Jean-Louis Dessalles

Denis Phan
email: denis.phan@univ-rennes1.fr

Louis

Emergence in multi-agents systems : cognitive hierarchy, detection, and complexity reduction part 1: methological issues

Introduction

In a pioneering book on "artificial society" and multi-agent simulations in social sciences, (Gilbert and Conte 1995) put the emphasis on "emergence" as a key concept of such approach: "Emergence is one of the most interesting issues to have been addressed by computer scientists over the past few years and has also been a matter of concern in a number of other disciplines, from biology to political science" (op.cit. p.8). More recently, Agent based Computational Economics (ACE) put the emphasis on the question of emergence, following for instance (Tesfatsion 2002a) or [START_REF] Axtell | The Emergence of Classes in a Multi-agent Bargaining Model in[END_REF] The present paper provides a formal definition of emergence, operative in multi-agent framework designed by Agent Oriented Programming, and which makes sense from both a cognitive and an economics point of view. Starting with a discussion of the polysemous concept of emergence, the first part of this paper is dedicated to clarifying the question by focussing on the problem of modelling cognitive agents in artificial societies. The key questions are introduced by way of a paradigmatic example. The second part of this paper is dedicated to introducing and discussing operative definitions and related implications. In order to illustrate our formal definition of emergence, a companion paper [START_REF] Phan | Emergence in multi-agent systems: cognitive hierarchy, detection, and complexity reduction part II: Axtell, Epstein and Young's model of emergence revisited[END_REF] discusses the ACE population game model of [START_REF] Axtell | The Emergence of Classes in a Multi-agent Bargaining Model in[END_REF] and builds a multi-level-model based on the formal framework introduced in this paper.

From emergentism to emergent behaviour in ACE model

In this section, we first discuss different definitions of emergence, and the related background. In order to focus on the problem of modelling cognitive agents in artificial society, we next considering a paradigmatic example, and briefly discuss Schelling's model of spatial segregation [START_REF] Schelling | Models of Segregation[END_REF][START_REF] Schelling | Dynamic Models of Segregation[END_REF][START_REF] Schelling | The Construction of Social Reality[END_REF], which is a pioneering study of an emerging social phenomenon in social science.

Emergence: one word, several meanings

The notion of emergence has several meanings. In the vernacular language, emergence denotes both a gradual beginning or coming forth, or a sudden uprising or appearance; to emerge also means to become visible, in example, emergence denotes the act of rising out of a fluid. This latter sense is close to its Latin roots, where emergere is the opposite of mergere: to be submerged. In the following, we relate the "act of rising out" to the arising of some phenomenon in a process, and note the fact that to become visible presupposes some observer. In other words, the common sense of emergence is linked to the meaning of a process that produces some phenomenon that might be detected by an observer. In the field of science, emergence has been used by Newton in optics. By the 19th century the word "emergent" is introduced into the fields of biology and philosophy. In the latter, Emergentism has a long history, from Mill's chapter: "Of the Composition of Causes" in System of Logic (1843) to the contemporary debates about the philosophy of mind, known as "the mind -body problem". For a synthesis, see among others: [START_REF] Mclaughlin | The rise and fall of British emergentism[END_REF][START_REF] Mclaughlin | Emergence and supervenience[END_REF]; Van de Vijver, 1997; [START_REF] Emmeche | Explaining emergence-towards an ontology of levels[END_REF]). Philosophical emergentism deals with questions of both reductionism and holism. (Lewes 1874) for instance places emergence at the interface between levels of organisation. For descriptive emergentism, the properties of the "whole" cannot be defined by the properties of the parts, and results in part from some irreducible macro causal power.

In this debate around the definition of emergence, some authors have proposed to distinguish between different kinds of emergence, as for example "nominal", "weak" and "strong" emergence for [START_REF] Bedau | Weak Emergence[END_REF][START_REF] Bedau | Downward causation and the autonomy of weak emergence, Principia 6-1 June, special issue on Emergence and Downward Causation[END_REF], or "weak" "ontological", and "strong" emergence for (Gillet 2002a-b). Both authors refer to debates about reductionism as well as about the so-called mind-body problem, discussing in particular the notion of Supervenience, introduced by [START_REF] Davidson | Mental Events[END_REF][START_REF] Davidson | Actions and Events[END_REF] and discussed by [START_REF] Kampis | Self-Modifying Systems in Biology and Cognitive Science Pergamon 26[END_REF][START_REF] Kim | Supervenience and Mind[END_REF][START_REF] Kim | Emergent properties[END_REF][START_REF] Kim | Making sense of Emergence[END_REF] from the point of view of emergence. As "weak" emergence deals with upward causation and reductionism, Gillet and Bedeau relate "strong emergence" to the question of "downward causation" [START_REF] Kampis | Self-Modifying Systems in Biology and Cognitive Science Pergamon 26[END_REF][START_REF] Bedau | Downward causation and the autonomy of weak emergence, Principia 6-1 June, special issue on Emergence and Downward Causation[END_REF] or "macro-determinism", widely advocated by [START_REF] Sperry | A modified concept of consciousness[END_REF][START_REF] Sperry | Discussion: Macro-versus micro-determinism (A response to Klee)[END_REF][START_REF] Sperry | In defense of mentalism and emergent interaction[END_REF] to deal with the mind-brain interactions, and by [START_REF] Campbell | Downward causation, in hierarchically organized biological systems[END_REF]) to deal with hierarchically organized biological systems. According to strict downward causation, the behaviour of the parts (down) is determined by the behaviour of the whole (up). For instance, parts of the system may be restrained by some act in conformity with rules given at the system level. Causation would come "downward" in conformity with a holist principle rather than upward, according to a reductionist principle.

In this paper, we do not address theses questions directly, as we limit ourselves to discussing social behaviours in artificial societies; but the opposition between downward versus upward causation proves to be a central one in the field of social sciences. According to [START_REF] Granovetter | Economic Action and Social Structure: The problem of embeddedness[END_REF], the sociologist's approach would be "over socialized" (downward) while the economist's approach would be "under socialized" (upward/methodological individualism). Currently, both approaches have been sophisticated and are often mixed. The present paper is an attempt to integrate them in one single framework, in which the 'whole' is a collective of agents (up-ward causation / methodological individualism), but the agents are in are to some extent constrained by the whole (downward causation), by way of the "social dimension" of their belief as well as their perception of social phenomena. For the purpose of this paper, we rely on the distinction, proposed by [START_REF] Muller | Des systèmes autonomes aux systèmes multi-agents : interactions, émergence et systèmes complexes Rapport de l[END_REF] in the field of multi-agent systems, between "weak" and "strong" emergence. The latter refers to a situation in which agents are able to witness the collective emergent phenomena in which they are involved, which opens the road for both upward and downward causation.

In Agent based Computational Economics, "emergence" is strongly related to the Santa Fe approach to complexity (SFAC). In accordance with descriptive emergentism, SFAC calls "emergence" the arising at the macro level of some patterns, structures and properties of a complex adaptive system that are not contained in the property of its parts. But conversely, emergence can often be explained by upward mechanisms. Interactions between parts of a dynamic system are the source of both complex dynamics and emergence. An interesting part of the emergence process concerns the forming of some collective "order" (coherent structures or patterns at the macro level) as a result of agents' interactions within the system's dynamics, in the presence of a specific attractor. For the observer, this collective order makes sense by itself and opens up a radically new global interpretation, because it does not initially make sense as an attribute of the basic entities.

Formally, in multi-agent systems, emergence is a central property of dynamic systems based upon interacting autonomous entities (the agents). The knowledge of entities' attributes and rules is not sufficient to predict the behaviour of the whole system. Such a phenomenon results from the confrontation of the entities within a specific structure of interaction. That is, better knowledge of the generic properties of the interaction structures would make it easier to have better knowledge of the emergence process (ie. morphogenetic dynamics). From this point of view, to denote a phenomenon as "emergent" does not mean that it is impossible to explain or to model the related phenomenon. For this reason [START_REF] Epstein | Agent-Based Computational Models and Generative Social Science[END_REF]) uses the word "generative" instead of "emergent" in order to avoid a philosophical debate about emergence.

Various attempts have been made to define emergence in an "objective" way. Some definitions refer to self-organisation [START_REF] Varela | The embodied mind[END_REF], to entropy changes (Kauffman 1990), to non-linearity (Langton 1990), to deviations from predicted behaviour (Rosen 1985;[START_REF] Cariani | Adaptivity and emergence in organisms and devices[END_REF] or from symmetry [START_REF] Palmer | Broken Ergodicity[END_REF]). Other definitions are closely related to the concept of complexity (Bonabeau et al. 1995a(Bonabeau et al. , 1995b;;[START_REF] Cariani | Adaptivity and emergence in organisms and devices[END_REF][START_REF] Kampis | Self-Modifying Systems in Biology and Cognitive Science Pergamon 26[END_REF]. In statistical physics (Galam, 2004), as well as for models in economics or social sciences explicitely based upon theses models (see for instance [START_REF] Durlauf | Statistical Mechanics Approaches to Socioeconomic Behavior[END_REF](Durlauf , 2001) and the pioneering work of [START_REF] Galam | Sociophysics: a new approach of sociological collective behavior[END_REF]), emergence may be related with an order parameter which discriminates between at least two phases, each one with a different symmetry associated respectively to a zero and non-zero value of the order parameter. Each problem has its specific order parameter. For instance in the Ising model, where individual spins can takes the value {-1, +1}, the order parameter is the magnetization M , given by the sum of all the spin values divided by their total number. When M = 0, the state is paramagnetic, i.e. disordered in the spin orientations, while long range order appears as soon as M = 0. A majority of spins are then oriented along either -1 or +1, and an order is likely to emerge. Two ordered phases are thus possible in principle, but only one is effectively achieved. The order parameter provides a "signature" for the emergent phenomenon. Although these definitions make use of concepts borrowed from physics and information science, they all involve inherently contingent aspects, as the presence of an external observer seems unavoidable. Even a change in entropy supposes that an observer be able to assess the probability of various states.

The unavoidable presence of an observer does not preclude, however, the possibility of extending the definition of emergence to include non-human observers or observers that are involved in the emerging phenomenon. In our quest for "strong emergence", we wish to assign the role of the observer to elements of the system itself, as when individuals become aware of phenomena affecting the whole society. This kind of self-observation is only possible because what is observed is a simplified state of the system. Emergence deals precisely with simplification.

What does emerge in Schelling's model of spatial segregation?

Schelling's model of spatial segregation [START_REF] Schelling | Models of Segregation[END_REF][START_REF] Schelling | Dynamic Models of Segregation[END_REF][START_REF] Schelling | The Construction of Social Reality[END_REF] is a pioneering example of an emerging phenomenon resulting from social interaction. Schelling's aim was to explain how segregationist residential structures could spontaneously occur, even when people are not so very segregationist themselves. The absence of a global notion of segregationist structures (like the notion of ghettos) in the agent's attributes (preferences) is a crucial feature of this model. Agents do not choose between living or not living in a segregationist structure, but have only local preferences concerning their preferred neighbourhood. Moreover, people have only weak segregationist behaviour, but the play of interactions generates global segregation. In Schelling's original model, agents were placed on a 8-by-8 chessboard as shown in Figure ?? (Java applet). Taking the "colour" of agents as criterion for discrimination, agents choose a location where to live, depending on their individual tolerance threshold of different colours in their neighbourhood. Agents interact only locally with their 8 direct neighbours (within a so-called "Moore" Neighbourhood). No global representation about the residential structure is available to them. Though agents may be weakly segregationist (each agent would stay in a neighbourhood with up to 62.5% of people with another colour), segregation occurs. Schelling used the following rule: an agent with one or two neighbours will try to move unless one of the two neighbours has the same colour as its own (which means a local tolerance of 50% ); an agent with three to five neighbours requires at least two agents of same colour to stay (that is 33%, 50% and 60% local tolerance), and one with six to eight neighbours will stay if at least three of them are of the same colour (50%, 57,1%, 62,5% local tolerance). Under Schelling's behavioural assumption, a "fully integrated structure" (Fig- ure ??-a) is an equilibrium (an order) because no agent wishes to move. A "fully integrated structure" is a structural pattern in which agents' colours alternate in all directions. Because of border effects, no agent is located in the corners. The "fully integrated structure" is an unstable equilibrium. A slight perturbation is sufficient to induce a chain reaction and the emergence of local segregationist patterns. In his example, Schelling extracted twenty agents at random, and added five at random in the free spaces. The discontented agents (crossed in Figure ??-b) move at random towards a new location in agreement with their preferences. These moves generate new discontented agents by a chain reaction until a new equilibrium is reached. In such equilibrium, local segregationist patterns appear, like in Figure ??-c.

Local interactions are sufficient for spatial homogeneous patterns to occur; spatial segregation is an emerging property of the system's dynamics, while not being an attribute of the individual agents. Sometimes, local integrated (non-homogeneous) patterns may survive in some niches. But such integrated structures are easily perturbed by random changes, while homogeneous structures are more stable (frozen zones). Complementary theoretical developments on Schelling's model of segregation can be found in the growing literature on this subject, for instance among economists like (Zhang 2004a-b), [START_REF] Pancs | Schelling's Spatial Proximity Model of Segregation Revisited[END_REF], 2004), or sociologists like (Broch Mare 2004). Examples of advances in empirical investigations can be found in [START_REF] Clark | Residential Preferences and Neighborhood Racial Segregation: A Test of the Schelling Segregation Model[END_REF], (Sethi Somanathan 2001), (Koeler, Svoretz 2002), and experimentations in Ruoff, (Schneider 2004). Our aim in this paper is to address emergent phenomena, as instantiated in Schelling's model, in a new way. Emergence is currently debated for its cognitive and sociological aspects, from ontological and epistemic perspectives, in relation with the modern philosophy of mind (for a selection of papers, see for instance (Intellectica 1997), and (Gilbert 1995), for links with sociology. There is also a debate within the artificial intelligence, artificial life and artificial society fields see (Gilbert,Conte,1995) in this later field. Entering or even summarizing those debates would fall outside the scope of the present paper. But some fundamental questions are worth asking about knowing in what way emergence occurs in Shelling's model. Who is the observer? What does the higher level of organisation consist in? For whom does this level make sense? (Figure ??) In various definitions of emergence, the presence of an external observer seems unavoidable. Levels of organisation depend on an observer being able to discern subparts in the system and appropriate relations between them. There is no consistent way to say that some new phenomenon occurs at a higher level, be it some new form of operational closure or any form of deviation from expected behaviour, unless there was some pre-existing way to observe that higher level.

Emergence in ACE : from case studies to a formal definition

The first and second subsections provide two definitions coherent both with the design of multi-agent systems used in Agent Based Computational economics (Tesfatsion 2002; [START_REF] Phan | From Agent-Based Computational Economics towards Cognitive Economics[END_REF] and with important related features, like cognitive hierarchy, detection, and complexity. The first one from (Bonabeau, Dessalles 1997) defines the emergence as an unexpected complexity drop in the description of the system by a certain type of observer. The second one from [START_REF] Muller | Des systèmes autonomes aux systèmes multi-agents : interactions, émergence et systèmes complexes Rapport de l[END_REF]) defines emergence as a phenomenon observed at the interface of description levels. The latter definition introduces a useful distinction between "weak" and "strong" emergence.

Emergence as a complexity drop

In (Bonabeau, Dessalles 1997), emergence is defined as an unexpected complexity drop in the description of the system by a certain type of observer. Such a definition is claimed to subsume previous definitions of emergence, both structural (dealing with levels of organisation) and epistemological (dealing with deviation from some model's predictions). In each case, the observer is able to detect a structure, such as the presence of relations holding between parts of the system, or some form of behaviour like a characteristic trajectory. Structural emergence occurs whenever the system turns out to be more structured than anticipated. This augmentation of structure can be characterised by a decrease of complexity.

E = C exp -C obs

Here, E stands for the amplitude of the emergence, C exp is the expected structural complexity and C obs the structural complexity actually observed. Structural complexity is defined as the algorithmic complexity relative to a given set of structural descriptors.

Algorithmic complexity, as defined by Kolmogorov, Chaitin and Solomonov, is defined by the shortest description that can be given of the system using a Turing Machine [START_REF] Li | An Introduction to Kolmogorov Complexity and Its Applications[END_REF]). This definition is sometimes considered of little use for finite systems, as the set of all systems of same size can be ordered; since each of these system can be characterised by its rank, nothing prevents the actual system to appear as the simplest one if it happens to be number one. In order to use algorithmic complexity to describe finite system, we abandon the generality of Turing machines, considering that the description tools are imposed by the observer. We define the relative algorithmic complexity (RAC) of a system as the complexity of the shortest description that a given observer can give of the system, relative to the description tools available to that observer. Emergence occurs when RAC abruptly drops down by a significant amount.

For our purpose here, we must restrict the definition. We consider a specific class of observers, in order to get closer to what human observers would consider as emergence. Following [START_REF] Leyton | A generative theory of shape[END_REF], we impose the observer's description tools to be structured as mathematical groups. In other words, any level of organisation that can be observed has operational closure and is structured as a group, and the only structures that can be observed are the invariant of a group of operations. Moreover, the observer is supposed to have hierarchical detection capabilities. This means that all elements of the system that the observer can consider have themselves a group structure. The observer may be considered as being a 'Leyton machine', for which any structure is obtained through a group-transfer of other structures [START_REF] Leyton | A generative theory of shape[END_REF].

Let us illustrate how emergence results from a complexity drop in Schelling's model. In a first stage, the external observer reconstructs the system by transferring (in the Leyton sense) one abstract inhabitant to form the entire population. The transfer group, in this case, is the group of 2-D translations. The operation is costly in terms of complexity, as each individual translation has to be instantiated. Then each abstract inhabitant is assigned a colour. This latter operation can be achieved through a transfer by the binary group Z/2Z. In a second stage, the external observer is now able to detect homogeneous clusters. She reconstructs the system in a different way. One first abstract cluster is obtained by translating one abstract inhabitant, as previously. Then this first cluster is itself translated to give the whole set of clusters. Finally, clusters are assigned colours through the binary group. Emergence, in this example, comes from the fact that the second construct is significantly simpler than the first one. The reason is that there are less colour assignments: only one per cluster instead as one per inhabitant. A crucial requirement for the emergence to be noticeable is that the shape of clusters be simple. For the system to be fully instantiated, the second construct must reshape the limits of each cluster through various groups of geometrical transformations. If there were no colours, or if the clusters had random shapes, there would be no gain in complexity. Conversely, emergence would be maximum in the extreme case in which all clusters had identical shapes, e.g. if they were square blocks.

Each transfer group can be seen as an organisation level. In Schelling's model, there could be more levels of organisation, for instance if clusters were arranged in a chessboard-like pattern. The Leytonian construct would be different and less com-plex in this case: the first cluster would be assigned a colour, then it would be duplicated through a binary symmetry group operating in colour space, then the couple would be transferred through the group of integer translations of the plan.

For structural emergence to occur, it is important that there be an unexpected complexity decrease. This may happen either because the higher structure detection was delayed, as when you take time to recognise a Dalmatian dog in a pattern of black and white spots. It may also happen when adding a new observable, instead of increasing the overall complexity of the system for the observer, paradoxically deceases it [START_REF] Bonabeau | Detection and Emergence[END_REF]. This latter case is well illustrated by our extension of Axtell et al.'s experiment (see Phan, Galam, Dessalles, 2005).

Emergence occurring in a system with several levels

Following Forrest's definition of emergent calculation [START_REF] Forrest | Emergent Computation : Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks[END_REF]), (Müller 2002) defines emergence in SMA as occurring between two organisation levels, distinguishing the process and the observation of that process. The process concerns the evolution of a system formed by entities in interactions. These interactions may generate observable epiphenomena. At the observation level, epiphenomena are interpreted as emerging through specific calculation (i.e. like order parameter). For Müller, "weak emergence" arises when the observer is external to the system, while "strong emergence" arises when the agents involved in the emerging phenomenon are able to perceive it. In this later configuration the identification of epiphenomena by the agents in interaction in the system will involve a feedback from the observation to the process. There is a coupling between the process level and the observation level by the way of the agents. Emergence is thus immanent in such a system.

More specifically, for Müller, a phenomenon is emergent if:

• (A) There is a system composed of agents in interaction with each other and with their environment. The description of this system as a process is formalized in a language D • (B) The dynamics of this system produces a structural phenomenon observable in the "traces of execution" • (C) The global phenomenon is observed by an external observer (weak emergence) or by the agents themselves (strong emergence) and is described in a language distinct from D.

When compared with Forrest's definition [START_REF] Forrest | Emergent Computation : Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks[END_REF]), Müller's definition presupposes the existence of two languages of description, which are distinct according to the level considered. This distinction only materializes the presence of levels already hypothesised by Forrest. On the other hand, it is interesting to note that Müller distinguishes the system formed by the interacting agents from the process that governs their behaviour. This enables him to choose the position of the level of observation with respect to the agents. Müller's contribution lies then mainly in the distinction between two categories of emergence according to the position of the level of observation w.r.t. process. In strong emergence, agents are observers themselves, this de facto entails a feedback loop between the micro (agent based) level of observation and the macro level of the process. In weak emergence, the observer is external with the process and there is no necessarily coupling.

Müller illustrates weak emergence by means of the example of foraging ants which move between their nest and a food source. Each ant deposits on its passage some traces of pheromone which attract the other ants, and create an interaction between them [START_REF] Axtell | The Emergence of Classes in a Multi-agent Bargaining Model in[END_REF]. These interactions build a stable and observable phenomenon ( 2). An external observer may interpret this phenomenon as a "path". Moreover, the accumulation phenomenon based on interaction drives the ant colony to find the shortest path between their nest and a source of food. Emergence is weak because the dynamics depends only on the traces of pheromone (1-2) and not on the qualification of these traces as an "shortest or optimal path", which does not exist in the ants' head.

The category of strong emergence is important for to model artificial societies [START_REF] Gilbert | Emergence in social simulations[END_REF]. Indeed, the reflexivity meditated by the agents' "consciousness" appears to be a determinant characteristic that distinguishes systems involving human agents from systems made of non conscious or material entities.

In Schelling's model, there would be strong emergence if agents, rather than merely sampling neighbouring densities, were able to perceive forming homogeneous clusters in the town and if their perception could affect their decisions. Strong emergence is particularly important in economic modelling, because the behaviour of agents may be recursively influenced by their perception of emerging properties. Emerging phenomena in a population of agents are expected to be richer and more complex when agents have enough cognitive abilities to perceive the emergent patterns. Such feedback loops between emerging collective patterns and their cognitive components clearly occur among agents in human societies. They may obey laws that are still to be understood. Our aim here is to design a minimal setting in which this kind of strong emergence unambiguously takes place.

Conclusion

To summarize, if there is strong emergence in the sense of Müller, the system becomes reflexive, through the mediation of the agents. (A) Agents are equipped with the capacity to observe and to identify an epiphenomenon in the process which represents the evolution of the system in which they interact. This capacity of observation and the field of such observation must then be sufficiently broad to encompass the phenomenon as a global one. (B) The agents can describe this epiphenomenon in a "language" other than that which is used to describe the process (C) The identification of an "emergent" epiphenomenon by the agents involves a change of behaviour, therefore a feedback of the level of observation on the process Emergent phenomena are naturally described in a two-level architecture (Figure 3). In such a framework, objects at the two levels only exist because some observer is able to detect them. The detected object at the upper level is composed by objects of the first level. Correspondingly, the upper level detector is triggered by the activity of lower level detectors. The system's complexity, defined as the minimal description that can be given of its state, drops down by a significant amount when an upper-level According to this point of view, one can reinterpret the Müller's definition using a distinction due to Searle (1995) between entities that are independent of the observer (the process and the phenomena which results from it) and entities that occur within the observer (identification and interpretation of an epiphenomenon). According to this interpretation, emergence becomes a category relative to an observer, and in the case of a human observer (or an agent supposed to be represented an human), a subjective category. Note that Müller's definitions and the above definition of structural emergence as complexity drop are compatible. Müller's distinction between two description languages presupposes that the upper language, available to the observer, provides it with a simpler description of the epiphenomena than what was available at the process level.

In order to illustrate our formal definition of emergence, a companion paper (Phan, Galam, Dessalles 2005) discusses the ACE model of (Axtell and Epstein and Young 2001) and builds an extension based on the formal framework introduced in this paper. In the basic model, agents tend to correlate their partners' behaviour with fortuitous visible but meaningless characteristics (tags). On some occasions, these fortuitous tags turn out to be reliable indicators of dominant and submissive behaviour in an iterative Nash bargaining tournament. One limit of this model is that dominant and submissive classes remain implicit within the system. Classes only emerge in the eye of external observers (weak emergence). We enhance the model to allow for strong emergence. In a two-level framework, agents get an explicit representation of the dominant class whenever that class emerges, thus implementing strong emergence.

( 1 -

 1 a) fully integrated population equilibrium (1-b) discontented agents are crossed (1-c) convergence after 4 iterations Source: http://perso.univ-rennes1.fr/denis.phan/complexe/schelling.html and[START_REF] Phan | From Agent-Based Computational Economics towards Cognitive Economics[END_REF]

Fig. 1 .

 1 Fig. 1. Original (checkerboard) Schelling Model

Fig. 2 .

 2 Fig. 2. Questions of emergence

Fig. 3 .

 3 Fig. 3. Parallelism between hierarchies : description, observations and conceptual level detector becomes active, as its activity subsumes the activity of several lower-level detectors.According to this point of view, one can reinterpret the Müller's definition using a distinction due to Searle (1995) between entities that are independent of the observer (the process and the phenomena which results from it) and entities that occur within the observer (identification and interpretation of an epiphenomenon). According to this interpretation, emergence becomes a category relative to an observer, and in the case of a human observer (or an agent supposed to be represented an human), a subjective category. Note that Müller's definitions and the above definition of structural emergence as complexity drop are compatible. Müller's distinction between two description languages presupposes that the upper language, available to the observer, provides it with a simpler description of the epiphenomena than what was available at the process level.In order to illustrate our formal definition of emergence, a companion paper (Phan, Galam, Dessalles 2005) discusses the ACE model of (Axtell and Epstein and Young 2001) and builds an extension based on the formal framework introduced in this paper. In the basic model, agents tend to correlate their partners' behaviour with fortuitous visible but meaningless characteristics (tags). On some occasions, these fortuitous tags turn out to be reliable indicators of dominant and submissive behaviour in an iterative Nash bargaining tournament. One limit of this model is that dominant and submissive classes remain implicit within the system. Classes only emerge in the eye of external observers (weak emergence). We enhance the model to allow for strong emergence. In a two-level framework, agents get an explicit representation of the dominant class whenever that class emerges, thus implementing strong emergence.


Nicolas Sillitoe

Jean-Philippe Karr

Johannes Heinrich

Thomas Louvradoux

Albane Douillet

Laurent Hilico
email: laurent.hilico@lkb.upmc.fr

H+ Sympathetic Cooling Simulations with a Variable Time Step

Keywords:

In this paper we present a new variable time step criterion for the velocity-Verlet algorithm allowing to correctly simulate the dynamics of charged particles exchanging energy via Coulomb collisions while minimising simulation time. We present physical arguments supporting the use of the criterion along with numerical results proving its validity. We numerically show that H+ ions with 18 meV initial energy can be captured and sympathetically cooled by a Coulomb crystal of Be + and HD + in less than 10 ms, an important result for the GBAR project.

Introduction

A Paul Trap allows very long trapping times for ions, which in combination with cooling leads to applications in fields such as high resolution spectroscopy [1,2], quantum computation, quantum simulations [3] and cold chemistry [4,5]. Some ions such as 9 Be + can be conveniently laser cooled [6,7], most, however, cannot. One way to overcome this is sympathetic cooling whereby instead of trapping only the species of interest another species, which can be laser cooled, is simultaneously trapped. The species which cannot be laser cooled will thermalise via Coulomb interaction with the other species, forming a cold two-component Coulomb crystal with a temperature bounded by the Doppler cooling limit, e.g. 0.47 mK or 60 neV in the case of Be + . Sometimes the ions cannot be created in situ and therefore have to be externally loaded at relatively high energies of 0.1-10 eV. Such is the case of highly charged ions [8] and antimatter ions [9] that are (or will be) created in dedicated sources and are of interest for fundamental physics experiments. One example is the GBAR experiment which aims to cool H+ ions made of an antiproton and two positrons at CERN and study their free fall to measure the gravity constant ḡ on antimatter [10][11][12].

One crucial step of the GBAR project is the capture and sympathetic cooling of H+ ions, so it is important to accurately evaluate the sympathetic cooling time by a laser cooled Be + ion crystal. Sympathetic cooling of externally loaded ions has been recently achieved for Ar 13+ [8,13] but the dynamics of the process have been little studied so far [14] especially for the case of very different mass-to-charge ratios as is the case in GBAR (9:1) [15]. Our goal is to numerically study this Dopplercooling step. In Sec. 2, we briefly introduce the numerical model used for the simulations. In Sec. 3, we discuss the choice of the simulation time step and propose a new scheme to well describe Coulomb interactions that lead to sympathetic cooling. In Sec. 4, we discuss our first numerical results showing that H+ can be cooled by a laser cooled Be + /HD + ion crystal.

Ion crystal dynamics model

For the GBAR experiment, the idea [11] is to sympathetically cool a high velocity H+ ion using a laser cooled trapped Be + ion crystal. In a linear RF Paul trap, a laser cooled ion crystal in the Coulomb crystal regime has an ellipsoidal shape [16] as shown in Fig 1 . The inter-ion distance is a few tens of microns and for ion numbers N of a few thousand the crystal typically has dimensions of a few millimeters. We therefore have a low density mesoscopic system which would be poorly described by mean-field methods so we cannot use NlogN approximate methods [START_REF] Chapman | Parallel Computing : from Multicores and GPU's to Petascale[END_REF] for the Coulomb interaction and we have to exactly compute it using the N 2 all-pairs approach. We solve Newton's equations including the time-dependent confinement electric fields of the linear trap, the exact Coulomb force between all ion pairs and the laser interaction [START_REF] Zhang | [END_REF][19][20][21][22][23].

The confinement field derives from the potential [15] V(x, y, z, t) = (U 0 + V RF cos(Ωt))

x 2 -y 2 2r 2 0 + 1 2 m i ω 2 i,z (z 2 -(x 2 + y 2 )/2), (1)
including the radial confinement in the x and y directions. For this study, we use U 0 =0.1 V , V RF =100 V, r 0 =3.5 mm and Ω=2π × 13 MHz. The longitudinal confinement in the z direction is described in terms of the axial oscillation frequency ω z =2π×100 kHz for H+ (which is smaller by a factor of √ 3 and 3 for HD + and 9 Be + respectively).

We describe the interaction with the cooling laser as a stochastic process of absorption (depending on the ion's velocity through Doppler effect) spontaneous and stimulated emission, adding the corresponding velocity kicks to the laser cooled ions [START_REF] Sillitoe | Physics with charged trapped particles[END_REF][START_REF] Rouse | [END_REF]. The laser cooling beam is aligned with the trap axis. The waist of 1 mm is located at the trap center. The laser detuning is -Γ where Γ=19 MHz is the natural width of the Be + cooling transition and laser intensity is 1.5 times the saturation intensity.

The ion trajectories are computed using the velocity-Verlet algorithm [26] given by

         x i a i v i →            x i+1 = x i + v i δt + a i δt 2 2 a i+1 = F(x i+1 , t i+1 ) v i+1 = v i + a i +a i+1 2 δt (2)
where

x i = x(t i ), v i = v(t i ), a i = a(t i ), F(x i , t i )
is the force at time t i and δt is the integration time step.

Choice of the integration time step

To accurately describe the Radio Frequency trapping potential (RF) of the linear Paul trap the integration time step δt needs to verify δt << 2π/Ω (3)

As we will show, the proper description of coulomb interactions between ions can lead to time steps orders of magnitude smaller than what Eq. ( 3) prescribes. Eq. ( 3) therefore gives an upper bound on the time step that can be used. We have checked that setting it to 0.1 ns (about 1/769 of the RF period) in our simulations, the trajectory of a single ion in the RF field is converged for simulations longer than 10 ms. The description of laser cooling in terms of random absorption and emission events imposes time steps much longer than the optical period, otherwise one would have to describe the laser interaction in terms of Bloch equations as discussed in [START_REF] Rouse | [END_REF]. For Be + cooling at 313 nm, the optical period is 1 fs, so the time step can be adapted over several orders of magnitude.

Coulomb interaction simulations with a fixed time step

In Figure 2 we consider a Coulomb collision between two particles and illustrate that if the time step is too long, a Coulomb collision between two ions may be so poorly described that the two ions go through each other instead of repelling each other. To understand the time step requirements of simulating the Coulomb interaction we simulated head-on 1D Coulomb collisions of two ions of equal masses and initially separated by 1 mm using a constant time step velocity-Verlet algorithm in the absence of the trapping field and the laser interaction. We send one ion at a given energy onto the other ion at rest. This problem has an analytical solution which predicts that the projectile ion transfers all its kinetic energy to the second ion.

In Fig. 3 we show the energy of the projectile ion after the collision versus time step for different projectile energies. At a given projectile energy we can see that for a too long time step the ions don't exchange much energy. However, there is a threshold time step below which we can reproduce the expected result of the projectile ion losing all its energy. Notice the intermediate regime where the time step is close to being small enough, the outgoing energy of the projectile ion can fluctuate quite wildly as the ions can come closer than their minimum approach distance, numerically adding energy to the system. We can interpret the threshold time step by saying that in a time step the ions should move much less than their minimum approach distance. At the beginning of the collision most of the mechanical energy is in the kinetic energy E in of the projectile ion going at speed v in in the lab reference frame. The minimum approach distance d min is therefore given by with q 1 , q 2 the charges of the two ions and µ = m/2 the reduced mass. The displacement should obey δr ≈ v δt << d min leading to

d min = q 1 q 2 2πǫ 0 µv 2 in = q 1 q 2 πǫ 0 mv 2 in (4)
δt << q 1 q 2 πǫ 0 mv 3 in = q 1 q 2 √ m √ 8πǫ 0 E -3 2 in ( 5
)
where we have obtained the right hand side of the equation by upper bounding the relative speed of the two ions v by v in . We have fitted the threshold time steps found by such simulations to δt = cE

-3 2 in
and have found excellent agreement, finding that c should be approximately 4 times smaller than the right hand side of Eq. ( 5) for correct simulations. Figure 3 shows that the threshold time step is as small as 1 ps for only 0.3 eV of initial kinetic energy. This makes sympathetic cooling simulations of high temperature particles with a constant time step extremely demanding.

Variable time step criterion

Realistic dynamics of an ion crystal may involve fast ions and require very short time steps, e.g. if collisions with neutrals or exothermic reactions take place or as in the present case, if a fast ion is injected in a cold ion crystal to be sympathetically cooled. In this section, we show that a variable time step scheme allows us to have much longer time steps on average while accurately describing Coulomb interactions.

From the ideas of Sec. 3.1, we say that at every time step, for every ion pair, the relative change in distance δd i j should obey δd i j << d i j (6) with d i j the distance between the two ions. We can reformulate the inequality in Eq. ( 6) as δd i j = αd i j (7) with α a constant to be chosen such that α << 1. For velocity-Verlet integration position updates are given by

δr i = v i δt + 1 2 a i δt 2 (8)
therefore the displacement d i j between two ions is upper bounded by

δd i j ≤ v i j δt + 1 2 a i j δt 2 (9)
with v i j and a i j the relative velocity and acceleration. Inserting Eq. ( 9) in Eq. ( 7) and solving the second degree equation for δt one finds the following time step

δt i j = -v i j + v i j 2 + 2 a i j α d i j a i j . (10)
Eq. ( 10) is specific to the case of a Velocity Verlet integration. Indeed, we have found that approximating δd i j by v i j δt wasn't sufficient to describe a Coulomb interaction because as the ions approach their minimal approach distance and as the velocity v i j vanishes the second term 1 2 a i j δt 2 in Eq. ( 9) can no longer be neglected.

The variable time step scheme is therefore to apply Eq. ( 10) to every ion pair and to update δt at every time step using δt = min i, j δt i, j .

The all pairs computation of this variable time step scheme adds a lot of computation to the already expensive O(N 2 ) Coulomb evaluations because it involves three more square roots. Also, it requires more data transfers than the Coulomb force evaluations because it involves not only the particles' positions, but also their speeds and accelerations. This variable time step scheme slows down the code by a factor of ∼ 3.

To verify this time step scheme, we simulated head-on 1D collisions of two ions with no trapping force nor laser cooling. We varied the parameter α from 1 down to 1/5000. In Fig. 4 every point shows the maximum value of the ratio of the outgoing energy to the incoming energy of the projectile ion E out /E in over 20000 simulations with collision energies in a geometric progression from 0.1 meV to 1 eV. For α 1 the time step is too long and the ratio is far from the analytically expected result of zero but as α decreases, the ratio rapidly converges to zero. In Sec. 4, we use α = 1/100, which ensures an accurate description of the Coulomb collisions.

As a side note, one may elect to simulate at a constant time step such that Eq. ( 7) is valid for all ion pairs at all time steps. This may be achieved if the energy of any ion has an upper bound, known in advance, during the duration of a simulation. One could also upper bound relative velocities and accelerations to twice the maximum velocity and twice the maximum acceleration respectively, and lower bound the distance between two ions by the lowest distance found during the calculation of the Coulomb interaction. That way one could bring down the additional computational cost of the time step calculation to O(N) at the cost of smaller time steps.

H+ sympathetic cooling

In this section, we study the capture and sympathetic cooling of an H+ ion by a cloud of 500 laser cooled Be + ions and 200 HD + ions. The light HD + ions undergo a tighter radial RF confinement and are located around the trap axis as in Fig. 1. The HD + is sympathetically cooled by the 9 Be + and its purpose is to serve as an intermediary of more favorable mass ratio 3, compared to 9, for the sympathetic cooling of the H+ . Indeed it is known from classical mechanics that optimal energy transfer in collisions occurs when the masses are equal. We have performed 5 simulations by varying the random number series used for ion position initialisation and laser interaction. All of them give very similar results and one is detailed in Fig. 5. The simulation first thermalises the 500 Be + and 200 HD + ions using laser cooling (not shown in Fig. 5) leading to the ion crystal shown in Fig. 1. At t =3 × 10 -4 s, the projectile H+ ion is added at rest close to the trap axis at x 0 = y 0 = 0 and z 0 = 3 mm with a standard deviation ∆z 0 = ∆x 0 = ∆y 0 = 5 µm corresponding to an initial potential energy of 18.5 meV. Figure 5 shows that the projectile ion oscillates back and forth through the ion crystal for several ms before being captured and cooled. When the oscillation amplitude is large, the projectile ion spends most of its time out of the ion crystal where it isn't cooled. Figure 5(d) shows that v z (t) oscillates with a flat top behaviour corresponding to the Be + /HD + crystal crossing. This is due to the fact that inside the ion crystal, the total electric field (trapping + Coulomb) is essentially zero such that the projectile ion does not feel any force. Figure 5(e) is a zoom on the flat top region. It shows that v z fluctuates due to collisions with the trapped Be + or HD + ions. The net effect of the crystal crossing is a slight decrease of the projectile axial velocity that results in projectile capture after many crossings.

Figure 5(f) shows a coarse grain view of the time step evolution with time. The solid and dashed lines correspond to the minimum and average time step over 50 ns time intervals. The minimum time step fluctuates due to Coulomb interactions within the crystal. One can see that when the projectile crosses the crystal, the time step is significantly reduced because the fast ion can come close to the Be + or HD + ions.

Figure 5(a) shows the trajectories of the projectile ion in the radial plane. Figure 6(a) shows the x, y and z contributions to the mean macro-motion kinetic energy (expressed in Kelvin) of the Be + and HD + ions and Fig. 6(b) those of the projectile ion. One can see that the axial kinetic energy lost by the projectile ion when crossing the ion crystal is partly transferred into radial kinetic energy and also directly to the ion cloud explaining the spikes in the Be + and HD + temperatures. This energy is damped by the laser cooling process with a few ms scale leading to cooling of all projectile degrees of freedom and a stable behaviour. The projectile ion temperature slowly decays from more than 400 K in the z-direction down to the mK regime in less than 10 ms.

Conclusion

We have shown that simulating ionic interactions incurs a requirement on the time step to properly describe the Coulomb interaction. We have proposed and tested a variable time step scheme to accurately describe the Coulomb interaction while minimising the simulation time. Using this scheme, we have performed accurate numerical simulations of sympathetic cooling of an H+ ion by laser cooled Be + and HD + ions, showing that sympathetic cooling can be performed in less than 10 ms for a initial kinetic energy of 18.5 meV (more than 400 K). This result is very important to assess the feasibility of the Doppler sympathetic cooling step in the GBAR project. We will pursue these simulations to determine the dependence of the cooling time on the initial energy of the H+ injected into the laser cooled crystal and on the size of the crystal. We also want to study sympathetic cooling of H+ by a Be + cloud as the HD + improves cooling but is an extra experimental constraint.

Figure 1 .

 1 Figure 1. Projection in the xy (left) and zy (right) planes of a simulated ion crystal made of 500 Be + and 200 HD + . The laser cooling beam is applied towards the increasing z direction, pushing the Be + ions in that direction. The HD + ions are more likely located on the other side of the cloud. The arrow indicates the location of the H+ ion at the end of the simulation shown in Fig. 5.

Figure 2 .

 2 Figure 2. Coulomb collision between two ions in the frame of the target ion. (a) The time step is short enough and the collision is well described. (b) The time step is too long and the ions go through each other instead of repelling each other.

Figure 3 .

 3 Figure 3. Left: Outgoing energy of a projectile ion after colliding with a stationary ion of equal mass 9 u starting 1 mm away from each other, for different projectile ion energies, versus the constant time step used to simulate the collision. Arrows indicate the threshold time step below which the collision is well described. Right: The open circles show the threshold time step versus projectile initial kinetic energy, solid line is a fit to δt = cE -3 2 in .

Figure 4 .

 4 Figure 4. Maximum of the ratio of the outgoing energy to the incoming energy E out /E in of the projectile ion after a head-on collision obtained in a 1D model. The maximum is computed over 20000 collisions ranging from 0.1 meV to 1 eV. The ions start 10 cm away.

Figure 5 .

 5 Figure 5. Trajectory of an H+ ion initially at rest at a distance z 0 =3 mm from the center of the trap containing the Be + /HD + ion crystal shown in Fig. 1. (a) x(t) and y(t) radial coordinates. (b) Axial position z(t). The white lines indicate the longitudinal Be + /HD + ion crystal size. (c) Axial velocity v z (t). (d) Detail of v z (t) showing oscillations as the H+ ion goes back and forth through the ion crystal. (e) Further zooming of v z (t) showing that the H+ ion is slowed down while crossing the ion crystal. (f) Minimum (solid line) and average (dashed line) time step per 10 -8 s interval.

Figure 6 .

 6 Figure 6. (a) For Be + and HD + : time evolution of the mean macro-motion kinetic energy along the x, y and z directions obtained by averaging the velocities over one RF period. (b) Same quantities for the H+ projectile ion, but obtained by averaging over 50 RF periods to improve the readability of the curve. The horizontal dashed line indicates the Be + Doppler limit per degree of freedom, i.e. 0.16 mK.

Acknowledgements

This work was supported by the ANR-13-IS04-0002-01 BESCOOL grant and the COMIQ ITN. J.-Ph. Karr acknowledges Institut Universitaire de France.


domain: sde sdv

text:
Meng Li

Zhenlin Liang

Myriam D Callier

Emmanuelle Roque D'orbcastel

Shunkui Wang

Xiefa Song

Ying Liu
email: yingliu@dlou.edu.cn

Emmanuelle Roque D'orbcastel C

Xiaona Ma

Linlin Sun

Xian Li

Nitrogen and organic matter removal and enzyme activities in constructed wetlands operated under different hydraulic operating regimes

Keywords: Mariculture wastewater, constructed wetland, Salicornia bigelovii, enzyme activity, removal performance

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

Introduction

Global aquaculture production, as an alternative source of high-quality protein, expanded at an average annual rate of 5.8% during 2005-2014, to 73.8 million tons (FAO 1 , 2016). Marine aquaculture releases a large quantity of wastewater. Without proper treatment, the discharged dissolved nitrogenous substances (e.g. NH 4

+ , NO 2 -, NO 3 -) and organic matter could have a detrimental effect on aquatic organisms and give rise to eutrophication in receiving ecosystems [START_REF] Hongfang | Integrated water quality, emergy and economic evaluation of three bioremediation treatment systems for eutrophic water[END_REF]Wu Haiming et al., 2015). Mariculture effluents therefore need to be treated properly to avoid environmental hazards.

Many conventional biological methods, including submerged bio-filters, trickling filters, rotating biological contactors and fluidized bed reactors, have been applied worldwide in aquaculture wastewater purification (Van Rijn, 1996). Compared with these costly approaches in terms of installation and operation as well as energy consumption [START_REF] Papenbrock | Sustainable Treatment of Aquaculture Effluents-What Can We Learn from the Past for the Future?[END_REF], constructed wetlands (CW) are now attracting more attention and are considered promising for being environmentally-friendly and for their cost and efficiency features (Shpigel et al., 2013;Wu Haiming et al., 2015). Over the past few decades, CW have proved to be functional in treating domestic municipal wastewater [START_REF] Kivaisi | The potential for constructed wetlands for wastewater treatment and reuse in developing countries: a review[END_REF], agricultural effluents (Wood et al., 2007), landfill leachates [START_REF] Justin | Combined purification and reuse of landfill leachate by constructed wetland and irrigation of grass and willows[END_REF] and industrial sewage water 1 Food and Alimentation Organization [START_REF] Guittonny-Philippe | Selection of wild macrophytes for use in constructed wetlands for phytoremediation of contaminant mixtures[END_REF]. CW can also effectively remove nitrogen and organic matter from catfish, shrimp and milkfish pond effluents [START_REF] Schwartz | Constructed wetlands for treatment of channel catfish pond effluents[END_REF][START_REF] Sansanayuth | Shrimp pond effluent: pollution problems and treatment by constructed wetlands[END_REF][START_REF] Lin | Nutrient removal from aquaculture wastewater using a constructed wetlands system[END_REF]. Recently, mariculture effluent purification has become increasingly important with the expansion of aquaculture and the development of more intensive landbased marine farms (Webb et al., 2012).

The CW purification performance is mostly attributed to the combined functions of microbes and filtering materials, which could be complemented by hydrophyte (Truu Marika et al., 2009). As an effective way to describe the general conditions of CW substrate microbial populations (Margesin et al., 2000a;Margesin et al., 2000b), substrate enzyme activity (EA) plays a vital role in nitrogen and organic matter transformations (Zhou et al., 2005;[START_REF] Reboreda | Enzymatic activity in the rhizosphere of Spartina maritima : Potential contribution for phytoremediation of metals[END_REF]). Urease, for example, catalyzes the hydrolysis of urea into ammonia and carbon dioxide; dehydrogenase is an indicator of microbial activity in CW beds, considering its function in oxidizing organic matter by transferring electrons and protons from substrates to acceptors (Zhang et al., 2013;[START_REF] Baddam | Activity of soil enzymes in constructed wetlands treated with swine wastewater[END_REF]. Consequently, measuring enzyme activities in CW helps to provide useful information in understanding and controlling the purification activity of the microorganisms.

According to the hydrology and flow paths, CW can be divided into three categories: surface flow constructed wetlands (SFCW), horizontal sub-surface-flow constructed wetlands (HSSF-CW) and vertical-flow constructed wetlands (VFCW) (Vymazal, 2007). Previous studies have

shown that a single-stage CW is unable to achieve adequate total nitrogen (TN) removal due to its inability to provide favorable conditions simultaneously for nitrification and denitrification (Zhi et al., 2015). One common way to enhance TN removal is to configure the hybrid systems using different categories of CW or to couple CW with other types of treatment system (i.e. the electrolysis system and the microbial fuel cell system) [START_REF] Ayaz | Effect of recirculation on nitrogen removal in a hybrid constructed wetland system[END_REF]Zhao et al., 2013;[START_REF] Ju | Intensified nitrogen and phosphorus removal in a novel electrolysis-integrated tidal flow constructed wetland system[END_REF]. However, it is difficult to popularize these systems, because they will inevitably bring extra land occupation and capital investment or require complex operating conditions. An alternative to improve the purification capacity of single-stage CW is to adjust the hydraulic operating regime, which may affect the substrate microorganisms, thus enhancing the wastewater purification performance of sub-surface flow CW without additional cost (Zhi & Ji, 2014). Batch flow (also called tidal flow), Continuous flow and Intermittent flow are three common hydraulic operating regimes used in sub-surface CW [START_REF] Faulwetter | Microbial processes influencing performance of treatment wetlands: a review[END_REF]. CW with Batch operating regimes generate a rhythmic sequential cycle of "flooding" and "draining/resting" phases: wetlands are filled with wastewater for a determined period and completely drained before injection of the next batch of wastewater. In Intermittent flow operation, wetlands are not drained before refilling with wastewater [START_REF] Caselles-Osorio | Impact of different feeding strategies and plant presence on the performance of shallow horizontal subsurface-flow constructed wetlands[END_REF]. To date, only a few studies focusing on the three operating regimes and treatment performance have been published [START_REF] Faulwetter | Microbial processes influencing performance of treatment wetlands: a review[END_REF], and, in particular, little information is available about relating the removal performance of CW under different hydraulic operating regimes to substrate enzyme activities. The relationships between enzyme activities and aquaculture effluent concentrations would promote our ability to understand the treatment processes and better monitor the wetland management in order to control the effluent quality reliably.

CW for marine aquaculture wastewater treatment necessitate the selection and use of hydrophytes with a high salinity tolerance. As illustrated in previous studies, reed, cattail (Typha angustifolia L.), P. australis, mangroves and Salicornia spp. are common halophytes used in mariculture effluent purification [START_REF] Alongi | Present state and future of the world's mangrove forests[END_REF][START_REF] Lin | Nutrient removal from aquaculture wastewater using a constructed wetlands system[END_REF][START_REF] Lin | Performance of a constructed wetland treating intensive shrimp aquaculture wastewater under high hydraulic loading rate[END_REF]Shpigel et al., 2013). Among these, Salicornia bigelovii, is often used due to its high nutrient removal capacity at seawater salinity, as well as its promising commercial value (potential use in the health, cosmetic and nutraceutical industries) [START_REF] Brown | Halophytes for the treatment of saline aquaculture effluent[END_REF][START_REF] Manhee | Salicornia herbacea: botanical, chemical and pharmacological review of halophyte marsh plant[END_REF][START_REF] Quintã | Growth and nitrogen uptake by Salicornia europaea and Aster tripolium in nutrient conditions typical of aquaculture wastewater[END_REF].

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This paper presents the results of a 78-day experiment using pilot-scale CW planted with Salicornia bigelovii and fed with artificial mariculture wastewater under different hydraulic operating regimes. An original feature of the study is that it focuses at the same time on 1), evaluating the effects of hydraulic operating regimes (i.e. Intermittent, Continuous, Batch I, Batch II, Batch III) on CW performance, considering the nitrogen and organic matter removal efficiencies and removal rates and plant growth and 2), investigating the potential of urease activity (UA) and dehydrogenase activity (DA) as indicators to describe CW performance with Salicornia bigelovii in mariculture wastewater treatment.

Material and Methods

The 78-day experiment was conducted using five triplicate pilot CW systems on an intensive recirculating Atlantic salmon farm (i.e. Oriental Ocean Ltd., located in Shandong Province, China) from 28 July 2016 to 13 October 2016. The five triplicates were performed under the five hydraulic operating regimes described in 2.2. Each CW system included one barrel and three square tanks. Plants in the CW (i.e. Salicornia bigelovii) were grown initially in Weifang City, Shandong Province, China. They went through thirty-day salt acclimation to adapt to the fish-rearing salinity before being planted in the CW.

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Artificial wastewater was made of uneaten feed and faeces collected from an Atlantic salmon RAS following the steps described by Zhang et al. (2011). Uneaten feed and salmon faeces were firstly oven dried (105°C for 48 h). After grinding to powder, they were then mixed with seawater (i.e. 250 g powder in 1 L seawater) and transferred into a closed container for seven days to carry out anaerobic fermentation; finally, the "mother liquid" was obtained after filtration through bolting-silk (Mesh: 100). During the experimental period, artificial wastewater was treated separately in the fifteen CW under different hydraulic operating regimes. Salicornia production, nitrogen content in plants and four water quality parameters in each CW were monitored. Principal components analysis (PCA) was used to identify the optimal regime.

Filter construction and operation

The pilot CW system is shown in Fig. 1 The activity of N and organic matter removal related to substrate enzymes (i.e. urease and dehydrogenase) was determined five times over the 78 days. The substrate samples (100 g haydites) were taken randomly at six points from each CW upper layer (3-7 cm depth), considering the higher enzyme activity in sediment upper layers [START_REF] Niemi | Temporal and soil depth-related variation in soil enzyme activities and in root growth of red clover (Trifolium pratense) and timothy (Phleum pratense) in the field[END_REF][START_REF] Baddam | Activity of soil enzymes in constructed wetlands treated with swine wastewater[END_REF]. The samples were then mixed and air dried in the laboratory for 24 hours. UA was determined using the procedure described by [START_REF] Klose | Urease activity of microbial biomass in soils as affected by cropping systems[END_REF]. DA was measured using the TTC-method according to Zhu et al. (1995).

Statistical analysis

The mean, standard deviation, one-way analysis of variance (ANOVA), principal components analysis (PCA) and correlation analysis were calculated using Microsoft Excel and SPSS 21.0.

Over the study, plant growth rate, nutrient removal efficiency, nutrient removal rate and enzyme activity under different hydraulic operating regimes were analyzed by ANOVA for LSD tests. The statistical analysis was considered significant below 0.05 (p<0.05).

In the experiment, various parameters could change widely even with similar flow conditions.

Hence, in order to understand better the effects of different flow regimes, PCA was used as a

Results

Water temperature and pH values

Over the entire experiment, no significant difference (P > 0.05) was observed in water temperatures and pH values in the various flow regime treatments. Water temperature varied from 17.8 to 27.0℃ (23.4 ± 3.3℃), and pH values from 7.8 to 8.6 (8.1 ± 0.1).

Salicornia production

Plant growth rate and nitrogen retention in plants under different flow regimes are shown in Table 1. At the end of the experiment, the average Salicornia fresh weights under the five operating regimes (from Mode 1 to Mode 5) were 16.9 ± 2.7, 25.9 ± 4.5, 17.6 ± 3.3, 17.0 ± 1.3 and 16.7 ± 3.0 g ind -1 respectively. Plants in CW with Continuous operating regimes grew faster (P < 0.05) than in any other regimes, with a growth rate of 40.4 ± 9.9 g m -2 d -1 . There is no significant difference between the Salicornia growth rates under the other four operating CW in Intermittent flow operation had also significantly lower (p<0.05) TN removal efficiency and removal rate over the experiment (9.4 ± 5.8 % and 174.0 ± 104.9 mg m -2 d -1 respectively).

The COD concentrations over the sampling time as well as the overall removal performance are shown in Fig. 2e and Table 2. Average COD removal efficiency was not significantly dif-

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ferent (p>0.05) between the five hydraulic operating treatments and was maintained in the range of 33.9 -44.6 %. However, the average COD removal rates of the CW under the five hydraulic regimes were significantly different. CW in Continuous flow had far higher average COD removal rates (1421.6 ± 365.4 mg m -2 d -1 ) (p<0.01) than CW in the other flow regimes (501.9 to 873.6 mg m -2 d -1 ).

Principle component analysis (PCA) of CW treatment performance

The PCA extracted two principle components (i.e. PC1 and PC2) from ten observations of potentially correlated variables and received a single factor score (FS) reflecting the CW performance. The ten observations of variables included plant growth and nitrogen retention, waste removal efficiency and removal rate. Based on Eigenvalues (>1), two variable PC were extracted, accounting together for 90.4% of the observed variability (Fig. 3). Nitrogen retention, NO 3 --N removal rate and removal efficiency of TAN, NO 3 --N and TN had high positive loadings on the PC1 axis and negative loading on the COD removal efficiency. On the PC2 axis, there were high positive loadings for plant growth rate and the TAN and COD removal rates.

Eigenvalues for PC1 and PC2 were 5.883 and 3.159 respectively. Based on these values, the expressions to calculate FS1, FS2 and FS are as below:

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Where, FS1 means the factor score for PC1, FS2 means the factor score for PC2 and the FS means the factor score.

Discussion

4.1. CW with a Salicornia bigelovii bed as the bioreactor unit

One main objective of this study was to assess the ability of CW planted with Salicornia bigelovii to recycle mariculture wastewater under different hydraulic operating regimes. Over the experiment, Salicornia grew well in CW and the amount of nitrogen retained in plant tissues (Table 1) is comparable with that measured by Webb et al. ( 2012 The COD removal performance obtained in our study (0.5 to 1.4 g m -2 d -1 of removal rates, 33.9-44.6% of removal efficiency) is in line with previous studies using sub-surface flow wetlands for fresh water aquaculture wastewater purification [START_REF] Naylor | Treatment of freshwater fish farm effluent using constructed wetlands: the role of plants and substrate[END_REF]Sindilariu et al., 2007). Sindilariu et al. (2007) used sub-surface flow CW to treat flow-through trout

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wastewater in Bavaria, Germany and obtained a COD removal rate of 0.4 to 1.4 g m -2 d -1 , with a removal efficiency of 24.3 to 52.2%. [START_REF] Naylor | Treatment of freshwater fish farm effluent using constructed wetlands: the role of plants and substrate[END_REF] used synthetic aquaculture wastewater and found a COD removal efficiency ranging from 52.8% to 91.1% in six subsurface wetlands with different filtering materials.

Effects of hydraulic operating regimes on CW removal performance

In this study, the Batch operating regime was more efficient in removing TAN, NO 3 --N and TN than the Continuous and Intermittent regimes. Clearly, Batch loadings enhanced N removal, which agrees with previous CW investigations, e.g. for the treatment of piggery sewage and domestic wastewater (Sun et al., 2005;[START_REF] Chan | Domestic wastewater treatment using batch-fed constructed wetland and predictive model development for NH 3-N removal[END_REF]Zhang et al., 2012;[START_REF] Jong | Contaminant removal in septage treatment with vertical flow constructed wetlands operated under batch flow conditions[END_REF]. In Batch modes, the oxygen transportation and consumption rate in the CW filter beds could be greatly promoted by the alternating "ponding" and "resting" phrases (Sun et al., 1999). This is closely related to sustaining aerobic conditions within CW beds for the growth of attached microorganisms biodegrading nitrogen wastes [START_REF] Chan | Domestic wastewater treatment using batch-fed constructed wetland and predictive model development for NH 3-N removal[END_REF]. In Intermittent operation, CW were filled with wastewater immediately after draining, with no "resting" phase, which limited the oxygen addition compared with the Batch modes.

In the present study, the three Batch operating regimes had different TN removal, considering the different "ponding" and "resting" period: Batch Ⅲ> Batch Ⅱ> Batch Ⅰ. As illustrated by [START_REF] Lin | Nutrient removal from aquaculture wastewater using a constructed wetlands system[END_REF] and [START_REF] Hadad | Macrophyte growth in a pilot-scale constructed wetland for industrial wastewater treatment[END_REF], nitrification and denitrification are the main microbial processes responsible for nitrogen removal in wetlands. TN removal would be enhanced with a proper anaerobic environment and sufficient carbon source for denitrification process [START_REF] Jong | Contaminant removal in septage treatment with vertical flow constructed wetlands operated under batch flow conditions[END_REF]. Therefore, the ponding and resting periods are both important for TN removal: the ponding phase promotes an oxygen-deficient microenvironment in the filter beds and ensures a sufficient wastewater residence time for denitrification, while the resting phase provides re-oxygenation conditions for nitrification after the ponding period [START_REF] Jong | Contaminant removal in septage treatment with vertical flow constructed wetlands operated under batch flow conditions[END_REF]. Furthermore, the increased ponding period from Batch Ⅰ to Batch Ⅲ allows more nutrients to be supplied for microorganisms under aerobic (early period of ponding after a sufficient rest period) and anaerobic (extended period of ponding) conditions enhancing the N removal (Sun et al., 2005).

When examining the three Batch regimes, we can conclude that Batch Ⅲ (19 h ponding, 5 h resting) showed a higher nitrogen removal through allowing maximum wastewater-substrate (i.e. biofilm) contact and promoting the oxygen transfer by drawing air from the atmosphere into filter beds when "ponding" and "resting" periods were alternating. It indicates that CW performed well with mariculture wastewater, considering Salicornia growth and organic and nitrogen removal efficiency.

However, the effects of hydraulic operating regimes on COD removal efficiency were different from those on N removal. Our results showed that in Intermittent or Batch operating regimes, removal efficiencies of COD were not improved compared with a Continuous flow regime. This agrees with the investigations of Caselles-Osorio and García (2007) and Zhang et al. ( 2012), who found no difference in COD removal of CW at different feeding strategies with synthetic and urban wastewater. However, more oxidized conditions are generally observed in Batch-fed wetlands, which therefore encourages COD removal compared with a Continuous flow [START_REF] Faulwetter | Microbial processes influencing performance of treatment wetlands: a review[END_REF]. Considering this, a study will be conducted to understand further the COD removal mechanisms, e.g. to relate the redox conditions and the substrate microbial community in CW treating mariculture wastewater under different hydraulic operating regimes to COD removal capacity.

Enzymatic activity response to mariculture effluents

Oxygen availability, organic matter and nutrient availability are common factors affecting enzyme activities in wetlands [START_REF] Baddam | Activity of soil enzymes in constructed wetlands treated with swine wastewater[END_REF]. In our study, correlations between substrate enzyme activity and nutrient concentrations (i.e. TAN, NO 3 --N, TN and COD) varied greatly (Table 4). UA had a significant negative correlation with TAN and TN concentrations, which agrees with previous investigations [START_REF] Kong | Enzyme and root activities in surfaceflow constructed wetlands[END_REF][START_REF] Cui | Evaluation of nutrient removal efficiency and microbial enzyme activity in a baffled subsurface-flow constructed wetland system[END_REF][START_REF] Baddam | Activity of soil enzymes in constructed wetlands treated with swine wastewater[END_REF]. From an ecological point of view, inverse relationships were observed between enzyme activity and nutrient availability (Sinsabaugh et al., 1993) considering the repressiondepression and end-product inhibition of enzymes [START_REF] Chrost | Environmental control of the synthesis and activity of aquatic microbial ectoenzymes[END_REF]. As an N resource for nitrification [START_REF] Dong | Soil bacterial communities in constructed wetlands treated with swine wastewater using PCR-DGGE technique[END_REF] as well as the end product of urea hydrolysis (Thorén, 2007), decreased NH 4 + concentration stimulates urease enzyme microbial production for urea hydrolyze. This also explains the higher UA in CW in a Batch operating regime: during the "resting" period, filter beds drain completely enhancing oxygen transfer to improve nitrification [START_REF] Ni | Correlation Among Soil Enzyme Activities, Root Enzyme Activities, and Contaminant Removal in Two-Stage In Situ Constructed Wetlands Purifying Domestic Wastewater[END_REF]. This is in line with the better N removal performance in Batch operation evidenced by the higher PC1 scores. Consequently, UA in the rhizosphere can be used as the major indicator to estimate N removal performance of CW in treating mariculture wastewater.

Dehydrogenase, expressing the biological oxidation processes of substrate microorganisms [START_REF] Nannipieri | The potential use of soil enzymes as indicators of productivity, sustainability and pollution[END_REF], had the highest activity in CW with Batch operating regimes (Batch I). It is known to promote the oxidation conditions in CW [START_REF] Jong | Contaminant removal in septage treatment with vertical flow constructed wetlands operated under batch flow conditions[END_REF]. Dehydrogenase, which is sensitive to oxygen levels, has been proposed to measure global soil microbial activity in aerobic conditions [START_REF] Caravaca | Microbial activities and arbuscular mycorrhizal fungi colonization in the rhizosphere of the salt marsh plant Inula crithmoides L. along a spatial salinity gradient[END_REF]. Furthermore, it has been shown that the activity and decomposition ability of dehydrogenase is dependent on organic substance availability [START_REF] Baddam | Activity of soil enzymes in constructed wetlands treated with swine wastewater[END_REF]. A more accurate representation and analysis of the relations between DA and oxygen levels, as well as the organic substance availability in CW under different operating regimes, necessitate further research. The correlation analysis in the present research suggests that DA has the potential to be an indicator in estimating the removal performance of CW in mariculture wastewater treatment.

Conclusion

This study on the nitrogen and COD removal capacity of a single-stage HFCW under different operating regimes (i.e. Intermittent, Continuous, Batch I, Batch II and Batch III) has produced the following new elements:

 CW with Salicornia have the potential to remove nitrogen and organic matters in mariculture wastewater, with nitrogen removal rates of 174.0 to 603.6 mg•m -2 •d -1 , COD removal rates of 501.9 to 1421.6 mg•m -2 •d -1 ; and 9.0 to 39.8 mg N m -2 •d -1 retained in Salicornia tissues.

 Batch III operating regime (19 h ponding, 5 h resting) gives the best performance considering removal efficiency and the removal rate of nitrogen and organic matter as well as Salicornia growth.

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 UA and DA are good potential indicators in evaluating CW performance with Salicornia in mariculture wastewater treatment: UA and DA have a negative correlation with TAN and TN concentrations, but a positive correlation with COD concentration.

To conclude, CW with a Salicornia bigelovii bed can act as a bioreactor unit to recycle mariculture nitrogen and COD effluents with the same efficiency as found in previous studies. The Batch regime showed higher nitrogen removal promoting the oxygen transfer.

However, COD operating regimes did not differ. In our study, correlations between substrate enzyme activity and nutriment concentrations varied greatly, in line with the nutrient removal performance. Our study suggests that UA in the rhizosphere can be used as an indicator to estimate N removal performance and that UA can potentially be an indicator in estimating the removal performance of CW in mariculture wastewater treatment. Further investigations are necessary to develop complex and precise expressions using UA and DA with more predictive power, and to understand the COD removal mechanisms, e.g. to relate the redox conditions, the microbial community and diversity role in CW treating mariculture wastewater. Besides, the pilot CWs in our experiment give a proof of concept, but are specific to the tested experimental conditions. Other experiments at a

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farm level taking the seasonal variations (i.e. temperature and solar energy) into account have to be conducted and will permit to validate our results.

Acknowledgements

This

2 -

 2 (A). Artificial wastewater was stored in a tank (4.65 × 2.25 × 0.60 m, W × L × H), and distributed into five barrels (D, 0.90 m; H, 0.67m); wastewater was pumped from each barrel to the three parallel CW (0.30 × 0.30 × 0.30 m, W × L × H) using peristaltic pumps. After purification by CW, wastewater drained out of the cylindrical barrel by gravity. During the experimental period, each CW had twelve individual Salicornia bigelovii plants and the flow rate was maintained at 100 ml.min -1 .The fifteen identical sequencing Batch sub-surface flow (SSF) CW microcosms (five sets × three replicates) were built as shown in Fig.1(B): Their filter beds were constructed of polypropylene random (PPR) frames, placed on a stainless steel stand above the cylindrical barrels and filled to 80 mm of clean, graded smooth cobblestone (Ø 30-50 mm) to allow a smooth sub-surface flow. The cobblestone was overlaid with a sheet of plastic mesh (0.2 mm 2 pore size) to separate the two layers and a 100 mm layer of clean haydites (Ø 5-8 mm). The first layer of haydites was covered with plastic mesh (0.074 mm 2 pore size) and a second layer of smaller haydites (120 mm, Ø 3-5 mm).2.2. Experimental designFive trials were performed simultaneously under different flow regimes, including Mode 1 (Intermittent: hydrostatic test for 6 h, four batches per day); Mode 2 (Continuous); Mode 3 (Batch Ⅰ: 12 h flooding, 12 h resting); Mode 4 (Batch Ⅱ: 16 h flooding, 8 h resting); Mode 5 (Batch Ⅲ: 19 h flooding, 5 h resting). The different flow regimes were controlled manually throughout the experiment. The CW were fed with Atlantic salmon wastewater for one year before the experiment started.2.3. Sampling and analysisWater samples were taken every week from the inlet and outlet of each CW. The pH and water temperature were measured and recorded using a YSI pH 100. The samples were refrigerated at 4℃ in labelled polystyrene bottles for chemical analysis. Water samples were analyzed for total ammonium nitrogen (TAN), nitrite (NO performed following the seawater quality standard protocol[START_REF] China | Monitoring and Determination Methods for Water and Wastewater (4e.)[END_REF]; NO 3 --N was measured using ultraviolet spectrophotometry according to Gong Z J (2005); TN concentration was analyzed through the combined digestive method described byXing D L (2006) and COD concentration was determined by the oven-heating method according to[START_REF] Shen | Determination of seawater chemical oxygen demand by oven heating[END_REF].

  multivariate data reduction technique to generate scores representing trends observed between simultaneously-measured indicators(Turnbull et al., 2005). PCA reduces the dimensionality of possibly correlated variables by using orthogonal transformation into a set of values of linearly uncorrelated variables (principal components)(Zhao & Tan, 2015). The variables addressed in the PCA were water quality index (four data sets of TAN, Nitrate, TN and COD), Salicornia growth as well as nitrogen retention in plants. The relative contribution of each variable within the different principal components (PC) was obtained along with factor scores (FS) for each of the valid PC (Eigenvalues > 1) for each treatment within the data set.

2 -

 2 regimes. The values for Intermittent and Batch modes were 25.7 ± 2.8 (Intermittent), 27.0 ± 3.9 (Batch Ⅰ), 26.0 ± 2.3 (Batch Ⅱ) and 25.3 ± 4.6 g m -2 d -1 (Batch Ⅲ) respectively. Over the experiment (78 days in total), Salicornia retained 2792.3, 2521.8 and 1935.3 mg N m -2 in Batch Ⅰ, Batch Ⅱ and Batch Ⅲ operating regimes respectively, while Salicornia under Intermittent flow retained only 633.3 mg N m -2 .3.3. Mariculture effluent purificationACCEPTED MANUSCRIPTThe influent and effluent concentrations, as well as the removal performance of TAN, NO TN are shown in Fig.2a-d and

  flow had the lowest (147.6 ± 85.3 mg m -2 d -1 ). No significant accumulation of NO 2 --N (less than 0.025 mg L -1 ) was observed in the effluent of the CW under five operating regimes. Also, no significant difference was observed for NO 3 --N removal efficiency between the five CW hydraulic regime treatments (p>0.05). However, CW with Intermittent operating regimes had an NO 3 --N accumulation (negative removal efficiency and removal rate) and CW in the three Batch operations had higher NO 3 --N removal rates (average of 126.6-229.2 mg m -2 d -1 ) compared with Intermittent and Continuous treatments (-18.1 and 14.7 mg m -2 d -1 respectively).

3. 5 .

 5 Substrate enzyme activityUA and DA throughout the experiment and their correlations to nitrogen (i.e. TAN, and organic matter (COD) concentrations are shown in Fig.4and Table4respectively. Significant differences in UA and DA were observed between Batch, Continuous and Intermittent operating treatments. With regard to the correlations, UA and DA had a significant positive correlation with COD concentrations, but a negative correlation with TAN and TN concentrations (p<0.05).

  ), who found a 1.09 mol N m -2 (i.e. 173.4 mg N m -2 d -1 ) retention in Salicornia europaea agg. in an 88-day experiment with wastewater from marine fish and shrimp in RAS. Over the same period, in the present study, the CW also removed TN (174.0 to 603.6 mg N m -2 d -1 ), which is in line with the TN removal rates of CW withSalicornia (144.2, 203.6 and 868.0 mg N m -2 d -1 ) recorded by Webb et al. (2012); Shpigel et al. (2013); Webb et al. (2013).

FiguresFig. 1

 1 FiguresFig.1The pilot CW system (A) and a single CW unit (B) (a, settlement tank: 4.65 m×2.25 m×0.60 m, W×L×H; b, cylindrical barrel: D= 0.90 m, H= 0.67 m; c, pilot wetland: 0.30 m× 0.30 m× 0.30 m, W×L×H. Mode 1: Intermittent flow operation; Mode 2: Continuous flow operation; Mode 3: Batch I; Mode 4: Batch II; Mode 5: Batch III) Fig. 2 Dynamics of TAN (a), NO 2 --N (b), NO 3 --N (c), TN (d) and COD (e) concentrations in the influent and effluent of five hydraulic operating regimes.

Fig. 3 HighlightsFigure 1 Figure 2 Figure 3

 3123 Fig. 3 Factor loading plots for principal component analysis in the experimental phase (PGR -Plant growth rate; NR -Nitrogen retention in plant; TANRR -TAN removal rate, NitrateRR -Nitrate removal rate, TNRR -TN removal rate, CODRR-COD removal rate; TANRE -TAN removal efficiency, NitrateRE -Nitrate removal efficiency, TNRE -TN removal efficiency, CODRE -COD removal efficiency) Fig. 4 Temporal values of urease (UA) and dehydrogenase (DA) activities in CW under different hydraulic operating regimes

Figure 4

 4 Figure4

Table 2 .

 2 Relatively constant reductions (26.6 ± 14.2 to 37.2 ± 13.7 %) of TAN were achieved in all CW throughout the experiment without significant difference (p>0.05). CW in Continuous and Batch Ⅲ modes had a higher removal rate(432.8 ± 219.3 and 456.9 ± 198.8 mg m -2 d -1 respectively) while CW with Intermittent

Table 3

 3

presents the principal component scores and sorting. Batch operating regimes scored higher in FS1 while Continuous flow operation scored the highest in FS2. Batch Ⅲ ranked first for the FS scores. CW with Intermittent flow had the lowest score for FS1, FS2 and FS.

  work was supported by the Projects in the National Science & Technology Pillar

	Program (2011BAD13B04); National Natural Science Fund of China (No. 31472312,
	41306152, 31402283); and The Innovation and Entrepreneurship Talents Programs of
	Qingdao (13-CX-16).

Table 2

 2 Influent concentration (IN), effluent concentration (OUT), removal efficiency (RE)and removal rate (RR) of CW under five operating regimes.

	Parameters	Operating regime	IN (mg L -1 )	OUT (mg L -1 )	RE (%)	RR (mg m -2 d -1 )
			Intermittent		0.69 ± 0.13	26.6 ± 14.2 a 147.6 ± 85.3 d
			Continuous		0.68 ± 0.11	28.0 ± 11.9 a	432.8 ± 219.3 ab
	TAN	Batch Ⅰ	0.95 ± 0.10	0.65 ± 0.12	30.4 ± 13.5 a	234.8 ± 116.7 d
			Batch Ⅱ		0.66 ± 0.10	30.1 ± 11.5 a	309.1 ± 134.0 bc
			Batch Ⅲ		0.59 ± 0.10	37.2 ± 13.7 a	456.9 ± 198.8 a
			Intermittent		1.15 ± 0.27	-6.0 ± 35.8 a	-18.1 ± 240.7 a
			Continuous		1.11 ± 0.42	1.1 ± 33.6 a	14.7 ± 705.2 a
	NO 3	--N	Batch Ⅰ	1.14 ± 0.22	0.96 ± 0.35	12.7 ± 34.8 a	126.6 ± 364.6 a
			Batch Ⅱ		0.99 ± 0.33	10.5 ± 29.4 a	133.6 ± 437.6 a
			Batch Ⅲ		0.94 ± 0.34	16.5 ± 30.8 a	229.2 ± 477.3 a
			Intermittent		2.82 ± 0.40	9.4 ± 5.8 b	174.0 ± 104.9 c
			Continuous		2.80 ± 0.47	10.4 ± 7.6 b	520.4 ± 393.2 a
	TN	Batch Ⅰ	3.12 ± 0.43	2.60 ± 0.49	16.8 ± 9.8 a	415.7 ± 218.2 ab
			Batch Ⅱ		2.65 ± 0.46	15.2 ± 7.4 ab	500.0 ± 203.4 a
			Batch Ⅲ		2.64 ± 0.38	14.9 ± 7.7 ab	603.6 ± 315.5 a
			Intermittent		1.27 ± 0.41	41.2 ± 9.9 a	501.9 ± 174.2 e
			Continuous		1.25 ± 0.59	44.6 ± 16.4 a	1421.6 ± 365.4 a
	COD	Batch Ⅰ	2.14 ± 0.57	1.44 ± 0.64	35.7 ± 20.5 a	560.7 ± 260.7 de
			Batch Ⅱ		1.46 ± 0.60	33.9 ± 16.1 a	726.0 ± 332.3 cde
			Batch Ⅲ		1.45 ± 0.61	34.0 ± 18.1 a	873.6 ± 481.1 c

Shpigel, M., Ben-Ezra, D., Shauli, L., Sagi, M., Ventura, Y., Samocha, T., Lee, J.J. 2013.

Constructed wetland with Salicornia as a biofilter for mariculture effluents.

Aquaculture, 412-413, 52-63. Sindilariu, P.-D., Schulz, C., Reiter, R. 2007. Treatment of flow-through trout aquaculture effluents in a constructed wetland. Aquaculture, 270(1), 92-104. Sinsabaugh, R.L., Antibus, R., Linkins, A., McClaugherty, C., Rayburn, L., Repert, D., Weiland, T. 1993

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