesis, the corresponding mathematical models are developed below. Conventional models of oscillators [START_REF] Klerman | On mathematical modeling of circadian rhythms, performance, and alertness[END_REF], [START_REF] Smolen | A reduced model clarifies the role of feedback loops and time delays in the drosophila circadian oscillator[END_REF], [START_REF] Goldbeter | Computational approaches to cellular rhythms[END_REF] have different complexity. There exist also methods to design generic oscillating systems [START_REF] Efimov | Yakubovich's oscillatority of circadian oscillations models[END_REF] of any complexity. However, as it was observed in [START_REF] Forger | Reconciling mathematical models of biological clocks by averaging on approximate manifolds[END_REF], [START_REF] Efimov | Controlling the phase of an oscillator: a phase response curve approach[END_REF] any oscillating system on the limit cycle can be fully characterized by its current phase and the form of limit cycle (i.e. amplitude of oscillations). Therefore, if an exact genetic or biochemical nature of oyster oscillations is not clear, then in order to preserve the model simplicity, the oyster rhythm can be represented by any oscillator, and a particular attention has to be paid to a relation of the phase of this oscillator and environmental rhythms. In [START_REF] Antle | Gates and oscillators: a network model of the brain clock[END_REF], [START_REF] Forger | Reconciling mathematical models of biological clocks by averaging on approximate manifolds[END_REF] variants of Van der Pol oscillator [START_REF] Kanamaru | Van der pol oscillator[END_REF] have been used for modelization of circadian rhythms for different animals. Van der Pol oscillator has a simple planar mathematical model with just two parameters that allows the form of the limit cycle and the period of oscillations to be tuned:

ξ1 = α ξ 2 + µ ξ 1 - 4 3 ξ 3 1 + u , ξ2 = -αξ 1 , (8)
where ξ 1 ∈ R and ξ 2 ∈ R are the model states, α > 0 determines the model oscillation velocity (adjustment of this parameter regulates the period of oscillation for the model); µ > 0 is a parameter to determine the shape of oscillations (µ ≈ 0 for almost harmonic oscillations, µ ≥ 2 leads to a nonlinear profile); u ∈ R is the model input that can be used for the entrainment. In our case the parameter α has to be selected in order to ensure the period of oscillations of 24 hours for the first hypothesis and for the third one, for instance. The form of oscillations on the limit cycle, i.e. the value of parameter µ, is less important since in the model ( 6), [START_REF] James | Modelling pollution dispersion, the ecosystem and water quality in coastal waters: a review[END_REF] the shape of c k can be taken into account later in the function F (•) and by tuning the parameters θ (the value µ = 2 is used in this work for all computations). Therefore, the functions G(•) and D(•) in ( 7) can be defined based on Van der Pol equations discretized using the Euler method:

ξ 1,k = ξ 1,k-1 + T α ξ 2,k-1 + µ ξ 1,k-1 - 4 3 ξ 3 1,k-1 + u k , ξ 2,k = ξ 2,k-1 -T αξ 1,k-1 , c k = max{0, ξ 1,k }, (9)
where T = 1 hour is the sampling time, c k is the positive part of ξ 1 and u k is the resetting input, which has to be specified. The entrainment regulates the phase of oscillations (synchronizes the exogenous cues and endogenous rhythms), the mechanism of entrainment and phase resetting can be well analyzed using the Phase Response Curve approach [START_REF] Efimov | Controlling the phase of an oscillator: a phase response curve approach[END_REF], [START_REF] Efimov | Phase resetting control based on direct phase response curve[END_REF]. For example, for the first hypothesis we select u k = ρ max{0, s k }/ max 1≤k≤L |s k |, where ρ > 0 is the scaling parameters that is selected in order to harmonize the amplitude of the input u k and the dimension of the limit cycle. The selection max{0, s k } is applied since for the oyster rhythm the daylight is the principal zeitgeber, and the light is emitted when the sun is above the horizon only. For the first hypothesis, u k = s k , is the position of the sun. While for the second hypothesis, u k has the following form:

u k = [λ s λ w ] [s k w k ] T (10)
where λ s and λ w are the weights regulating the influence of sun position s k and tide level w k on the circadian oscillation.

For the second hypothesis, in addition to the sunlight, we have also tide/water level as zeitgeber. In order to harmonize the amplitude of the water level, we have selected w k as w k = ρw k / max 1≤k≤L |w k |.

To generate the signal c k using the proposed model it is necessary to properly assign the initial phase for the oyster clock model (initial position on the limit cycle), which has to be coordinated with the current zeitgebers activity. A possible solution is to apply to the model the input patterns extracted from the first month of the experiment (or the last one in our case, since the experiment duration is 1 year and the inputs-sun position, moon position and the tide level have annual periodicity) several times in order to entrain the oscillator.

B. ARMAX model

The ARMAX (auto-regressive-moving-average with exogenous inputs) model is one of the most popular structures used for identification in various fields of science [START_REF] Walter | Identification of parametric models[END_REF], [START_REF] Nelles | Nonlinear System Identification[END_REF], [START_REF] Ljung | System identification[END_REF]. Its advantages include linearity with respect to all signals and parameters, different effective methods for calculation of the parameters, simplicity of stability analysis of the obtained model, robustness and sensitivity with respect to perturbations. Therefore, the function F (•) in ( 6) is selected in the following form: have considered three different situations. First, in case 1, we assumed that both inputs have equal weights i.e. λ s = λ w = 0.5. Second, in case 2, more weights on tide level were considered (λ w = 0.75, λ s = 0.25). Finally, in case 3, more weights on sunlight were imposed (λ w = 0.25, λ s = 0.75). The impact of these three cases on oysters can be seen in Fig. 11. From this figure, it can be seen that the performance of the model based on equal weights has better performance than the other two cases. Following this observation, we have considered equal weights on both sunlight and tide level for further analysis & verification.

B. Verification

To evaluate the obtained accuracy of the designed model two performance costs J and J p have been calculated. The cost J estimates the average amplitude of k (the approximation errors in the model): j = h j+ν -ĥj+ν , ĥj+ν = Φ T j θ, 1 ≤ j ≤ L-ν and The cost J p evaluates the prediction quality of the model on an infinite time interval: e j = h j+ν -hj+ν , 1 ≤ j ≤ L -ν and

J = L-ν j=1 2 j L -ν .
J p = L-ν j=1 e 2 j L -ν where hk = h k , 1 ≤ k ≤ ν, hν+j = ν i=1 θ h i hν+j-i + µ z=0 θ s i sν+j-z + µ z=0 θ m i mν+j-z + µ z=0 θ w i w ν+j-z + µ z=0 θ r i r ν+j-z + µ z=0 θ i ν+j-z + µ z=0 θ c i c ν+j-z , 1 ≤ j ≤ L -ν
are the estimates of the valve positions h k generated independently by the designed model in the presence of the same inputs.

Examples of the obtained estimates ĥk and hk (for ν = µ = 72, i.e. the oysters have 3 days of memory) for the second hypothesis are shown in Fig. 12, with performance costs J = 0.08 and J p = 0.19. We conclude from this example that the model demonstrates a sufficiently good accuracy of representation of the physiological behavior of oysters.

C. Application to ecological monitoring

As it has been noted in the Introduction, ecological monitoring is in some part expensive and invasive of the environment under study (an extensive or poorly planned monitoring carries a risk of environmental degradation). This fact may be critical in wilderness areas or those that are averse to human presence. Some monitoring techniques may be very damaging, at least to the local population and can also degrade public trust in scientists carrying out the monitoring. That is why remote sensing and mathematical modeling become very important. Obviously, the application of a far-reaching mathematical modeling can reduce the cost of monitoring, while improving its safety and accuracy. The area of population of bivalves is rather large, and the developed physiological model can serve for water quality monitoring, if we would compare the real measurements h k obtained by an embedded electronic unit on a bay and the estimates provided by the model hk . For example, the following daily monitoring residual can be computed:

r k = 1 24 23 z=0 |h k-z -hk-z | (13)
for all 24 ≤ k ≤ L, where an averaging on 24 hours is used in order to decrease sensitivity of the residual with respect to measurement noises. For the dataset collected at the Eyrac pier in 2007, the obtained residual r k is shown in Fig. 13. It is worth to stress that the Eyrac pier in the Bay of Arcachon is located in a fairly clean and well-protected area, but as we can see, the residual presented a peek value at the beginning of the December 2007. In fault detection literature [START_REF] Chanthery | Fault isolation on request based on decentralized residual generation[END_REF], [START_REF] Wang | Fd4c: Automatic fault diagnosis framework for web applications in cloud computing[END_REF], [START_REF] Ren | Fault diagnosis and tolerant control for discrete stochastic distribution collaborative control systems[END_REF], [START_REF] Vasu | Mvem-based fault diagnosis of automotive engines using dempster -shafer theory and multiple hypotheses testing[END_REF], the peak is known as fault (i.e. deviation from normal behavior). So, the detection of this fault is equivalent to the detection of pollution. The peak actually corresponds to a time period of heavy rain. Since the output of a storm sewer is located at about 10-15 meters from the oysters and as there was no change of salinity at that precise time (Fig. 6 bottom), we suggest that some unknown contaminant, washed by the rain, could have reach them. This simple case study justifies the utility of the developed approach in automated systems tracking silent pollution.

V. CONCLUSION

The paper presents the first development of a dynamical physiological model for oysters, which takes into account an influence of external cycles (daylight, moonlight and tides), externally influencing factors (like precipitation and water salinity level) and internal clocks as well. A generic "black-box" modeling approach has been used, and NARX structure of the model has been selected. It properly fits with the idea that the clock mechanism in oysters is drive by tide and sunlight simultaneously. The obtained model has been successfully applied for automatically and fast detecting an abnormal deviation of behavior which occurred following a rainy period in Arcachon, France.

A limitation of this work lies in the fact that it can not highlight/isolate the source of abnormalities. Moreover, there are abnormalities which are not related to pollution. One example is spawning i.e., the behaviour of the female oysters during reproduction [START_REF] Ahmed | A fault detection method for automatic detection of spawning in oysters[END_REF]. So, to determine the origin of the abnormalities could be considered for future work. One way of dealing this problem would be to observe the behaviour of oysters in response to various kinds of pollutants in the laboratory environment.

Figure 1 .

 1 Figure 1. Graphical representation of the distance being estimated by the electrodes

Figure 2 .

 2 Figure 2. Location map (Courtesy of Google Maps), see also http:// molluscan-eye.epoc.u-bordeaux1.fr/

Figure 3 .

 3 Figure 3. [22] Synoptic representation of the system, from field to laboratory: (1) Oyster equipped with two electrodes and 1st level electronic card in a waterproof case (immersed); (2) electrical connection between the first and the second electronic cards (umbilical); (3) 2nd level electronic card out of water; (4) GPRS antennae (5) GPRS and Internet connection; (6) Marine Station of Arcachon (Master unit) ready for daily update and for feeding internet (Google: molluscan eye); (7) daily update on internet for the general public (restricted access) and professionals (full access).

Figure 4 .

 4 Figure 4. Examples of normalized valve distance of three oysters during 10 days (sampling period, Ts = 1.6 sec.)

Figure 5

 5 Figure 5. a) Sun and moon position, tide level (left column-original signal, right column-zoomed version) during a whole year (2007) b) Frequency spectrum of the signals.

Figure 6 .Figure 7 .

 67 Figure 6. Precipitation (top) and water salinity level (bottom) during the year 2007 (one data point each day)

Figure 8 .

 8 Figure 8. Structure scheme of the generic model (6),[START_REF] James | Modelling pollution dispersion, the ecosystem and water quality in coastal waters: a review[END_REF]

Figure 9 .

 9 Figure 9. Structure scheme of the model for H1 and H2

Figure 10 .Figure 11 .

 1011 Figure 10. Comparative performance of two different hypothesis based model with actual data

Figure 12 .

 12 Figure 12. The results of the model numerical verification

Figure 13 .

 13 Figure 13. Residual for water quality monitoring

  are 0.4474, 0.5651, 0.4811, 0.5335, 0.3739, 0.4824, 0.3504, 0.4654, 0.2446, 0.1083, 0.4606, 0.2378, -0.181 and 0.3871 respectively.

							Oyster no. 1
		1
		0.5
	Normalized valve distance	120 0 120 0 0.5 1	121 121	122 122	123 123	124 124	125 125 Oyster no. 7 Oyster no. 10	126 126	127 127	128 128	129 129	130 130
		1
		0.5
		120 0	121	122	123	124	125	126	127	128	129	130
						Days of the year 2007

For example, see the US Mussel Watch, http://ccma.nos.noaa.gov/about/ coast/nsandt/musselwatch.aspx.

http://www.mosselmonitor.nl/

http://molluscan-eye.epoc.u-bordeaux1.fr/

http://www.shom.fr/

Acknowledgment: The authors thank Ifremer Arcachon and Isabelle Auby for kindly providing precipitation and salinity data for the Eyrac pier, Bay of Arcachon, 2007.

Hafiz Ahmed is partially supported by the regional council of Nord Pas de Calais, France. This work was partially supported by the Government of Russian Federation (Grant 074-U01) and the Ministry of Education and Science of Russian Federation (Project 14.Z50.31.0031).

1 http://europa.eu/legislationsummaries/environment/ waterprotectionmanagement/l28017aen.htm; http://water.epa.gov/scitech/swguidance/standards/criteria/aqlife/index.cfm; http://frdc.com.au/environment/aquaticenvironment/Pages/default.aspx.

 [START_REF] Galang | Real-time detection of water pollution using biosensors and live animal behaviour models[END_REF]θ = [θ h 1 , . . . , θ h ν , θ s 0 , . . . , θ s µ , θ m 0 , . . . , θ m µ , θ w 0 , . . . , θ w µ , θ r 0 , . . . , θ r µ , θ µ , . . . , θ µ , θ c 0 , . . . , θ c µ ] T ,

where the positive values sk = max{0, s k } and mk = max{0, m k } of the signals s k and m k respectively are used to model an influence of the sunlight and moonlight (the sun and the moon are above the horizon and deliver the light when s k and m k are positive only). Formally the proposed function F (•) is nonlinear with respect to its arguments s k and m k (it contains max{•}). The nonlinear model under consideration including the effect of circadian clock has the NARX structure ( 6), [START_REF] James | Modelling pollution dispersion, the ecosystem and water quality in coastal waters: a review[END_REF] for the selected F (•) and G(•), D(•). A summary of NARX type model can be found in [START_REF] Siegelmann | Computational capabilities of recurrent narx neural networks[END_REF], [START_REF] Lu | Multiscale asymmetric orthogonal wavelet kernel for linear programming support vector learning and nonlinear dynamic systems identification[END_REF].

IV. HYPOTHESIS SELECTION, VERIFICATION AND ANALYSIS

Using the Least Square method [START_REF] Nelles | Nonlinear System Identification[END_REF], [START_REF] Ljung | System identification[END_REF], [START_REF] Walter | Identification of parametric models[END_REF], the estimates θ of the parameters θ have been calculated for the dataset collected at the Eyrac pier, the Bay of Arcachon, France, 2007:

where Υ = [h ν+1 , . . . h L ] T and the jth row of the matrix Φ, for all 1 ≤ j ≤ L -ν.

A. Hypothesis selection

In III-A1, we have considered two different hypothesis, namely H1 & H2. Performance comparison of models based on H1 and H2 with experimental data can be seen in Fig. 10. From these results, no definitive conclusion can be drawn regarding the superiority or inferiority of any individual hypothesis. Both of them are almost identical. We are working with oysters living in real-life situation i.e. in the sea, therefore oysters behaviors are influenced by a multitude of factors (and not only by the sun and moon position or water tide or precipitation or water salinity level). Hence, our suggestion in this case is that the effect of different cyclic inputs on oysters, like circadian clocks, might be better observed if we can place them in a controlled laboratory environment. In that case, we can experiment with individual inputs and will be able to observe the response of oysters to that input. However, in our current situation we think that the second hypothesis is more realistic than the first one as it involves both sunlight and tide at the same time. For marine animals, to consider the effect of tide along with sunlight on internal clocks is a very natural choice. So, for further analysis, we have selected the model based on hypothesis 2.

In hypothesis 2, the internal clock of oysters is influenced by sunlight and tide at the same time. So, a natural question is: what is the impact of individual inputs (sunlight and tide) on the behavior of oysters? To attempt to answer this question, we Hafiz Ahmed was born in Dhaka, Bangladesh. He obtained M.Sc. degree in system, control and information technology in 2013 from Joseph Fourier University, Grenoble, France. His M.Sc. thesis was done at the Electric Power Network team of Laboratory of Electrical Engineering and Power Electronics (L2EP), Lille. Since October, 2013 he is a PhD student at the Non-A team of Inria, Lille, France where he works on modelling and estimation of biological rhythms in oysters. His current research interests include modeling, identification, control and stability analysis of dynamical systems with application to environmental monitoring, system biology and renewable energy. He is a student member of IEEE and IEEE control system society. Mohamedou Sow is a research engineer at ADERA, an organism whose members are academics, engineers and entrepreneurs operating in the laboratories of the Aquitaine region. He is mathematician, statistician and member of the EA team at UMR CNRS 5805 EPOC. He studied at the Institute of Mathematics of Bordeaux where he obtained his Master 2 degree before defending, in 2011, his thesis on the development of nonparametric and robust models at the University Bordeaux 1. He is in charge of the development, the adaptation and the integration to the operational chain of all the codes used in our data production system. He is participating in the management of the material platform, which is the base of our system of production.

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