Hussein Baalbaki
email: hussein.baalbaki@ext.isep.fr

Hussein Hazimeh
email: hussein.hazimeh@ul.edu.lb

Hassan Harb
email: hassan.harb.1@ul.edu.lb

Rafael Angarita
email: rafael.angarita@isep.fr

KEMA: Knowledge-Graph Embedding Using Modular Arithmetic

Keywords: ; Knowledge Graph Embedding, Knowledge Graphs, Link Prediction, Reasoning, Modular Arithmetic

Knowledge graph is a knowledge representation technique that helps representing entities and relations in a machine understandable way. This promising trend suffers from the problem of incompleteness that was best solved by link prediction. Indeed, link prediction is the most successful method for understanding the structure of the large knowledge graphs. Knowledge graph embedding KGE is one of the best link prediction methods. Its effectiveness is mainly affected by the accuracy of learning representations of entities and relations. In this paper, we propose a new knowledge graph embedding model called KEMA ( Knowledge-graph Embedding using Modular Arithmetic). KEMA has the ability to represent simple and complex relations in an efficient way. Consequently, this allows our model to outperform the majority of the existing models. Mainly, KEMA depends on representing the relations in a knowledge graph by modular arithmetic operations applied between entities. Experimental results on multiple benchmark knowledge graphs verify the accurate representation, low complexity and scalability of KEMA.

I. INTRODUCTION

Knowledge graph (KG) rises recently as one of the best ways for knowledge representation. We have seen the construction of many KGs of different sizes, domains, and coverage, like Freebase [START_REF] Bollacker | Freebase: a collaboratively created graph database for structuring human knowledge[END_REF], Yago [START_REF] Suchanek | Yago: a core of semantic knowledge[END_REF], and WordNet [START_REF] Miller | Wordnet: a lexical database for english[END_REF]. KG is a multi-relational graph built of nodes representing real world entities such as objects and events. These entities are connected by edges representing the relations and interactions between them. KG is represented by a set of triplets that shows the relations linking the entities. KG has proven to be effective in many real-world applications like recommender systems [START_REF] Zhang | Collaborative knowledge base embedding for recommender systems[END_REF], natural language processing [START_REF] Yang | Leveraging knowledge bases in lstms for improving machine reading[END_REF], and question-answering [START_REF] Hao | An end-to-end model for question answering over knowledge base with cross-attention combining global knowledge[END_REF].

Although a KG may consist of a huge number of entities and relations, it is usually incomplete. It is impossible for a KG to cover every single entity or relation in whole world, no matter how huge this KG is. This is called the completeness problem of KG. This challenge represents one of the main issues facing KGs that researchers are working to solve. Link prediction emerges as efficient way to overcome the KG completeness problem. Subsequently, link prediction is used to predict not only the existence of a relation between two entities, but also the specific type of this relation. However, these predictions are infeasible using traditional methods. So the need for novel link prediction approaches like Knowledge graph embedding arises. Knowledge graph embedding (KGE) methods have proven to be very effective applied in link prediction. KGE embeds a KG into a continuous vector space while preserving certain information of the graph. Generally, KGE replaces any object (entity, relation, ..) with a vector of continuous numbers holding this object semantics. Mainly, KGE models differ in how these numeric vectors are used. and divided into three categories accordingly. The first one is the Translational that consider relations as a motion between entities. The second category is Tensor factorization that uses tensors for embedding vectors processing. The third category is the Neural network, in which the embedding vectors are fed to neural networks for training.

In this paper, we introduce a novel knowledge graph embedding model based on the modulus operation called as KEMA. Indeed, KEMA adopts a new way for dealing with embedding vectors away from translational, tensor factorization, and neural networks. Our model relies on the modular arithmetic mathematical operation. Since modular arithmetic is an equivalence relation, it helps handling different types of knowledge graph relations such as symmetry, inversion, and composition. Moreover, KEMA can deal with relations of complex mapping patterns like one-to-many, many-to-one, and many-to-many. To prove the effectiveness of our proposed model, we evaluate KEMA on a set of knowledge graph benchmark datasets including FB15k-237 [START_REF] Toutanova | Observed versus latent features for knowledge base and text inference[END_REF] and WN18RR [START_REF] Dettmers | Convolutional 2d knowledge graph embeddings[END_REF], and we compared the results to state-of-the-art approaches.

The rest of the paper is organized as follows. Section II gives an overview about different knowledge graph embedding models existing in the literature. Section III explains the modular arithmetic mathematical operation and its working way. Section IV presents KEMA, our proposed model. The obtained simulation results are exposed in Section VI. Finally, we conclude the paper and provide directions for future work in section VII.

II. RELATED WORK

In the literature, we can distinguish between three types of knowledge graph embedding categories [START_REF] Dai | A survey on knowledge graph embedding: Approaches, applications and benchmarks[END_REF]: (1) Translationbased models; (2) Tensor factorization-based models; (3) Neural network-based models.

A. Translation-based models

The first translational-based model is called TransE [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF]. Typically, TransE considers the relation between two entities as a translation operation in embedding space that starts by the head entity and leads to the tail. A score function f is used to compute the authenticity of the given triplet (h, r, t): f r (h, t) = |h+r-t|. Although TransE shows a high efficiency when applied in large-scale knowledge graph embedding, it still struggle when dealing with complex relations such as 1 -N, N -1, and N -N. In order to overcome such challenge, the authors of [START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF] proposed an extension of TransE called TransH. Indeed, TransH assigns a hyper-plane to each relation, so that the heads and the tails of this relation are projected to. This model enables each entity to have different embedding representations depending on the relation involved in. In [START_REF] Ji | Knowledge graph embedding via dynamic mapping matrix[END_REF], TransR focuses on the entities carrying various semantic meanings. As a result, TransR expands the relationspecific hyper-planes concept of TransH to relation-specific spaces. Compared to transE and transH, transR makes a significant performance improvement but still has some gaps. One TransR weakness is sharing one projection matrix by both head and tail. The attributes of the same entity may differ according to its position in a relation (head / tail). To solve this problem, TransD [START_REF] Ji | Knowledge graph embedding via dynamic mapping matrix[END_REF] solves this problem by creates two different projection matrices for each single relation. The first matrix is used for head projection and the other is for the tail projection. Lastly, the authors of [START_REF] Sun | Rotate: Knowledge graph embedding by relational rotation in complex space[END_REF] proposed RotatE that represents the relation between two entities as rotation motion that starts from the head entity and ends by the tail.

B. Tensor factorization-based models

The idea behind tensor factorization-based models is based on representing all the triplets of a knowledge graph in a 3D binary tensor X. Two dimensions of X are of size n, the number of the entities in KG, while the third dimension is of size m, the number of relations in KG. S r is (n * n) slice of X that represents the relation r. The index S r [head][tail] of the slice S r is filled with 1 if the relation between the head and the tail entities holds, otherwise it is filled by 0. The obtained tensor X is then broken down using factorization into a set of embedding matrices that are assigned to entities and relations. RESCAL [START_REF] Nickel | A three-way model for collective learning on multi-relational data[END_REF] uses Rank -d factorization to obtain three matrices:

X = ARA T , (1)
where A is a 2D matrix carrying the semantics of the KG entities, A T is its transpose, and R is the 3D embedding matrix of the relations in KG. Accordingly, the scoring function of a given triplet (h, r, t) is calculated as follow:

f r (h, r) = h T m r t, (2)
where h T is the transpose of h embedding vector, m r is a 2D slice of R holding the relation r embedding matrix, and t is the tail embedding vector. To reduce the calculation complexity, a simplified version of RESCAL called DistMult is proposed in [START_REF] Yang | Embedding entities and relations for learning and inference in knowledge bases[END_REF].In DistMult, any relation matrix m r , obtained after factorization is considered to be diagonal with a score function:

F = h T diag(m r )t. (3)
This step not only facilitates calculations, but it also shows improvement in terms of performance. Moreover, in order to capture the pairwise compositional representations of entities, HolE is proposed in [START_REF] Nickel | Holographic embeddings of knowledge graphs[END_REF]. Basically, HolE relies on a circular correlation with the following score function

f r (h, t) = r T (h ⋆ t) (4)
HolE reduces the composite representation complexity compared to tensor product. Lastly, ComplEx [START_REF] Trouillon | Complex embeddings for simple link prediction[END_REF] was proposed as extension of DistMult, where it closes the gap resulting from the inability of DistMult to deal with asymmetric relations by integrating a complex space as follows:

f r(h, t) = Re(h t * diag(r) -t) (5)
where Re(•) denotes the real part of a complex value, and t represents the complex conjugate of t.

C. Neural network-based models

Neural networks are used for expressing complex nonlinear projections. They become recently a hot topic used to embed a knowledge graph into a continuous feature space. Particularly, Semantic Matching Energy SME [START_REF] Bordes | A semantic matching energy function for learning with multi-relational data[END_REF] is a neural networkbased model that calculates the energy of a given triplet (h, r, t) by applying two projection matrices, M lef t is applied for the head h and the relation r embedding vectors, while M right is applied for relation r and the tail t embedding vectors. Then, the results are given to a fully connected layer that returns the score of the semantic matching energy. ConvKB [START_REF] Nguyen | A novel embedding model for knowledge base completion based on convolutional neural network[END_REF] is another model that uses convolutional neural network (CNN) to capture the latent semantic information in the triplets. In such model, the embedding vectors of the elements of a triplet are combined to form a matrix. Then, the matrix is fed to a convolution layer to produce multiple feature maps. Finally, these feature maps are concatenated and projected to a score that is used to estimate the authenticity of the triplet. Neural Association Model NAM [START_REF] Liu | Probabilistic reasoning via deep learning: Neural association models[END_REF] utilizes a deep neural network structure to represent a KG. After representing each element of a triplet by embedding vector, it concatenates the head entity vector and the relation vector to a single vector. The single vector is then fed to the next layer. Finally, NAM calculates the score by applying the output of the last hidden layer z L with the tail embedding vector t:

f r (h, t) = σ(z L t) (6)
where σ(•) is a sigmoid activation function.

III. OUR EMBEDDING MODEL: KEMA

Knowledge graph embedding is the process of representing the entities and relations of a given knowledge graph using numerical vectors. In this way, mathematical operations can be applied to these vectors in order to help studying and predicting the links connecting the entities. In this paper, we introduce a new embedding KG approach called KEMA. Indeed, KEMA does not follow any of the classifications detailed in the related work section. It relies on one simple mathematical operation called modular arithmetic. The objective of KEMA is to predict the missing links connecting the entities of a given knowledge graph. As shown in Fig. 1, first, the input knowledge graph layer receives a knowledge graph as input. Then, KEMA embedding layer processes the knowledge graph components and embeds it to a low dimension continuous space. Finally, KEMA output layer returns a representative numerical vector for every entity and relation in the KG. These representative numerical vectors are then used for predicting links between KG entities.

A. Modular arithmetic

Modular arithmetic is a system of arithmetic that replaces all the numbers by their remainders of its division to a fixed number. Subsequently, the fixed number is an integer called "modulus". In modular arithmetic, every value of modulus m can be considered as a representative space mod(m). In this space, we can represent every integer i by its remainder r resulting from its division by m, as shown in Equation [START_REF] Toutanova | Observed versus latent features for knowledge base and text inference[END_REF]. Since all the remainders of the division by m are smaller than m itself, then all the representative integers in mod(m) space are smaller than m (Equation ( 8)).

i = m * x + r ⇐⇒ r = i mod(m), ∀ i ∈ Z, (7)
r = i mod(m) ⇐⇒ r ∈] -m, m[ (8)
where m, r, x ∈ Z Indeed, an important example to illustrate the process of the modular arithmetic in this paper is 12-hour clock. In such example, the modulus value is 12 and the day is divided into two 12-hour periods. Whenever the hours count exceeds 12, it wraps around, and returns the remainder value.

Usually, modular arithmetic produces a set of integers having the same remainder when dividing by m. These integers are considered equal in the mod(m) space, and are said to be congruent (≡), as shown in Equation ( 9).

x mod(m) = y z mod(m) = y x ≡ z (9)

B. KEMA Embedding Model

The novel idea behind KEMA is to represent the relation between two entities through modular arithmetic operation. In other words, the tail embedding vector is considered to be the projection of the head embedding vector in the modular arithmetic space of the relation embedding vector, as shown in Equation [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF].

t = h mod (r) (10)
where h, t, and r represent the embedding vectors of the head, the tail and the relation respectively.

The second layer of our model is called KEMA embedding model (see Fig. 1), and it shows the way the embedding vectors are assigned for entities and relations of a given KG. KEMA starts by assigning random vectors for entities and relations. Then, it modifies these vectors in a way it satisfies the score function shown in Equation [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF]. First, every index E h [j] in the vector of the head entity E h is subjected to modular arithmetic operation of modulus r[j], the j-th index of relation r. Then, the vector of numbers obtained from this operation is assigned to the tail entity E 3 of the relation r.

C. Types of Relations

Despite the simplicity of the calculation process used in KEMA, it has proved to be highly effective and accurate compared to other models. This simplicity can also be seen in the low complexity of both training and prediction processes. As well as simple relations, KEMA can effectively handle complex relations of KG such as 1-N and N-N.

1) Simple Relations: Simple relation is that connecting no more than two entities, the head and the tail. According to the existing literature, three types of simple relation patterns are very important: symmetric, inverse, and composed patterns. All these patterns are covered by KEMA embedding model as follows:

• Symmetric Relation: This relation, switching between the head and the tail entities of a relation is possible. A relation r is said to be symmetric, if ∀x, y ∈ E, the set of entities (x, r, y) =⇒ (y, r, x)

• Inverse Relation: A relation r 2 is said to be inverse of relation r 1 whenever r 1 and r 2 have opposite directions connecting the same entities. A relation r 2 is the inverse of r 1 , if ∀x, y ∈ E, the set of entities in KG

(x, r 1 , y) =⇒ (y, r 2 , x) (12)
• Composed Relation: A relation r is said to be composed, if it can be broken down into two relations or more. A relation r is a composed relation, if ∃ r 1 , r 2 ∈ R, the set of relations in KG (x, r, z) + (z, r, y) =⇒ (x, r, y)

Where x, y, z ∈ E, the set of entities.

For Modular Arithmetic Let a, b, n ∈ Z such that:

a ≡ b(mod n) =⇒ a -b = kn, for some k ∈ Z =⇒ b -a = (-k)n and -k ∈ Z =⇒ b ≡ a(mod n)
Thus modular arithmetic is a symmetric relation.

Let a, b, n ∈ Z such that:

a ≡ b(mod n) =⇒ a -b = kn, for some k ∈ Z =⇒ b -a = (-n)k and -n ∈ Z =⇒ b ≡ a(mod k) mod(n) is inverse to mod(k). Thus modular arithmetic is an inverse relation. Let a, b, n, c ∈ Z, such that: a ≡ b(mod n) and b ≡ c(mod n). then a = b + kn, k ∈ Z and b = c + hn, h ∈ Z. a = b + kn =⇒ a = (c + hn) + kn =⇒ a = c + (hn + kn) =⇒ a = c + (h + k)n, h + k ∈ Z .
Hence a ≡ c(mod n) . Thus modular arithmetic is a composed relation. end 2) KEMA Complex Relations: The majority of the models proposed in the literature can deal with simple relations between KG entities, i.e 1-to-1 relations. However, relying on simple relationships to build knowledge is impractical. Contrarily, KEMA has the ability to handle both simple and complex relationships.

Giving a 1-to-N relationship r, the set of tails T = {t 1 , t 2 , ..t N } can share a unique head whenever all these tails are congruent in mod(r) space, Equation [START_REF] Nickel | A three-way model for collective learning on multi-relational data[END_REF]. Similarly, the set of heads H = {h 1 , h 2 , ..h N } can share the same tail whenever all these heads are congruent in mod(r) space, Equation [START_REF] Yang | Embedding entities and relations for learning and inference in knowledge bases[END_REF]. Moreover, KEMA allows the representation of N-to-N complex relationships, in which one relation can have several heads and tails at once, by combining both equations ( 14) and ( 15)

t 1 ≡ t 2 .. ≡ t N ⇐⇒ h = t mod (r), ∀ t ∈ T, (14)
h 1 ≡ h 2 .. ≡ h N ⇐⇒ t = h mod (r), ∀ h ∈ H, (15) For Modular Arithmetic Let a, b, n, c ∈ Z such that: a ≡ b(mod n) then a = b + kn, k ∈ Z =⇒ a = b + (k -c + c)n =⇒ a = b + cn + (k -c)n, k -c ∈ Z . Hence a ≡ b + cn(mod n) and a ≡ b(mod n)
Thus modular arithmetic holds for 1-N relations.

Given the 1-N relation:

a ≡ b + cn(mod n) and a ≡ b(mod n)
Since modular arithmetic is symmetric relation, then:

b + cn ≡ a(mod n) and b ≡ a(mod n)

Thus modular arithmetic can represent N-1 relations. By combining the 1-N and N-1 modular arithmetic relations, we conclude its ability to represent N-N relation, and thus modulus can represent all the complex relation patterns.

D. Analytical example

In this section, we illustrate an example to show the effectiveness of KEMA in terms of representing simple and complex relations. According to the input knowledge graph layer shown in figure 1, the sub graph shows the relations between three entities. Table I shows the embedding vectors that KEMA assigned to every entity and relation.

The relation "Spouse" is an example of the symmetric relation. In Fig. 1, the output layer of KEMA shows that this relation holds in both directions. Moreover, in Table II, the first row shows that the tail of the relation "Spouse" with head entity "Bob" is "Alice". On the other hand, the second row represents the opposite direction, where the tail of the relation "Spouse" with head entity "Alice" is "Bob". In Fig. 1, the relations "Child" and "Parent" show the inversion pattern of simple relations. In the first row of the Table III, "Alice" is the head of the relation "Child" while "Valeria" is its tail. In the opposite direction, the second row shows the relation "Parent", where "Valeria" is the head and "Alice" is the tail. Then the relations "Parent" and "Child" are said to be inverse.

Furthermore, Fig. 1 shows that the relation "Spouse" is a composed relation. Fig. 1 shows that the relation "Child" of head "Alice" and tail "Valeria", followed by the relation "Parent" of head "Valeria" and tail "Bob", can be replaced by the relation "Spouse" having the same head as "Child", and the same tail as "Parent". Indeed, the strength of KEMA in terms of representing complex relations is shown through the relations "Parent" and "Child" in Fig. 1. Since "Parent" has one head which is "Valeria", and two tails which are "Bob" and "Alice", then it is a complex relation of 1 -N mapping pattern. Whereas "Child" relation has two heads "Bob" and "Alice" connected to one tail "Valeria", representing N-1 pattern.

IV. SIMULATION RESULTS

In this section, we will show the experiment setting to implement our model followed by the discussion of the obtained results.

A. Experimental setting

To evaluate our model, we implemented KEMA using Ampligraph python library. Then, we compare it to the state-of-the-art models on two commonly used benchmark datasets: WN18RR, and FB15K-237. The main patterns of the relation in FB15k are symmetry, antisymmetry and composition [START_REF] Sun | Rotate: Knowledge graph embedding by relational rotation in complex space[END_REF]. To train and evaluate our model, we need to use negative triples, which are not available in both WN18RR and FB15K-237. As a result, we used to corrupt the positive triples of the datasets to generate negative samples for each positive. This is what is called the local closed world assumption. That is, for a triple, we randomly replace the entity in the subject or the object position by another, but not both at once.

We applied three tests to evaluate the performance of link prediction of KEMA. These tests rely on ranking each positive test triple against all its generated negatives according to its score. The first test is Mean Rank (MR) which is calculated as follow:

mean(rank t ) ∀t ∈ T

with T is the set of positive test triples, and rank t is the rank of triple t against its negatives.

The second evaluation test is Mean Reciprocal Rank (MRR). It is similar to MR, but it uses the reciprocal rank of a triple instead of its rank, what make it less sensitive to outliers [START_REF] Nickel | Holographic embeddings of knowledge graphs[END_REF]:

mean(1/rank t ) ∀t ∈ T

The last evaluation test is Hits@N, which counts the test triples having a rank less than or equal to N .

t N , where t N ∈ T, rank t N >= N

B. Main Results

In our simulation, we compared KEMA to several state-ofthe-art models including TransE [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF], DistMult [START_REF] Yang | Embedding entities and relations for learning and inference in knowledge bases[END_REF], ComplEx [START_REF] Trouillon | Complex embeddings for simple link prediction[END_REF], ConvE [START_REF] Dettmers | Convolutional 2d knowledge graph embeddings[END_REF], and RotatE [START_REF] Sun | Rotate: Knowledge graph embedding by relational rotation in complex space[END_REF]. We show the efficiency of our proposed model inferring the relation patterns for the task of predicting missing links. Tables IV shows the results of the evaluation tests of our model and the state-of-the-art models based on WN18RR and FB15K-237 datasets respectively. FB15K-237 dataset contains symmetry, anti-symmetry and composition relation patterns. The main pattern in this dataset is the composition [START_REF] Sun | Rotate: Knowledge graph embedding by relational rotation in complex space[END_REF]. The domination of the composition pattern can be inferred from the results shown in Table IV

Fig. 1 .

 1 Fig. 1. KEMA architecture.

Fig. 2 .

 2 Fig. 2. Composed relation example.

•

  WN18RR is a subset of WordNet, a KG that clusters words into synonym groups and features lexical relationships between words. It consists of 40,943 entities, 11 relation types, and 93003 triples. WN18RR contains symmetry, antisymmetry and composition relation patterns. The main pattern is the symmetry since almost each word has a symmetric relation in WN18RR, e.g., also -see and similar -to [13]. • FB15k-237 is a subset of Freebase, a large knowledge graph that stores general knowledge facts. It consists of 14951 entities, 237 relation types, and 310116 triples.

  . So that Table IV shows that the model TransE, representing composition and anti-symmetry patterns, outperforms ComplEx model representing symmetry and anti-symmetry patterns.

Furthermore, Table IV shows the superiority of KEMA over TransE, DistMult, and ComplEx in all the tests, due to its ability to perfectly represent composition and symmetry patterns. On the other hand, ConvE and RotatE surpass KEMA due to its ability to represent all the relation patterns of FB15K-237, which is composition, symmetry, and anti-symmetry.

Table IV shows the results of the evaluation tests of KEMA and the state-of-the-art models on WN18RR dataset. Similar to FB15K-237 dataset, WN18RR contains composition, symmetry and anti-symmetry relation patterns. Symmetry is the dominating pattern in this dataset. This conclusion can be easily inferred from the Table IV. So that the model DistMult, representing only symmetric relations, performs better than TransE representing both anti-symmetry and composition patterns. On WN18RR dataset, our model outperforms all the state-of-theart models. Although RotatE and ConvE both represent all the relation patterns contained in WN18RR, KEMA surpasses both models that confirms its high performance.

V. CONCLUSION AND FUTURE WORK

Link prediction is among the most prominent methods that solve the problem of incompleteness of Knowledge graph. It is used to predict the existence and the type of a relation connecting two entities. The more the knowledge graph is well represented, the more the predictions are accurate. In this paper, We proposed a novel knowledge graph embedding model (KEMA) that relies on modular arithmetic operation in representing relations between entities. KEMA applies modular arithmetic to the head entity with modulus equal to the relation vector. The main strength of our model lies in its ability to represent complex relations like one-to-many, in addition to representing symmetry, inverse, and composed simple relations. The results of our experiments show that KEMA outperforms the majority of the existing models in representation accuracy while preserving low level of complexity.

In the future work, we plan to build a complete KEMA framework that contains beside the proposed model a loss function and a suitable negative sampling method.


Didier Techer

Sylvain Milla

Damien Banas

Sublethal effect assessment of a low-power and dual-frequency anti-cyanobacterial ultrasound device on the common carp (Cyprinus carpio): a field study

Keywords: Ultrasounds, biomarkers, common carp, pond

The use of ultrasonication for cyanobacterial control in freshwater bodies has become increasingly popular during the last decades despite controversial efficiency on large scale application. Apart from that, little information is currently available regarding ultrasound toxicity potential towards non-target species. This work was designed to address this issue in the common carp using a low-power (7-9 W output) and dual-frequency (23 and 46 kHz) anti-cyanobacterial ultrasound device. Results showed that carps were unaffected by ultrasound exposure when exposed in floating cages in fish ponds over a 30-day period. The experiment duration was the main factor influencing all measured biological parameters in exposed and non-exposed organisms. Indeed, it was positively associated with an increase in fish condition factor. Cortisol level also tended to slightly increase over the number of days of experiment but its variation did not enable to sort out any ultrasound exposure-related stress. Moreover, an overall diminution along the experimental period of the expression level of a set of biomarkers could be reported, encompassing cellular antioxidant enzyme activities such as superoxide dismutase (SOD), glutathione peroxydase (GPx), catalase and glutathione S-transferase (GST), and lactate dehydrogenase activity. Subtle changes in these biomarkers were dependent of the type of enzyme activity and especially of the origin offish (i.e., sampled pond) regardless of the presence of ultrasound equipment, reflecting thereby fish adaptation to local environmental conditions in each pond. In conclusion, this study does not provide indication that ultrasonication in the aforementioned conditions affects the welfare and physiological homeostasis of carps.

1.

Introduction __________________________________________________________________

Cyanobacterial (blue-green algal) blooms frequently occur in many fish ponds, especially in fertilized ones where they can sometimes represent the major part of the total algal biomass (Sevrin-Reyssac and Pletikosic 1990). Algal blooms usually start in summer and can last until autumn subsequently to the combined effects of water eutrophication and temperature warming as light intensity increases (Sevrin-Reyssac and Pletikosic 1990). This phenomenon is often accompanied with the production of a wide range of toxins, i.e., cyanotoxins mainly in the form of intracellular organic molecules [START_REF] Paerl | Ecology of blue-green algae in aquaculture ponds[END_REF]Sevrin-Reyssac and Pletikosic 1990). These cyanotoxins maybe released in large quantities into surrounding water after cell lysis and pose a significant threat to the environment and human health [START_REF] Paerl | Ecology of blue-green algae in aquaculture ponds[END_REF]Sevrin-Reyssac and Pletikosic 1990). Various strategies for the control of harmful algal blooms including the use of biological methods (e.g., biomanipulation, allelopathic treatments), engineering processes (e.g., sediment dredging, water mixing), and physico-chemical treatments (e.g., ultrasonic radiation, copper-based algaecide application) have been proposed over the last decades [START_REF] Ahn | Growth inhibition of cyanobacteria by ultrasonic radiation[END_REF][START_REF] Barrington | The use of hydrogen peroxide to remove cyanobacteria and microcystins from waste stabilization ponds and hypereutrophic systems[END_REF]Jančula and Maršálek 2011 Recently, several laboratory-scale experiments have suggested biocidal ultrasound effects against cyanobacteria based on (i) the collapse (or implosion) of gas vesicles/vacuoles following cavitation phenomena, (ii) the occurrence of detrimental free radical reactions, (iii) the increase in photosynthetic pigment damages (particularly phycocyanin) with subsequent disruption of the photosynthetic activity, and finally the effective cyanobacterial growth inhibition [START_REF] Rajasekhar | A review of the use of sonication to control cyanobacterial blooms[END_REF]. Consequently, numerous patents have been deposited worldwide and concomitant ultrasound devices (some still in development) claiming to inhibit microalgae growth have been successively commercialized [START_REF] Rajasekhar | A review of the use of sonication to control cyanobacterial blooms[END_REF]. Marketed products usually cover a wide range of acoustic power as well as ultrasound frequencies varying from 20 kHz to 1.7 MHz [START_REF] Rajasekhar | A review of the use of sonication to control cyanobacterial blooms[END_REF]). Nevertheless, it is important to point out the inconstancies in some studies regarding the ultrasound treatment efficiency against cyanobacterial blooms [START_REF] Lürling | Beating the blues: is there any music in fighting cyanobacteria with ultrasound?[END_REF]. As a matter of fact, the lack of the system functioning details (usually protected by patents), the deficiency of a clear consensus for data format reporting often limit critical reviewing and comparisons between published results. Yet, it is usually assumed that longer exposure times to ultrasounds would result in significant cellular damages leading to cyanobacterial growth inhibition, which maybe partly due to the narrow area effectively covered by ultrasonication processes [START_REF] Rajasekhar | A review of the use of sonication to control cyanobacterial blooms[END_REF]. Regardless the uncertainties surrounding the efficacy of the currently available anti-cyanobacterial devices in situ, the large scope of application for ultrasound-based water treatment technologies, that encompasses microbial control in water treatment plants, as well as in aquaculture facilities, reservoirs, and ornamental water bodies, requires a better knowledge of their potential (eco) toxicological impacts on non-target aquatic species such as fish [START_REF] Colucci | Ultrasonic algae control literature review[END_REF][START_REF] Doosti | Water treatment using ultrasonic assistance: a review Proceedings of the international Academy of[END_REF][START_REF] Drabkova | A review of in-lake methods of cyanobacterial blooms control and management. CyanoData-The Glogal Database of Methods for Cyanobacterial Blooms Management, Centre for Cyanobacteria and their Toxins wwwcyanodatanet[END_REF]. Indeed, fish are the key component organisms of surface water ecosystems that maybe directly exposed to ultrasounds during sonication treatments. Recently, ultrasonic hearing has been reported for a number of fish species belonging to the widespread clupeidae family [START_REF] Astrup | Ultrasound detection in fish-a parallel to the sonar-mediated detection of bats by ultrasound-sensitive insects? Comparative biochemistry and physiology part a[END_REF][START_REF] Popper | Response of clu-peid fish to ultrasound: a review ICES journal of marine science[END_REF]) Moreover, fish exhibit physiological antioxidant system potentially sensitive to wave radiation and free radical reactions [START_REF] Milowska | Effect of ultrasound on nucleated erythrocytes[END_REF]. This work primary aims to investigate the potential sublethal effects on the fish physiology of a long-term exposure to ultrasounds using the common carp fish species (Cyprinus carpio) as a model. This fish species is widespread in eutrophic lakes and reservoirs in Europe and Asia and is often found in most aquaculture ponds [START_REF] Jeney | Use and exchange of aquatic resources relevant for food and aquaculture: common carp (Cyprinus carpio L.)[END_REF]. Juvenile carps were chronically exposed to a lowpower electric ultrasound device continuously emitting a dualfrequency of 23 and 46 kHz. After respectively 7 and 30 days of ultrasonication exposition, fish were sacrificed, condition factor indices were determined, and a panel of biochemical markers linked to fish physiological homeostasis were assessed, encompassing: (i) hepatic antioxidant enzyme biomarkers, i.e., total superoxide dismutase (total SOD), catalase (CAT), total glutathione peroxydase (total GPx), and glutathione S-transferase (GST) activities, (ii) lactate dehydrogenase activity related to cellular energetic metabolism, and (iii) circulating cortisol levels subsequent to stress.

2.

Material and Methods __________________________________________________________

Ethical statement

All applied treatments and procedures on fish were in compliance with the general guidelines of the Council of European Communities (European Union, No 2010/63/CEE) as well as the French Animal Care Guidelines

Ultrasound exposure system

The used ultrasound system consisted on a dual-frequency ultrasound device emitting continuous signals and powered by a solar floating platform. There were two transducers operating independently. They were immersed at a depth of around 0.5 m with one emitting at an average frequency of 23 kHz andthe otherat46 kHz. The two frequencies are simultaneously transmitted using the two transducers mounted adjacent one another, with a distance of 10 cm between them. The supplied power to the transducers was initially fixed at 15 W. According to the manufacturer (SOFCHEM; TWIN-f® derived ultrasonic system), this apparatus has been especially developed for algae growth inhibition. Other technical specificities are proprietary information but the reader can refer to a related online technical documentation for more information, http://www.sofchem.fr/antialgues_fluid_impact. htm. Moreover, details about the transmitters' directivity (unidirectional), their emission level at 23 and 46 kHz, as well as the characterization of the theoretical signal resulting from the combination of [23/46 kHz] (as measured by SinapTec Ultrasonic Technology for SOFCHEM in an 8 m × 6 m × 6.5 m fresh water basin) are illustrated in Fig. 1.The measurement of the resulting emitted acoustic signals in water was carried out using a Brüel & Kjaer Type 8103 hydrophone. This kind of calibrated waterborne-sound transducers are omnidirectional over a wide frequency range from 0.1 Hz to 180 kHz with a receiving sensitivity of211 dB re 1 V/μPa. They are generally used in a laboratory or industrial context, and they are known to be particularly suitable for acoustic investigations of marine mammals and cavitation study (more technical specificity available online at https://www. bksv.com/en/products/transducers/acoustic/microphones/ hydrophones/8103). Acompletedescription of the receiving chain used for acoustic signal measurements with the Brüel & Kjaer Type 8103 hydrophone is given in Fig. 2 3203D]. The oscilloscope was used on site whereas the BLogging Multimeter^ was used in the laboratory. The sound pressure level (SPL in dB re 1 μPa) measured by the hydrophone could be determined from a knowledge of the hydrophone free field sensitivity, the gain in the measurement system, and the amount of voltage measured according to the equation [START_REF] Au | Principles of marine bioacoustics[END_REF]:

SPL = |Mh|  G + 20 log (V)
where Mh is the free field voltage sensitivity of the hydrophone in dB re 1 V/μPa, considering that the hydrophone is connected to an amplifier of gain G in dB, and V is the voltage read off the oscilloscope (or multimeter).

Fish care and experimental design

Two-year-old common carps were procured from the fish farm-ing pond situated near the outdoor INRA facility of La Bouzule farm (Laneuvellotte, Meurthe-et-Moselle, France). Batches of no more than 50 fish were kept for a four-week acclimation-observation period into aquaculture polyester tanks previously filled with 2.8 m3 of continuously aerated tap water. Considering that neither mortality nor abnormal behavior were reported through this period, fish were then transferred in experimental ponds for further ultrasound exposure study. Experimental ponds consisted on five formerly gravel pits currently used as fish ponds. Fish in two ponds were used as controls (without any sonication treatment), and in the three others were exposed to ultrasounds. The five ponds displayed quite similar physicochemical parameters in the range of pH [8.2-9.6], conductivity [177-480 μS cm1], NO3 [0-0.02 mg L1], PO43 [0-2.64 mg L1], SO42 [13.1-39.9 mg L1], Ca2+ [17.1-61.7 mg L1], Mg2+ [5.7-9.9 mg L1], Na+ [7.6-28.9 mg L1], K+ [1.3-6.2 mg L1]. In each pond, three 1 m3 floating cages (1 m × 1 m × 1 m) with a flexible nylon netting (1 cm × 1 cm meshes) were assembled. For ponds concerned by ultrasonication, three cages were respectively at 1,10, and 30 m away from the ultrasound devices. Three cages were also introduced into the control ponds, and they were spaced by the same distances as those fixed for ultrasound treated ponds, i.e., 9 m between the first and the second cage and 20 m between the second and the third cage. Twelve fishes were randomly distributed into each cage of the different ponds. They were allowed for an additional acclimation period of 13 days in each of these experimental ponds after which ultrasound exposure started. During the whole acclimation and exposure period, fish were daily fed at 2% of the total biomass at 8 A.M. using an automatic fish feeder (with commercial food pellet, Ø 0.5 cm, Carpe extrudée-coul 3, Le Gouessant). Following the acclimation period, four fishes from each cage and at each distance of respectively 1, 10, and 30 m were sampled, corresponding to the "T0" sampling date. The same procedure was followed after 7 days (T+7) and 30 days (T+30) of ultrasound exposure; fish were also sampled accordingly in control ponds.

Fish sampling, morphometric measurements, and blood collection

At each sampling date, four fishes were randomly collected per cage, i.e., n = 4 fish per distance per pond. They were immediately anesthetized (on the inflatable boat used to reach each corresponding cage on the ponds) by immersion into tricaine methanesulfonate solution (MS-222, 0.3 g/L) buffered with 0.6 g/L NaHCO3 (Sigma-Aldrich Chemical Co., St. Louis, MO, USA). Length (cm) and weight (g) were determined in order to calculate condition factor indices according to Fulton's formula [START_REF] Nash | The origin of fulton's condition factor : setting the record straight[END_REF]):

Blood was collected in a maximum delay of 3 minutes following fish net collection and stored on ice in heparinised microtubes before centrifugation (1700 g for 25 min) at the laboratory for plasma recovery. Aliquots of plasma were then stored at 80 °C until further measurement of cortisol levels by ELISA. Following blood sampling, fish were killed by a blow to the head prior to ventral dissection using a scalpel. Then, liver fragments (~200 mg) were collected, snap-frozen into liquid nitrogen on boat and stored at 80 °C at the laboratory until further processing.

Cortisol level measurement

Measurements of circulating cortisol levels were achieved directly onto plasma samples in coating buffers according to the manufacturer's instructions (DIASource). All measurements from each fish were assayed using commercial ELISA kits (Cortisol ELISA KAPDB270, DIASource), and results were calculated from means of duplicates for each sample

Tissue processing and biomarker determination

In order to investigate more thoroughly potential adverse welfare effect following fish exposure to ultrasounds, the assessment of LDH, total GPx, CAT, total SOD, and GST activities were conducted as current enzymatic biomarkers on fish livers collected from ultrasound treated and control ponds. All chemicals required for liver homogenization and enzymatic activity determination were procured from Sigma-Aldrich Chemical Co. (St. Louis, MO, USA) and were of analytical grade. Liver homogenates were obtained after bead-beating homogenization (zirconium oxide beads equal to 2× the mass of sample) in 2 mL screw-cap microcentrifuge tubes using a Bullet Blender [START_REF] Hoyt | Rapid, high-throughput homogenization of embryonic or larval zebrafish (Danio rerio) Nature Protocol Exchange Jančula D, Maršálek B (2011) Critical review of actually available chemical compounds for prevention and management of cyanobacterial blooms[END_REF] in five volumes of 100 mM Tris buffer (with 1 mM EDTA, 150 mM KCl, pH 7.8, 4 °C). The homogenates were centrifuged 10,000× g, 15 min at 4 °C, and the resulting supernatants (S9 fractions) were used for further protein content and enzyme activity determination in microtiter plate format with a Labsystem Multiskan EX microplate reader [START_REF] Techer | Acute toxicity and sublethal effects of gallic and pelargonic acids on the zebrafish Danio rerio[END_REF]. Protein content was determined on appropriate S9 fraction dilutions according to the method of [START_REF] Smith | Measurement of protein using bicinchoninic acid[END_REF]) (Thermo Scientific Pierce bicinchoninic acid (BCA) Protein Assay kit, No. 23225) with bovine serum albumin as the standard. Absorbances were read at 595 nm after an incubation period oß 0 min at 37 °C. Total SOD activity (EC 1.15.1.1) was measured by using Dojindo's highly water-soluble tetrazolium salt, WST-1 (2-(4-Iodophenyl)-3 -(4-nitrophenyl)-5-(2,4-disulfophenyl)-2Htetrazolium, monosodium salt) coupled with the xanthine oxidase activity (Sigma-Aldrich 19160 SOD determination kit) [START_REF] Peskin | A microtiter plate assay for superoxide dismutase using a water-soluble tetrazolium salt (WST-1)[END_REF]. One unit of SOD was defined as the amount of enzyme required for inhibiting WST-1 oxidation by 50% per minute. CAT assay (EC 1.11.1.6) was performed in microtiter plates using with 10 mM hydrogen peroxide as substrate [START_REF] Techer | Acute toxicity and sublethal effects of gallic and pelargonic acids on the zebrafish Danio rerio[END_REF]. One unit of CAT activity corresponded to the amount of H2O2 (in μmoles) decomposed per minute (with ɛ240 = 0.0394 cm2 μmole1). Total GPx activity (EC 1.11.1.9) was measured by the indirect method of [START_REF] Drotar | Evidence for glutathione peroxidase activities in cultured plant cells[END_REF]) using cumene hydroperoxide as substrate. One unit of GPx activity was defined as the amount of enzyme catalyzing the oxidation of 1 nmol of NADPH per minute. LDH activity (EC 1.1.1.27) was determined according to the protocol of [START_REF] Jesus | Lethal and sub lethal effects of the biocide chlorhexidine on aquatic organisms[END_REF]) with slight modifications as described in [START_REF] Techer | Acute toxicity and sublethal effects of gallic and pelargonic acids on the zebrafish Danio rerio[END_REF]. One unit corresponded to the amount of enzyme hydrolyzing one nanomole of NADH substrate per minute. The activity of GST (EC 2.5.1.18) was measured following the method of (Habig and Jakoby 1981) using 1-chloro-2,4-dinitrobenzene (CDNB) as substrate. One unit of GST activity was defined as the amount ofenzyme required to conjugate 1 nmol of CDNB perminute. All enzyme activity determinations were performed at 25 °C, and the wavelengths used for total GPx, GST, and LDH assays were 340 nm, whereas for SOD and CAT it was respectively fixed at 450 and 240 nm. For a defined sample, each enzyme activity was determined in duplicate from two different aliquots of the same liver homogenate sample, and finally expressed as U/mg protein.

The mean obtained from these measurements were then used for further calculations.

Data treatment and statistical analysis

All data were expressed as mean ± SE. Box-Cox power transformation was applied, and the assumption of normality and homogeneity of variance were checked using the Shapiro-Wilk test and the Browne-Forsythe test, respectively. Then, data from fish sampled from control and ultrasoundexposed ponds regarding the effects of the exposure period (0, 7, and 30 days of fish exposure in ponds), the distance (1, 10, and 30 m from ultrasound source), the ultrasound exposure scenario (presence/absence of ultrasonication), and the inherent environmental variability of ponds (ponds considered as a nested factor within the Bultrasound exposure^ factor) were analyzed using hierarchical (nested) ANOVA, followed by the Tukey multiple comparison procedure. Data were finally grouped according to the significance of factors as determined by nested ANOVA for a better clarity on histogram representation. All statistical analyses were carried out at an initial level of significance of p < 0.05, using Statistica v.10 software.

3.

Results and Discussion ________________________________________________________

According to the literature, the use of ultrasonication for water treatment purposes presents the advantage of the mechanical effects (due to vibrational resonance), leading to the cavitation and to cellular membrane dislocation with biochemical alterations such as oxidative damages that can inhibit cyanobacterial growth [START_REF] Rajasekhar | A review of the use of sonication to control cyanobacterial blooms[END_REF][START_REF] Shankar | Potential adverse ultrasound-related biological Effects: a critical review[END_REF]. To our knowledge, the present study is the first one addressing the issue of non-specific adverse health effects of an ultrasound device by measuring after along-term exposure to ultrasounds physiological indicators of stress (including condition factor and circulating cortisol level) as well as specific cellular biomarkers (namely, enzyme activity modulation) in a commonly farmed fish species.

In situ measurement of acoustic signals in ultrasound treated ponds

Data recovery from ultrasound devices at the end of experiments revealed that ultrasonication had actually occurred for an average of 22.5 h per day (continuously transmitted signals) in the exposed ponds owing to the specially engineered floating solar power-driven platforms. With a nominal power fixed at 15 W but reaching an effective level of 11 to 12 W in situ (depending on solar illumination), an average output power of 7 to 9 W (which was the effective electrical power provided to the transmitting transducers) could be recorded according to the on-board driver cards connected to both transducers. This power was sufficient for ultrasonication occurring at both frequencies of 23 and 46 kHz on average respectively in each pond. As reported in Table 1, peak to peak voltage dropped from 145 ± 18 mV at a distance of 1 m in front of the transducers to about 62 ± 30 mV at 10 m away from the emission source. Measured voltage kept on decreasing according to the distance from transducers, leading to a lowest value of 18 ± 9 mV at 30 m (Table 1). Thus, depending on the distance from the ultrasound transmitters (Table 1), the observed decrease of the acoustic signal level was not always consistent with a spherical divergence law-i.e., the signal amplitude should have been in first approximation always inversely proportional to the range to the source. Indeed, the decrease in peak to peak voltage between 10 and 30 m was observed with a ratio of 3 on amplitude (Table 1). Taking this into account, one should have expected values around 600 mV at 1 m (with a corresponding predicted SPL value of 215 dB, according to the equation from [START_REF] Au | Principles of marine bioacoustics[END_REF]), whereas only 145 ± 18 mV (and ~187 dB SPL, Table 1) were reported at this distance from the ultrasound transducers (Table 1). A hypothesis maybe that the measurements were done outside the main radiation lobe: this risk decreases with range (for obvious geometrical reasons); hence, it leads to a better measurement accuracy at 10 and 30 m of distance from the emission source. Data transformation in terms of sound pressure levels also reflected a significant loss of acoustic pressure level along the distance gradient, with recorded values varying from 187.7 (highest measured value at 1 m) to 152.6 dB SPL (lowest measured value at 30 m) (Table 1).

According to the literature, pressure level in the range of 180 dB re 1 μPa would not constitute a noticeable underwater Bnoise pollution^ [START_REF] Lurton | Analyse des risques pour les mammifères marins liés à l'emploi des méthodes acoustiques en océanographie[END_REF]. The observed diminution in peak to peak voltage as measured with the hydrophone may be largely due to the arrangement of theultrasound devices in water and to the pond configuration. Indeed, such decreases may be explained by common physical phenomena which are (1) the divergence of the wave surface when propagation range increases, and (2) the absorption of sound waves inside the surrounding medium (visco-thermo-chemical effect). Regardless the diminution in sound pressure level, in the framework of an ecological risk assessment any potential disturbance in normal fish physiology has to be sorted out prior to any large scale use of such an ultrasound technology

Fish condition factor and cortisol levels

Fish are well-known to display a broad range of physiological, behavioral as well as biochemical responses and adaptation following repeated and long-term exposure to environmental stressors [START_REF] Barton | Stress in fishes: a diversity of responses with particular reference to changes in circulating corticosteroids[END_REF][START_REF] Reinert | Biological indicators of stress in fish transactions of the American[END_REF]). In a previous laboratory experiment, [START_REF] Zimba | Ultrasound tested in channel catfish production systems[END_REF] reported that channel catfish fingerlings exposure to continuously emitting ultrasound sources drastically altered their feeding behavior (without mentioning sonication details). Nevertheless, this phenomenon was reversed when ultrasound equipment was turned off, thereby suggesting a reversible stressful effect of ultrasonication in a natural setting. Thus, as a starting point for a whole-body stress response investigation, condition factor was determined for all ultrasound exposed and non-exposed organisms at each sampling date (Fig. 3). Results indicated that the exposure period was the only factor affecting fish growth and global health condition (Table 2). As illustrated in Fig. 3, longer exposure period was associated with higher fish condition indices regardless treatment modality (i.e., ultrasound treated ponds vs non-treated ones), leading to the assumption that carps were not deterred at all from feeding with the designed ultrasound devices. Moreover, concern variations of circulating cortisol levels (Table 2, Fig. 4), these latter were mainly affected by: (i) exposure period (Table 2) with an overall higher cortisol production concomitant to a longer fish rearing period into cages (Fig. 4a), and (ii) distance (Table 2) with more elevated plasma hormone concentrations in fish sampled in the first cage series (at 1 m from ultrasound transducers) followed by those sampled at 10 m away and finally at 30 m away regardless the presence of an ultrasound device (Table 2; Fig. 4a,a′). The analyses also indicated slight variations depending on the studied pond (Table 2) but multiple comparison procedure did not enable to sort out any significant difference among treated and non-treated ponds. Since carp biomass was kept on increasing along the experimental period in all ponds (as reflected by enhanced condition factors during the exposure period), and taking into account that fish biomass per cage was well below the recommended maximum density of 150 kg m3 for this species [START_REF] Schmittou | Guidelines for Raising Principally Omnivorous Carps, Catfishes and Tilapias in Cages Suspended in Freshwater Ponds, Lakes and Reservoirs[END_REF], these observations would indicate that cortisol levels were altered by rearing conditions stricto sensu, notably by the confinement into the cages, rather than by environmental disturbances inherent to pond variability. As common carps are forage fish species, one may hypothesize that prolonged caging (up to 30 days in floating cages) would have been sufficient to stimulate stress-related hormone production in our experimental conditions. Indeed, cortisol is a major stressed-produced hormone invertebrates, and itis usually released proportionally to the magnitude and duration of the stressor [START_REF] Barton | Stress in fishes: a diversity of responses with particular reference to changes in circulating corticosteroids[END_REF][START_REF] Reinert | Biological indicators of stress in fish transactions of the American[END_REF]). However, it has to be pointed out that increases in plasma cortisol levels are an adaptive physiological response which is not systematically detrimental for the whole-animal performance and maintenance of the homeostatic mechanisms at longterm [START_REF] Barton | Stress in fishes: a diversity of responses with particular reference to changes in circulating corticosteroids[END_REF], and this has been herein illustrated by better carp growth condition indices (Fig. 3). Moreover, the observation that overall cortisol levels were quite lower in fish sampled at 30 m could be associated with the fact that these individuals were usually the last ones being sampled. By this way and because plasma cortisol level can occur rapidly, i.e., in delay of 3 min [START_REF] Nematollahi | Transcript levels of five enzymes involved in cortisol synthesis and regulation during the stress response in common carp: relationship with cortisol general and comparative[END_REF], one may easily hypothesized that fish from a longer distance of 30 m would have been already adapted to the stress consecutive to boat navigation onto water surface and sampling, leading to Breadjustment^ of cortisol concentrations to lower basal values for these distances (Fig. 4)

Enzymatic biomarker evaluation

In order to clear out more thoroughly potential sublethal effects following long-term ultrasound exposure, enzymatic biomarkers related to oxidative stress regulation (SOD, GPx, CAT) as well as biotransformation (GST) and cellular energetic metabolism (LDH) were measured on liver homogenates of both control and exposed fish (Fig. 5). The use of such a panel of cellular biomarkers is especially convenient in order to detect early organism alteration before it affects higher levels of biological organization with potentially irreversible ecological consequences [START_REF] Cossu-Leguille | Aquatic biomarkers[END_REF][START_REF] Van Der Oost | Fish bioaccumulation and biomarkers in environmental risk assessment: a review[END_REF]. Moreover, assessing the evolution of biomarker variation over time allows for a better understanding of the way that exposed fish may respond and adapt to the environmental stressors [START_REF] Cossu-Leguille | Aquatic biomarkers[END_REF][START_REF] Van Der Oost | Fish bioaccumulation and biomarkers in environmental risk assessment: a review[END_REF]. As illustrated in Fig. 5a,b,c,d,e, the main factor influencing biomarker changes was the exposure period (Table 2: nested ANOVA, p < 0.001 for SOD, GPx, CAT, GST, and LDH activities). Overall, enzymatic activities tended to decrease overtime and to stabilize at the end of experiments around an average value dependent of the type of enzyme assessed, regardless the application of an ultrasonication treatment (Fig. 5a, b, c, d, e andTable 2: nested ANOVA). The absence of any ultrasound effect was reinforced by the fact that the Bdistance^ factor (especially from ultrasound treated ponds) did not influence at all enzymatic activities variation (Table 2: nested ANOVA). Fish were affected to a lesser extent by the origin of the experimental pond itself (Table 2: nested ANOVA), meaning that the initial environmental variability occurring at each pond was the second main factor governing biomarker evolution over time. Moreover, as depicted in Fig. 5a′, b′, c′, d′, e′ following the multiple post-hoc test procedures, no specific trend could be reported when comparing fish enzymatic activities from different ponds. In other words, the results dealing with fish from control and/or exposed ponds could significantly differ from each other depending on the measured enzymatic activity which could lead to a completely dissimilar kinetics of change when focusing the attention on one category of enzyme to another (Fig. 5a′, b′, c′, d′, e′). SOD, GPx, CAT, and GST are four major enzymes of the fish's antioxidant defense system which can give early warning on sublethal effects involving reactive oxygen species (ROS) formation [START_REF] Cossu-Leguille | Aquatic biomarkers[END_REF][START_REF] Hermes-Lima | Oxygen in biology and biochemistry: role of free radicals[END_REF]. LDH has been also shown to be useful as an indicative effect criterion in aquatictoxicology [START_REF] Diamantino | Lactate dehydrogenase activity as an effect criterion in toxicity tests with Daphnia magna straus[END_REF]). Thus, these five categories of enzymes were chosen as biomarker of effects so as to give early warning about putative cell damages following ultrasound exposure. Indeed, ultrasounds are likely to produce thermal and mechanical effects, particularly in the focal area of the beam waves where they can lead to acoustic cavitation [START_REF] Shankar | Potential adverse ultrasound-related biological Effects: a critical review[END_REF]. This latter may be roughly defined as the interaction of ultrasounds with gas bubbles which can cause rapid and important changes in bubble size, and is often accompanied with an increased local temperature (up to 1000 °C) as well as ROS formation [START_REF] Rajasekhar | A review of the use of sonication to control cyanobacterial blooms[END_REF][START_REF] Shankar | Potential adverse ultrasound-related biological Effects: a critical review[END_REF]. Cavitation is favored at a long wavelength, i.e., at a low ultrasound frequency [START_REF] Rajasekhar | A review of the use of sonication to control cyanobacterial blooms[END_REF][START_REF] Shankar | Potential adverse ultrasound-related biological Effects: a critical review[END_REF]. Within this context, our results would indicate that carps were preserved from oxidative stress, and most probably from any adverse health effect resulting from mechanical ultrasound processes utilizing the low-power dual frequency ultrasound equipment.

4.

Conclusion __________________________________________________________________

In this study, ultrasonic acoustic signal measurements suggested a rapid decrease of acoustic power in such an open environment like aquaculture pond. Moreover, results did not reveal any adverse health effect of concomitant fish ultrasound exposure to both 23 and 46 kHz frequencies over a 30-day period. Indeed, the determination of condition factor variations suggested aconstant fish growth all over the experimental period. Besides, cortisol levels increases were affected by the duration of the experiment and distance between cages, which may be attributed to fish rearing and sampling conditions. The assessment of specific biochemical markers of cellular effects in the form of antioxidant enzymes and lactate dehydrogenase activity showed a global decrease of enzyme activities over time, with slight and local variations depending on the considered pond, thus suggesting a fish adaption to different environmental conditions in each pond regardless the exposure to ultrasounds. Further assessment of the sublethal effects of ultrasonication under various cyanobacterial bloom conditions (with potential cyanotoxin releases) would be required to completely warranty the eco-friendly properties of such a technology. References ___________________________________________________________________

Figure 1 .Figure 1 .

 11 Figure 1. Characterization of the ultrasonic sensor emission, as provided by SOFCHEM: a Directivity. b Sensitivity to the emission (transducer Lo). c Sensitivity to the emission (transducer Hi). d Signal acquisition using the hydrophone equipment (Brüel & Kjaer type 8103)

Figure 3 .Figure 4 .

 34 Figure 3. Condition factor assessment in fish at T0, T+7, and T+30 days of experiment in control (Ct) and ultrasoundexposed (Exp) ponds.

Table 1 . Acoustic signal level measurements in ultrasound treated ponds as a function of distance from transducers. Data are expressed as mean ± SE for peak to peak voltage (in mV; read from a digital multimeter coupled to a hydrophone) whereas ranges of sound pressure level (SPL) are reported in decibel (dB SPL)

 1

	Distance from ultrasound source (m)
		1	10	30
	Peak to peak voltage	145 ± 18	62 ± 30	18 ± 9
	(mV) Sound pressure level	187.4-187.7 158.6-185.3 152.6-175.1
	range (dB SPL)

Acknowledgements ____________________________________________________________

The authors would like to thank especially Vincent Dufour and Y. Ledore, A. Iuretig, and N. Boulez for their technical assistance. This work was financially supported by Région Lorraine and SO.GE.EAU. The authors also greatly thank P.O. Jost and J. Jost (Sofchem society) for their valuable help regarding the conception, use, and lending of ultrasonic devices