Christophe Rigaud
email: christophe.rigaud@univ-lr.fr

Van Nguyen
email: nhu-van.nguyen@univ-lr.fr

Jean-Christophe Burie
email: jean-christophe.burie@univ-lr.fr

Confidence criterion for speech balloon segmentation

This short paper investigates how to improve the confidence of speech balloon segmentation algorithms from comic book images. It comes from the need of precise indications about the quality of automatic processing in order to accept or not each segmented regions as a valid result, according to the application and without requiring any ground truth. We discuss several applications like result quality assessment for companies and automatic ground truth creation from high confidence results to train machine learning based systems.We present some ideas to combine several domain knowledge information (e.g. shape, text, etc.) and produce an improved confidence criterion.

I. INTRODUCTION

Digital comic content is produced to facilitate transport, reduce publishing cost and allow reading on screens from television to smartphones like newspapers and other documents. To get a user-friendly experience of digital comics on all mediums, it is necessary to extract, identify and adapt comic book content originally designed for paper printing [START_REF] Augereau | A survey of comics research in computer science[END_REF]. Comic book image content is composed of different textual and graphical elements such as panel, balloon, text, comic character and background.

The speech balloon is a major link between graphic and textual elements. They can have various shapes (e.g., oval, rectangular) and contours styles (e.g., smooth, wavy, spiky, partial, absent). Speech balloons entirely surrounded by a black line (closed) have attracted most of the researches so far. They were initially based on region detection, segmentation and filtering rules [START_REF] Arai | Method for real time text extraction of digital manga comic[END_REF], [START_REF] Ho | Panel and Speech Balloon Extraction from Comic Books[END_REF] and evaluated on small privates datasets. Liu et al. [START_REF] Liu | A clump splitting based method to localize speech balloons in comics[END_REF] proposed a clump splitting based localization method which can detect both closed and open speech balloons. They performed the evaluation on the eBDtheque [START_REF] Guérin | eBDtheque: A representative database of comics[END_REF] dataset using recall and precision metrics.

In addition, Liu et al. [START_REF] Liu | Textaware balloon extraction from manga[END_REF] and Rigaud et al. [START_REF] Rigaud | Text-independent speech balloon segmentation for comics and manga[END_REF] proposed approaches making use of text contained in speech balloons for segmenting speech balloon contours at pixel level. They both used the same evaluation metric (recall and precision) and dataset (eBDtheque) with a little difference that Rigaud et al. computed a confidence value within their contour candidate filtering operation.

All these approaches have been tested on datasets which give indication about how well they perform and make comparison possible with new researches. However, they can

cShape = 0.92% cShape = 0.22% cLex = 0.95% cLex = 0.00%
not give an indicator on a single detection out of the tested dataset, except [START_REF] Rigaud | Text-independent speech balloon segmentation for comics and manga[END_REF]. Private companies may not be satisfied by such evaluation because published datasets may not exactly reflect their private dataset characteristics. Moreover, a confidence value associated to each detected element would be helpful for deciding if it fits their requirements or requires extra processing.

In this paper we propose an improvement of an existing confidence criterion for speech balloon segmentation quality.

II. PROPOSED METHOD

We define the speech balloon segmentation confidence criterion as a score between zero and one encoding the confidence of each segmented region similarly to the confidence value introduced in [START_REF] Rigaud | Text-independent speech balloon segmentation for comics and manga[END_REF]. In [START_REF] Rigaud | Text-independent speech balloon segmentation for comics and manga[END_REF], the confidence value is based on two weighted variables such as the contained text (all connected components) alignment cAlign and segmented region shape cShape. We propose to strengthen the first parameter initially based on alignment features (distance and position analysis of neighbouring connected components) by replacing it by the confidence value computed from at least one Optical Character Recognition (OCR) system. OCR systems take into account a lot of features to recognise characters, words and text lines from images (e.g. alignment, shape, size, spaces, contrast) which increases their results reliability. Such systems usually provide a confidence value associated to each results (classification likelihood) but in-stead of using it , we preferred to use a readily observable quantity that correlates well with true accuracy of the recognized text as describe in [START_REF] Rigaud | Segmentation-free speech text recognition for comic books[END_REF]. This metric was originally proposed to compare OCR system output performances but in our case, we use it as an OCR independent indicator about the OCR output quality. We compute, for each OCR token, the minimum edit distance (Levenshtein distance) to its most probable lexical equivalent from a lexicon of the corresponding language (e.g. Grammalecte, WordNet). The sum of these distances d over all tokens is, therefore, a statistical measure for the OCR output, and the lexicality defined as cLex = (1 -mean Levenshtein distance per character ratio) is a measure for accuracy.

The second term cShape, as described in the original publication [START_REF] Rigaud | Text-independent speech balloon segmentation for comics and manga[END_REF], encodes the overall convexity of the balloon outline in order to find how similar to a perfect bubble (or rectangle) the balloon candidate is. It is defined as the ratio between the Euclidean perimeter of the convex hull of the measured shape S and the Euclidean perimeter of the measured shape S as follows:

cShape = arcLength(hull(S)) arcLength(S) (1)
The original Equation ( 2) from [START_REF] Rigaud | Text-independent speech balloon segmentation for comics and manga[END_REF] becomes as follows when we replace cAlign by cLex:

C = α × cLex + β × cShape (2)
The best weighting parameter values were validated as α = 0.75 and β = 0.25 in [START_REF] Rigaud | Text-independent speech balloon segmentation for comics and manga[END_REF] (α + β = 1). However, because cLex is based on really different features compared to the original cAlign parameter, they both need to be revalidated according to the desired application. The main advantage of replacing the alignment-based measure by a OCR-based measure is that it is much more reliable to detect the presence of text with a high confidence inside segmented regions, thanks to the growing progress of OCR systems [START_REF] Breuel | High performance text recognition using a hybrid convolutional-lstm implementation[END_REF]. However, if the OCR system is not able to recognize a part of text because it is written with an "unseen" typewritten font or handwritten style, it will result in a poor confidence score even if the segmentation region is a true positive. Also, words may be recognized as others, or with minor errors and still get a good confidence score in some cases. An example of the proposed confidence criterion is given Table I. In this table, segmented contours are represented in cyan and convex hulls in red in the first row. Wrong transcriptions are highlighted in red in OCR output in the second row. Corresponding confidences are given in the last row.

III. CONCLUSION

This short paper investigates how to compute a confidence criterion that can indicate speech balloon segmentation quality without requiring any ground truth. It relies on comics domain knowledge i.e. bubble-like shape and text content.

It may be suitable for continuous quality control in large digitization and indexation processes or automatic ground truth generation for machine learning techniques.

In the future, we would like to investigate other features that can improve further the quality of such confidence criterion. The combination with external information like the position in the panel and the overlap with other elements could be other sources of information to aggregate.

Table I EXAMPLES

 I OF CONFIDENCE CRITERION FOR CORRECT AND WRONG BALLOON SEGMENTATION.

	ALL RIGHT,	(i -.
	BRAD	. ,
	WHANK you!

ACKNOWLEDGMENT This work is supported by Research National Agency (ANR) in the framework of 2017 LabCom program (ANR 17-LCV2-0006-01), CPER NUMERIC program funded by the Region Nouvelle Aquitaine, CDA, Charente-Maritime French Department, La Rochelle conurbation authority (CDA) and the European Union through the FEDER funding.


Faten Mkacher
email: faten.mkacher@imag.fr

Andrzej Duda
email: andrzej.duda@imag.fr

Calibrating NTP

Keywords: time synchronization, Network Time Protocol (NTP), one-way delay, accuracy and precision

In this paper, we propose a method of improving the accuracy of NTP time synchronization by taking into account asymmetric transmission delays due to different bandwidth or routing on the forward and backward paths. The method consists of calibrating NTP synchronization by: i) deploying a time box with a GPS clock at a given client, ii) measuring the oneway transmission delay on the forward and backward path and finding the minimal delays, iii) using the minimal delays in the estimation of the clock offset at the client to take into account path asymmetry, and iv) recalibrating if routes change. The paper first reports on the measurements of one-way transmission delays between a client and a server interconnected by several routers. We then use the parameters of the delay distributions to estimate the clock offset at the client. To validate the proposed method, we have compared the clock offsets computed by standard NTP and calibrated NTP based on the GPS time reference. The measurements show significant improvement of the NTP time synchronization accuracy and precision.

I. INTRODUCTION

The Network Time Protocol (NTP) is one of the most widely used protocols for clock synchronization [START_REF] Mills | The Network Time Protocol (NTP)[END_REF], [START_REF] Mills | Network Time Protocol Version 4: Protocol and Algorithms Specification[END_REF]. NTP uses UDP over packet-switched networks to synchronize clocks between one or several time servers and clients. NTP defines several modes of operation, the client/server mode being the most commonly used one. In this mode, a client sends a request containing a timestamp to a time server that replies providing two other timestamps. The two-way packet exchange with timestamps allows estimating the time offset between the client and the server.

The precision of NTP time synchronization depends on the validity of the assumption related to symmetric transmission delays between the client and the server. If this assumption does not hold, which is a common case in the current Internet, the NTP synchronization scheme results in significant errors.

Freris et al. [START_REF] Freris | Fundamental Limits on Synchronizing Clocks over Networks[END_REF] showed that asymmetry cannot be measured in a pairwise synchronization system based only on recorded timestamps, even with an infinite number of round trip measurements. Due to this fundamental limitation, neither NTP nor Precision Time Protocol (PTP, IEEE 1588) can mitigate the error in the clock offset due to asymmetry without some estimation of one-way delays. Nevertheless, several authors proposed ways of accuracy improvement by estimating delay asymmetry coming from different bandwidth on the forward and backward paths [START_REF] Gotoh | Improvement of NTP Time Offset under the Asymmetric Network with Double Packets Method[END_REF], [START_REF] Tsuru | Estimation of Clock Offset from One-Way Delay Measurement on Asymmetric Paths[END_REF], [START_REF] Lee | An Enhanced IEEE 1588 Time Synchronization Algorithm for Asymmetric Communication Link using Block Burst Transmission[END_REF], [START_REF] Schriegel | Enhancement for a Clock Synchronization Protocol in Heterogeneous Networks[END_REF], [START_REF] Exel | Mitigation of Asymmetric Link Delays in IEEE 1588 Clock Synchronization Systems[END_REF], [START_REF] Lévesque | Improving the PTP Synchronization Accuracy under Asymmetric Delay Conditions[END_REF], [START_REF]A Survey of Clock Synchronization Over Packet-Switched Networks[END_REF], [START_REF] Hajikhani | A Recursive Method for Clock Synchronization in Asymmetric Packet-Based Networks[END_REF].

Asymmetric transmission delays are common in the Internet. Pathak et al. [START_REF] Pathak | A Measurement Study of Internet Delay Asymmetry[END_REF] studied one-way transmission delays on the PlanetLab testbed and showed that i) asymmetry is quite prevalent and ii) it can be attributed at least in part to the asymmetry in routing paths. They also presented conclusive evidence that delay asymmetry is a dynamic property that varies depending on routing dynamics.

In this paper, we propose a method of improving the accuracy of NTP time synchronization by taking into account asymmetric transmission delays due to different bandwidth or routing on the forward and backward paths. The method consists of: i) deploying a time box with a GPS clock at given client premises (we assume that the server has an accurate time source), ii) calibrating-measuring the one-way transmission delay on the forward and backward path and finding the minimal delays, iii) using the minimal delays in the estimation of the clock offset at the client to take into account path asymmetry, and iv) detecting changes in operating conditions to re-calibrate.

After calibration, the client does not longer use the time box and relies on NTP synchronization with a modified expression for the time offset. The proposed method requires re-calibration-when the operating conditions (e.g., routing) change between the client and the server, which we can detect with the ping and traceroute tools, we need to redo calibration to find the new parameters of the one-way transmission delay.

The motivation for calibrating NTP comes from SCP-Time [START_REF] Minalogic | Gorgy Timing SCPTime Box[END_REF], a research project on the dissemination of the certified legal time required in many forms of commercial transactions or applications. Through SCPTime, Gorgy Timing will provide time synchronization services to various clients with different precision over various protocols including NTP over the Internet.

In this paper, we first recall the principles of NTP time synchronization (Section II) and report on the measurements of one-way transmission delays between a client and a server interconnected by several routers (Section III). We present the histograms of the delays for different hours of a day. The shape of the delay distributions corresponds to a constant and a variable random part. We then use the parameters of the delay distributions to estimate the clock offset at the client (Section IV). Unlike many papers that validate proposed schemes with simulations, we perform measurement experiments to compare the clock offsets computed by standard NTP and calibrated NTP based on the GPS time reference (Section V). The measurements show significant improvement of the NTP time synchronization accuracy and precision. Finally, we discuss some related work (Section VI) and conclude (Section VII).

1 2 3 Client C c = t + 𝜃 1 2 Server t 1 1 1 2 1 2 T f 1 t 1 2 t 2 1 t 2 2 t 4 1 t 4 2 t 3 1 t 3 2 T f 2 T b 1 T b 2 C s = t

II. BASICS OF NTP

Fig. 1 presents the principle of NTP time synchronization in client/server mode. We adopt the standard NTP assumptions: the server has a perfect clock C s = t and the client wants to synchronize its clock C c = t + θ with the server, θ being the time offset between the client and the server.

Time synchronization relies on the two-way packet exchange. In general, the client can send n NTP requests to the server that responds with n responses (n = 2 in Figure 1; the implementation we use, can send up to 8 requests). The instants of sending and receiving packets are recorded and included in NTP packets: with packet j, the client learns timestamps t j 2 , t j 3 and knows timestamps t j 1 , t j 4 . Note that the client records timestamps according to its clock C c .

We denote forward (from the client to the server) and backward (from the server to the client) one-way transmission times: T j f and T j b . If we assume that the clock drift during the exchange is constant, we have the following relations:

t j 2 = t j 1 + T j f -θ j , j = 1, ..., n, (1)
t j 4 = t j 3 + T j b + θ j , j = 1, ..., n. (2)
If one-way transmission times are symmetric (T j f = T j b ), the time offset becomes:

θ j = (t j 2 -t j 1 ) + (t j 3 -t j 4 ) 2 , j = 1, ..., n. (3)
NTP uses this equation to compute the time offset.

In general, one-way transmission times are asymmetric (T j f = T j b ) and vary in time (T j f = T j+1 f

). In this case, the time offset becomes:

θ j = (t j 2 -t j 1 ) + (t j 3 -t j 4 ) 2 + T j b -T j f 2 , j = 1, ..., n (4)
We can observe that if one-way transmission times are symmetric (T j b = T j f ), the expression is the same as Eq. 3. Eq. 4 shows that the accuracy of NTP time synchronization depends on the difference of one-way transmission times so the assumption of symmetric one-way transmission times is the main source of accuracy errors. If we can estimate one-way transmission times in a more precise way, we can improve the accuracy of time synchronization.

Note that most NTP implementations send several NTP requests and compute round trip network delay δ j as follows:

δ j = (t j 4 -t j 1 ) -(t j 3 -t j 2 ), j = 1, ..., n (5)
They can then choose the best set j of timestamps for computing the time offset θ j based on the smallest δ j .

III. ESTIMATION OF ONE-WAY TRANSMISSION TIMES

The most common delay metric is Round Trip Time (RTT) defined by the IPPM (IP Performance Metrics) IETF group [START_REF] Almes | A Round-trip Delay Metric for IPPM[END_REF] as the time interval between the injection of the first bit of the packet into the network and the reception of the last bit of the packet, supposing the receiver resent the packet immediately after its reception. Measuring RTT does not require synchronized clocks at the hosts since the sender computes RTT only based on its clock.

RTT cannot capture path asymmetry, the fact that the path from a source to a destination (forward path) may differ from the path from the destination back to the source (backward path). The difference in the transmission delays over forward and backward paths may come from two sources. First, the links between routers may have different capacity, e.g., an ADSL line [START_REF] Tsuru | Estimation of Clock Offset from One-Way Delay Measurement on Asymmetric Paths[END_REF]. Second, it may also come from hot potato routing: when two ASes (Autonomous Systems) are competitors and have a peer-to-peer relationship in propagating Border Gateway Protocol (BGP) route advertisements, they have interest in getting rid of a given packet as soon as possible by forwarding them to the closest egress point in terms of the internal routing cost. Hot potato routing is a consequence of a rule in the BGP decision process stating that a router always prefers to use a route learned over an eBGP session compared to a route learned over an iBGP session. Hot potato routing results in asymmetric paths because each AS sends packets through its favorable exit point, the points being different for different ASes.

The one-way delay (OWD) metric [START_REF] Almes | A One-Way Delay Metric for IP Performance Metrics (IPPM)[END_REF] is the time interval between the injection of the first bit of the packet in the link and the reception of the last bit of the packet in the other measuring point. Its measurement requires synchronized clocks at the sender and the receiver.

We have set up an experiment to measure the one-way delays between a client and a server connected to different ASes. The client is at the Gorgy Timing premises in Grenoble, France, and the server is at the Observatoire de Paris in Meudon, France. Both the client and the server locally connect to 100 Mb/s Ethernets. Gorgy Timing uses Orange as an ISP over a 1 Gb/s link and Observatoire de Paris connects to Renater also over a 1 Gb/s link. Traceroute between the two end-points shows 14 intermediate routers on the forward and 11 routers on the backward path with an average RTT of 27 ms. The Internet connectivity between the client and the server has several interesting characteristics: there are several ASes on the path (3215 Orange, 5511 Opentransit, 3257 GTT, 2200 Renater), the end-points are connected to different The client runs Ledi Network ATS with Digi ConnectCore 9P 9215 card that provides NTP timestamps over SNMP. The server is Meinberg M1000/MRS at the Observatoire de Paris. The client and the server are synchronized with GPS with a precision of 50 ns.

We have measured T f and T b (index j skipped) at different hours of a day: 9AM, 3PM, and 8PM. Figures 2 and3 show the histograms for each direction. We can notice that the one-way delays are highly asymmetric with the difference of around 3 ms. The shape of the distributions also varies: the variance of the forward distribution is much greater than that of the backward one.

We can observe that one-way delays T f and T b include a constant and a variable random part: We can notice that the shape of the histograms is significantly different for forward and backward paths and the distributions do not vary much in time. To find the best fitting distributions of T f and T b , we have tested several most important distributions: Gamma, Weibull, Normal, and Log Gamma. Figure 4 shows the results of fitting distributions at 9AM using the Maximum Likelihood Estimation (MLE) algorithm. For T f , the best fitting distribution is a mixture of two Normal distributions:

T f = d min f + d f , (6)
T b = d min b + d b , (7)
p(x) = λ 1 N (µ 1 , σ 1 ) + λ 2 N (µ 2 , σ 2 ) (8)
with λ 1 = 0.5540935, λ 2 = 0.4459065, the mean values are µ 1 = 15659.26, µ2 = 15465.70, with standard variation of σ 1 = 76.42764, σ 2 = 315.51818. For T b , we have fitted a Gamma distribution:

f (x; α, β) = β α x α-1 e -βx Γ(α) , x, α, β > 0, (9)
with the following parameters: shape α = 38521 and rate β = 3.3, where Γ(α) denotes the Gamma function.

IV. CALIBRATING NTP

The goal of calibration is to take advantage of the oneway delay measurements to mitigate the systematic error We assume that the NTP client sends n NTP requests and obtains n responses with corresponding timestamps.

• Find packets that experience the shortest transmission delays (called lucky packets):

j f = arg min j (t j 2 -t j 1 ), (10)
j b = arg min j (t j 4 -t j 3 ), j = 1, ..., n, (11)
and use their timestamps for computing the time offset.

θ = (t j f 2 -d min f -t j f 1 ) + (t j b 3 + d min b -t j b 4 ) 2 . (12)
This expression corresponds to Eq. 4 with T j f and T j b replaced by d min

V. VALIDATION

To evaluate the improvement in accuracy of the proposed method, we compare the accuracy of time synchronization obtained by standard NTP given by Eqs. 3 and 5 with proposed calibrated NTP measured with respect to the GPS time reference-we deploy the NTP client with the modified way of computing the time offset (Eqs. 10, 11, and 12) and compare the accuracy of its estimation with GPS. The experiments took place at a given time of a day (9AM, 3PM, 8PM) with the measurement phase of one-way delay for 15 minutes during which the client sends trains of 8 NTP requests every 10 s followed by the measurements of the modified client with calibrated NTP during 15 minutes. Finally, we measured the performance of standard NTP also during 15 minutes. We repeated the experiments for several days and observed similar results.

Figures 5,6, and 7 show the histograms of the time offset for standard NTP (left) and calibrated NTP (right) at 9AM, 3PM, and 8PM. The figures present accuracy measured by µ, the mean value of the distribution and precision measured by σ, the standard deviation. We can observe significant elimination of the accuracy error due to asymmetry of one-way delays and improved precision (lower σ).

VI. RELATED WORK

Freris et al. [START_REF] Freris | Fundamental Limits on Synchronizing Clocks over Networks[END_REF] analyzed fundamental limits on synchronizing clocks over networks and showed that asymmetry cannot be measured only based on timestamps in a pairwise synchronization system even with an infinite number of round trip measurements. Lévesque and Tipper [START_REF]A Survey of Clock Synchronization Over Packet-Switched Networks[END_REF] surveyed the state of the art in clock synchronization over packet-switched networks and presented different mechanisms proposed to improve the synchronization accuracy of NTP and PTP.

Several authors considered exploiting delay characteristics to improve the precision of time synchronization by trying to estimate the difference in paths to take into account in the offset calculation. Tsuru et al. [START_REF] Tsuru | Estimation of Clock Offset from One-Way Delay Measurement on Asymmetric Paths[END_REF] considered the case of asymmetric delays due to the difference of bandwidth on the paths. The authors validated the scheme over an ADSL link with asymmetric bandwidth. The scheme does not address the case of asymmetric routes that we consider in our work.

The scope of our paper is NTP, nevertheless, PTP introduced some mechanisms to mitigate the negative effects of asymmetric links on synchronization accuracy [START_REF]A Survey of Clock Synchronization Over Packet-Switched Networks[END_REF]: residence time at intermediate nodes, D asym , asymmetric delay parameter, and peer-to-peer path correction. We review some other proposed mechanisms for mitigating asymmetry in PTP below.

In a network with non PTP switches, Zarick et al. [START_REF] Zarick | The Impact of Network Latency on the Synchronization of Real-World IEEE 1588-2008 Devices[END_REF] measured synchronization accuracy as low as 450 µs under the presence of asymmetric delays. Lee [START_REF] Lee | An Enhanced IEEE 1588 Time Synchronization Algorithm for Asymmetric Communication Link using Block Burst Transmission[END_REF] proposed to take into account asymmetric bandwidth based on link speed measurements. A slave initiates a block burst transmission at the master by an Asymm_Check_Req message, it measures the time interval for receiving the message burst from the master, and sends the burst back. The scheme allows to estimate the link speed ratio between the forward and backward path.

Schriegel et al. [START_REF] Schriegel | Enhancement for a Clock Synchronization Protocol in Heterogeneous Networks[END_REF] characterized the variable delays of wireless links and used the characteristics to compensate non-deterministic forwarding delays of PTP synchronization frames by using different send rates for Sync messages. They evaluated the method in a real setup consisting of a Real-Time Ethernet with a wireless extension. Murakami and Horiuchi [START_REF] Murakami | Improvement of Synchronization Accuracy in IEEE 1588 Using a Queuing Estimation Method[END_REF] proposed to add probing messages before and after Sync and Delay_Req messages in PTP to detect link utilization, which improved synchronization accuracy.

Exel [START_REF] Exel | Mitigation of Asymmetric Link Delays in IEEE 1588 Clock Synchronization Systems[END_REF] analyzed various asymmetry mitigation approaches for software timestamping and proposed a timestamp correction-based asymmetry compensation scheme that takes into account bandwidth asymmetry. He showed precision improvement with measurements using WLAN synchronization hardware.

Lévesque and Tipper [START_REF] Lévesque | Improving the PTP Synchronization Accuracy under Asymmetric Delay Conditions[END_REF] considered a PTP set up with PTP support on only a subset of nodes on the path between a client and a server. They proposed a probing-based mechanism to estimate asymmetry and improve the synchronization performance. The protocol is similar to that by Lee, but is lightweight and takes into account the per-packet control delays.

Hajikhani et al. [START_REF] Hajikhani | A Recursive Method for Clock Synchronization in Asymmetric Packet-Based Networks[END_REF] considered PTP in asymmetric packetbased networks and proposed a method to estimate the asymmetric random parts in one-way delays, however, they assumed that the constant parts of asymmetric delays are equal in both directions.

White Rabbit defines a calibration procedure [START_REF] Daniluk | White Rabbit Calibration Procedure, Version 1.1[END_REF] to estimate the asymmetry in fiber propagation latencies by connecting the WR master and the WR slave with oscilloscopes. The goal is similar to that of our scheme, but the procedure concerns the low physical layer with important measurement instrumentation.

VII. CONCLUSION

In this paper, we propose to calibrate NTP with the measurements of one-way transmission delay on the forward and backward path. Then, in the set up without the precise clock at the client, the NTP expression for the time offset takes into account asymmetry, which results in improved accuracy and precision.

Unlike many papers that use simulations, we have validated the proposed method by measurements of the clock offsets computed by standard NTP and calibrated NTP based on the GPS time reference showing significant improvement in accuracy and precision.

In future work, we plan to measure the stability of paths between a client and a server over longer time intervals to evaluate how frequently routing changes impact the operation of calibrated NTP.

The method may also benefit from maintaining several calibrated paths to multiple NTP servers. If the path to the primary server changes, the client can still use other NTP servers as backup. We plan to investigate this approach in future work.

Figure 1 .

 1 Figure 1. Principles of NTP

Figure 3 .

 3 Histograms of T b types of ISPs (Orange: commercial provider, Renater: public network with large capacity), and there is an asymmetric number of routers.

  where d min f , d min b are constant and d f , d b are random variables. We denote the average values of the distributions as Tf and Tb .

Figure 4 .Figure 5 .. 2 ) 3 )

 4523 Figure 4. Fitting the distribution of T f and T b , 9AM

•

  Use the estimates of minimum transmission times d min f and d min b in Eq. 4 for the time offset with the timestamps of packets j f and j b :

Figure 6 .

 6 Figure 6. Histograms of the time offset for standard NTP (left) and calibrated NTP (right), 3PM.

Figure 7 .

 7 Figure 7. Histograms of the time offset for standard NTP (left) and calibrated NTP (right), 8PM.

ACKNOWLEDGMENTS

This work has been partially supported by the French Ministry of Research project PERSYVAL-Lab under contract ANR-11-LABX-0025-01.


Amelia Carolina Sparavigna

The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences

In some previous works, we have discussed the groupoids related to the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers. These groupoid possess different binary operators. As we can easily see, other integer sequences can have the same binary operators, and therefore can be used to represent the related groupoids. Using the On-Line Encyclopedia of Integer Sequences (OEIS), we can also identify the properties of these representations of groupoids. At the same time, we can also find integer sequences not given in OEIS and probably not yet studied.

Mersenne numbers

We discussed the binary operator of the set of Mersenne numbers in [START_REF] Sparavigna | On a generalized sum of the Mersenne Numbers[END_REF][START_REF] Sparavigna | The q-Integers and the Mersenne Numbers[END_REF]. The numbers are given as M n =2 n -1 . The binary operator is: [START_REF] Stover | Groupoid." From MathWorld--A Wolfram Web Resource[END_REF] As shown in [START_REF] Sparavigna | The q-Integers and the Mersenne Numbers[END_REF], this binary operation is a specific case of the binary operator of q-integers, which can be linked to the generalized sum of Tsallis entropy [START_REF] Tsallis | Possible Generalization of Boltzmann-Gibbs Statistics[END_REF][START_REF] Curado | A new entropy based on a grouptheoretical structure[END_REF]. The binary operator can be used to have a recurrence relation:

M n+m =M n ⊕M m =M n + M m + M n M m
M n+1 =M n ⊕M 1 (2)
Here in the following, let us show the sequences that we can generate from (1) and [START_REF] Sparavigna | Composition Operations of Generalized Entropies Applied to the Study of Numbers[END_REF]. We use OEIS, the On-Line Encyclopedia of Integer Sequences, to give more details on them.

M 1 =0 , sequence 0, 0, 0, 0, 0, 0, … . [START_REF] Sparavigna | Binary Operators of the Groupoids of OEIS A093112 and A093069 Numbers (Carol and Kynea Numbers[END_REF][START_REF] Sparavigna | The groupoid of the Triangular Numbers and the generation of related integer sequences[END_REF][START_REF] Sparavigna | On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers[END_REF]31,63,127,255,511,1023,2047,4095,8191,16383,32767,65535,131071,262143,524287,1048575,2097151, and so on. The Mersenne numbers 2 n -1 . This sequence is OEIS A000225. (OEIS tells that these numbers are sometimes called Mersenne numbers, "although that name is usually reserved for A001348"). [START_REF] Sparavigna | On a generalized sum of the Mersenne Numbers[END_REF]26,80,242,728,2186,6560,19682,59048,177146,531440,1594322,4782968,14348906,43046720,129140162,387420488, and so on (OEIS A024023, a n =3 n -1 ). [START_REF] Sparavigna | On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers[END_REF]63,255,1023,4095,16383,65535,262143,1048575,4194303,16777215,67108863,268435455, and so on (OEIS A046092, a n =4 n -1 ).

M 1 =1 , sequence
M 1 =2 , sequence
M 1 =3 , sequence

And we can continue:

M 1 =4 , OEIS A024049, a n =5 n -1 ; M 1 =5 , OEIS A024062, a n =6 n -1 ; M 1 =6 OEIS A024075, a n =7 n -1
, and so on. An interesting sequence is M 1 =9 , A002283, a n =10 n -1 . Dividing this sequence by 9, we have the repunits A002275, a n =(10 n -1)/9 . The generalized sum of the repunits is given in [START_REF] Sparavigna | On Repunits[END_REF].

Fermat numbers

The group of Fermat numbers has been discussed in [START_REF] Sparavigna | The group of the Fermat Numbers[END_REF]. As explained in [START_REF] Weisstein | Fermat Number[END_REF], there are two definitions of the Fermat numbers. "The less common is a number of the form 2 n +1 obtained by setting x=1 in a Fermat polynomial, the first few of which are 3, 5, 9, 17, 33, ... (OEIS A000051)" [START_REF] Weisstein | Fermat Number[END_REF]. We used this definition.

F n =2 n + 1 F n +m =F n ⊕F m =(1-F n )+(1-F m )+ F n F m (3)
The binary operator can be used to have a recurrence relation:

F n +1 =F n ⊕F 1 (4)
Sequences can generate from (3) and (4). F 1 =0 , sequence 2, 0, 2, 0, 2, 0, … . ;

F 1 =1 , sequence 1, 1, 1, 1, 1, 1, …. . F 1 =2 , sequence 2, 2, 2, 2, 2, 2, … . F 1 =3 ,
+1 . F 1 =4 , sequence A034472, a n =3 n +1 ; F 1 =5 , sequence A052539, a(n) = 4^n + 1,
(using the notation of OEIS). Continuing with 6, we have A034474, a(n) = 5^n + 1. For 7, we have A062394, a(n) = 6^n + 1. And so on.

Cullen and Woodall numbers

These numbers had been studied in [START_REF] Sparavigna | On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers[END_REF]. Let us consider the Cullen numbers.

C n =n 2 n + 1 C n +m =C n ⊕C m =( 1 n + 1 m )(C n -1)(C m -1)+1 (5) C n +1 =C n ⊕C 1 (6) C 1 =1 , sequence 1, 1, 1, 1, 1, 1, 1
, and so on.

C 1 =2
, sequence 3, 4, 5, 6, 7, 8, 9, and so on.

C 1 =3 ,
W n +m =W n ⊕W m =( 1 n + 1 m )(W n +1)(W m +1)-1 (7) W n +1 =W n ⊕W 1 (8) W 1 =0 ,
W 1 =2 , sequence A060352, a(n) = n*3^n -1.
W 1 =3 , sequence A060416, a(n) = n*4^n -1. And so on.

Let us mention the case W 1 =9 , which is giving A064756, a(n) = n*10^n -1, that is, 199, 2999, 39999, 499999, 5999999, 69999999, 799999999, and so on.

Carol and Kynea Numbers

These numbers have been studied in [START_REF] Sparavigna | Binary Operators of the Groupoids of OEIS A093112 and A093069 Numbers (Carol and Kynea Numbers[END_REF]. Carol number is:

C n =(2 n -1) 2 -2
The binary operator is: __________________________________________________________

C n ⊕C m =6+C n C m +3(C n +C m )+2(C n +2)(C m +2) 1/ 2 +2( C m +2)(C n +2) 1/ 2 +2(C n +2) 1/ 2 (C m + 2) 1 /2 (9)
C n +1 =C n ⊕C 1 [START_REF] Tsallis | Possible Generalization of Boltzmann-Gibbs Statistics[END_REF] Here we have square roots, so we can obtain integer sequences only in some cases. Let us consider the Kynea numbers.

C 1 =-1 , sequence A093112, a(n) = (2^n-1)^2 -2,
K n =(2 n +1) 2 -2
The binary operator is:

K n ⊕K m =-2+[2+( K m +2) 1 /2 (K n +2) 1/ 2 -(K m +2) 1 /2 -(K n +2) 1/2 ] 2 (11) K n+1 =K n ⊕K 1 (10)
Here we have square roots, so we can obtain integer sequences only in some cases.

K 1 =-1 , sequence -1, -1, -1, -1, -1,
and so on.

K 1 =2
, sequence 2, 2, 2, 2, 2, 2, and so on.

K 1 =7 , sequence A093069, a(n) = (2^n + 1)^2 -2,

Oblong numbers

These numbers are discussed in [START_REF] Sparavigna | Groupoids of OEIS A002378 and A016754 Numbers (oblong and odd square numbers[END_REF]. The oblong number is defined as: O n =n(n+1) . It is given by OEIS A002378. An oblong number is also known as a promic, pronic, or heteromecic number. OEIS gives the list: [START_REF] Sparavigna | Composition Operations of Generalized Entropies Applied to the Study of Numbers[END_REF][START_REF] Sparavigna | Groupoid of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers)[END_REF][START_REF] Sparavigna | On Repunits[END_REF]20,30,42,56,72,90,110,132,156,182,210,240,272,306,342,380,420,462,506,552,600,650,702,756,812,870,930,992,1056, and so on. The binary operator is:

Again, as we did before we have:

O 1 =0
, sequence 0, 0, 0, 0, 0, and so on.

O 1 =2
, sequence OEIS A002378, as given above.

O 1 =6 , sequence, A002943, a(n) = 2*n*(2*n+1). O 1 =12 , sequence A045945, Hexagonal matchstick numbers: a(n) = 3*n*(3*n+1).
O 1 =20 , sequence 72, 156, 272, 420, 600, 812, 1056, 1332, 1640, 1980, and so on. Not given in OEIS.

Of course, we can repeat the same approach for the odd squares (A016754) numbers. Their binary operator is given in [START_REF] Sparavigna | Groupoids of OEIS A002378 and A016754 Numbers (oblong and odd square numbers[END_REF]. Also for the centered square numbers and the star numbers, we have the binary operators [START_REF] Sparavigna | Groupoid of OEIS A001844 Numbers (centered square numbers)[END_REF][START_REF] Sparavigna | Groupoid of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers)[END_REF], so we can find the related representations by means of integer sequences too. As previously told, among the generated sequences, news sequences are produced that can be interesting for further investigation of integer sequences.

Triangular numbers

These numbers are really interesting. The numbers are of the form (OEIS A000217):

T n = ∑ k=1 n k = n (n+1) 2
I have discussed them in [START_REF] Sparavigna | The groupoid of the Triangular Numbers and the generation of related integer sequences[END_REF]. For these numbers we can give two binary operators.

For the convenience of the reader, I show the results that we can obtain.

The first binary operator is [START_REF] Sparavigna | The groupoid of the Triangular Numbers and the generation of related integer sequences[END_REF]:

T n ⊕T m =T n +T m + 1 4 [1-(1+8 T n ) 1/ 2 -( 1+ 8T m ) 1/ 2 +(1+8 T n ) 1 /2 (1+8 T m ) 1 /2 ]
Again we consider T n+1 =T n ⊕T 1 , and change the value of T 1 . Here in the following the sequences that we generate.

T 1 =0 , sequence 0, 0, 0, 0, 0, 0, … .

T 1 =1 , sequence [START_REF] Sparavigna | Binary Operators of the Groupoids of OEIS A093112 and A093069 Numbers (Carol and Kynea Numbers[END_REF][START_REF] Sparavigna | Groupoid of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers)[END_REF][START_REF] Tsallis | Possible Generalization of Boltzmann-Gibbs Statistics[END_REF][START_REF] Sparavigna | On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers[END_REF]21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,231, and so on. And this is OEIS A000217, the sequence of triangular numbers. (8 n+ 3) .

Of course, we can continue and obtain further sequences. As previously told, we have a second binary operator for the triangular numbers [START_REF] Sparavigna | The groupoid of the Triangular Numbers and the generation of related integer sequences[END_REF]. It is the following:

T n ⊕T m =T n +T m + 1 4 [1+( 1+ 8T n ) 1/ 2 +(1+8 T m ) 1 /2 +(1+8 T n ) 1 /2 (1+8 T m ) 1 /2 ]
Again, let us consider T n+1 =T n ⊕T 1 as we did before.

T 1 =0 , sequence [START_REF] Stover | Groupoid." From MathWorld--A Wolfram Web Resource[END_REF][START_REF] Sparavigna | Binary Operators of the Groupoids of OEIS A093112 and A093069 Numbers (Carol and Kynea Numbers[END_REF][START_REF] Sparavigna | Groupoid of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers)[END_REF][START_REF] Tsallis | Possible Generalization of Boltzmann-Gibbs Statistics[END_REF][START_REF] Sparavigna | On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers[END_REF]21,28,36,45,55,66,78,91,105,120,136,153,171,190,210, and so on. OEIS A000217, the sequence of triangular numbers.

  sequence 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, and so on, the Fermat numbers. (OEIS A000051, a n =2

	n

  that is 7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, and so on. As told in [17], Cletus Emmanuel calls these "Kynea numbers" [17].

	K 1 =14 , sequence 98, 782, 6722, 59534, 532898, 4787342, 43059842,	387459854,
	3486902498, 31381413902, and so on. Not given in OEIS.

T 1

 1 =3 , sequence 10, 21, 36, 55, 78, 105, 136, 171, 210, 253, 300, 351, 406, 465, 528, 595, 666, 741, 820, 903, … . Searching this sequence in OEIS, we can easily find that it is A014105, that is, the Second Hexagonal Numbers: H n =n(2n+1) . T 1 =4 , sequence 12, 24, 40, 60, 84, 112, 144, 180, 220, 264, 312, 364, 420, 480, 544, 612, 684, 760, 840, 924, … OEIS A046092 (four times triangular numbers). =10 , sequence 36, 78, 136, 210, 300, 406, 528, 666, 820, 990, 1176, 1378, 1596, 1830, 2080, 2346, 2628, 2926, 3240, 3570, … OEIS A033585, that is, numbers: 2 n(4 n+1) . T 1 =11 , sequence 38, 81, 140, 215, 306, 413, 536, 675, 830, 1001, 1188, 1391, 1610, 1845, 2096, 2363, 2646, 2945, 3260, 3591, … OEIS A139276, that is, numbers n

	T 1 =6 , sequence 21, 45, 78, 120, 171, 231, 300, 378, 465, 561, 666, 780, 903, 1035, 1176,
	1326, 1485, 1653, 1830, 2016, … OEIS A081266 (Staggered diagonal of triangular spiral in
	A051682).
	T 1 =7 , sequence 23, 48, 82, 125, 177, 238, 308, 387, 475, 572, 678, 793, 917, 1050, 1192,
	1343, 1503, 1672, 1850, 2037, … OEIS A062725.

T 1


C Norsic

H Rabat

O Aubry

D Hong

Combination of non-thermal plasma and heterogeneous catalysis for paracetamol degradation in water

Many researches for the abatement of aqueous pharmaceutical pollutants in water by

Advanced Oxidation Processes (AOPs), including electrical discharge plasmas, have been performed in the last decade. In the present study, non-thermal plasma coupled to catalyst was used for the degradation of paracetamol in water. The plasma was produced in a reactor consisting in a multiple needle-to-plate DBD discharge configuration, while catalyst is a metal oxide based catalyst. In order to investigate the influence of the oxide nature, various home-made catalysts (iron or manganese -based), prepared by wet impregnating method, were tested. Comparisons of the results with or without catalyst on the paracetamol degradation and the physico-chemistry of the treated liquids were done, and they showed that the iron-based catalyst presented better results in terms of conversion and mineralization.

Concretely, coupling this catalyst to non-thermal plasma, after 30 min of treatment, the paracetamol conversion is 78 % with 45 % mineralization, against 51% and 3% respectively with plasma alone. The paracetamol degradation as a function of the treatment duration was investigated with this catalyst.

Introduction

Due to an important humans' drug consumption, many pharmaceutical compounds are present at low concentration in surface water and ground water, while various studies reported the presence of drug residues in drinking water even after treatment [1-2]. Water pollution with the pharmaceutical compounds is considered as a serious environmental problem since these chemicals have harmful effects on aquatic ecosystems and negative impacts on human health. In order to remedy this issue, Advanced Oxidation Processes (AOPs) have been developed [2][START_REF] Klavarioti | Removal of residual pharmaceuticals from aqueous systems by advanced oxidation processes[END_REF], since these processes such as the Fenton process, peroxone, UV oxidation, and Non-Thermal Atmospheric pressure Plasma (NTAP) generate many oxidizing species (O•, O3, OH•, H2O2…), very reactive with pollutants. The degradation of pharmaceutical compounds by NTAP was studied during the last decade [START_REF] Gerrity | An evaluation of a pilot-scale non-thermal plasma advanced oxidation process for trace organic compound degradation[END_REF][START_REF] Baloul | Paracetamol degradation in aqueous solution by non-thermal plasma[END_REF][START_REF] Mededovic | Side-chain degradation of atrazine by pulsed electrical discharge in water[END_REF] by using discharges in the gas phase in contact with the liquid or directly in the liquid (electrohydraulic discharges). Note that Electrohydraulic discharges have low energy efficiency for water decontamination [START_REF] Malik | Water purification by plasmas: which reactors are most energy efficient?[END_REF][START_REF] Hijosa-Valsero | Decontamination of waterborne chemical pollutants by using atmospheric pressure non-thermal plasma: a review[END_REF]. In this paper, the experiments carried out with a plasma reactor consisting in a multiple needleto-plate discharge DBD configuration are presented. The discharges are generated at the tip of the needles above liquid. With the aim of improving energy efficiency in plasma degradation process, catalyst was added in the liquid.

In literatures, various types of catalyst were studied combined with plasma. Carbon materials have been widely used due to their important adsorption efficiency and their catalytic property in the oxidizing environment [START_REF] Grymonpré | Suspended activated carbon particles and ozone formation in aqueous-phase pulsed corona discharge reactors[END_REF][START_REF] Zhang | Effect of granular activated carbon on degradation of methyl orange when applied in combination with high-voltage pulse discharge[END_REF]. Photocatalysts like TiO2 were also frequently studied with the plasma for the decomposition of organic pollutants in liquid media [START_REF] Wang | Kinetic analysis and energy efficiency of phenol degradation in a plasma-photocatalysis system[END_REF][START_REF] Marouf-Khelifa | TiO2-assisted degradation of a perfluorinated surfactant in aqueous solutions treated by gliding arc discharge[END_REF]. Ferrous salts were also often added in plasma system because these salts catalytically transform formed H2O2 into hydroxyl radicals via Fenton reactions [START_REF] Hao | Pulsed discharge plasma induced Fenton-like reactions for the enhancement of the degradation of 4-chlorophenol in water[END_REF][START_REF] Shen | Effect of various gases and chemical catalysts on phenol degradation pathways by pulsed electrical discharges[END_REF]. Like the classic Fenton catalysts (with ferrous salts), the heterogeneous Fenton-like catalysts can be used with plasma to convert H2O2 into reactive species, but few results have been reported to date. However, the heterogeneous Fenton-like catalysts can have several advantages over the homogeneous. It can easily be recycled or regenerated, and contrary to the homogeneous catalyst, the solid catalyst is easy to handle. The Fenton-like catalysts are frequently iron oxides based catalysts, but Fe in Fe oxides structures can be replaced by other cations like Co, Mn, Cr, Cu… [START_REF] Pereira | Iron oxide catalysts: Fenton and Fenton-like reactions-a review[END_REF]. These transition metal oxides are also well known to be very effective for ozone decomposition. It seems thus really interesting to combine non thermal plasma, which produces ozone, with a heterogeneous Fenton-like catalyst. Indeed, this catalyst can convert both, formed H2O2 into hydroxyl radicals, but also ozone into oxygenated radicals.

In the present study, various oxide based catalysts (Al2O3/GF, Fe2O3/Al2O3/GF and MnO2/Al2O3/GF) were tested in combination with the plasma for paracetamol degradation in water. These oxides were supported on Glass Fibers fabric (GF). The results are presented in terms of paracetamol conversion and mineralization. Comparisons of the results with or without catalysts and the physico-chemistry of the treated liquids were realized. The paracetamol degradation as a function of the treatment duration was also investigated.

Experimental

Experimental setup

The used NTAP reactor is showed in Figure 1 and was described in previous papers [START_REF] Baloul | Paracetamol degradation in aqueous solution by non-thermal plasma[END_REF][START_REF] Baloul | Preliminary Study of a Non-thermal Plasma for the Degradation of the Paracetamol Residue in Water[END_REF]. It is a DBD reactor with a multiple needles-to-plate configuration inside a vessel made of PVC where the working gas can be controlled. The working gas (air) was introduced through the needles with a total flow rate of 100 sccm. High voltage is applied to 12 needles. The grounded electrode is a copper film deposited on a dielectric epoxy plate. The liquid to be treated is above this dielectric and under the needle-electrodes. The distance between the tip of the needles and the surface of the liquid was 5 mm. The volume of liquid to be treated was 40 mL. The liquid was a solution of pure water containing paracetamol with an initial concentration of 25 mg.L -1 .

The catalyst was placed in the liquid to be treated above the dielectric. The discharges were generated thanks a High Voltage (HV) square waveform with a frequency of 500 Hz using a HV amplifier (Trek ® 20/20C) driven by a function generator (TG4001 TTI ® ).

Electrical measurements were realized by means of high-voltage (PE20 KV Lecroy ® ) probes connected to an oscilloscope (DPO 3054 Tektronic ® ). The dissipated power was determined using the so-called Lissajous method requiring the adding of a convenient capacitor in the discharge circuit.

Catalyst preparation

Glass Fiber fabric (GF) (Diall 135 g/m²) used as support had a circular shape of 110 mm in diameter. GF were then calcined to 400°C during 4 hours to remove the binder. A washcoat of alumina (Aluminum oxide nanopowder, 13 nm primary particle size from Aldrich ® ) was realized on calcinated GF to create a bearing layer for the active phase. The washcoat was prepared with 5 g of alumina, 0,7 mL of nitric acid and 20 mL of ultra-pure water [START_REF] Villegas | Wet impregnation of alumina-washcoated monoliths: Effect of the drying procedure on Ni distribution and on auto-thermal reforming activity[END_REF]. The mixture was stirred during 12 hours at room temperature by means of a magnetic rod. Glass fibers were immersed a few second in the washcoat solution, dried during 2 hours in a drying oven at 100°C, and then calcined under air at 400°C during 4h (2°C/min) to eliminate nitric acid and residual water. After these steps, supported catalyst Al2O3/GF was obtained.

Metal oxide catalysts of Fe2O3/Al2O3/GF and MnO2/Al2O3/GF were synthesized following the incipient wetness method. Al2O3/GF were impregnated with an aqueous solution of iron (III) nitrate nonahydrate (Aldrich ® ) or manganese (II) nitrate aqueous (Strem Chemicals ® , 50-52%) with a metal oxide loading of 10 wt.%. The obtained solid was then dried overnight at 100°C and after calcined under air, during 4h at 300 °C for manganese and 400 °C for iron oxide.

Analytical methods

The paracetamol concentration was quantified using an UV-Visible absorption spectrophotometer (Cary 60 UV-Vis Agilent Technologies ® ) and the Beer Lambert equation from the absorption peak of paracetamol at the wavelength of 244 nm. The concentrations of the formed NO3 -and H2O2 were estimated using a photometer MultiDirect from Lovibond ® . pH and conductivity were measured with a Accumet XL600 (Fisher Scientific ® ). A TOC-L (SHIMADZU ® ) was used to determine the Total Carbon (TC), Inorganic Carbon (IC) and by subtracting the Total Organic Carbon (TOC) in the solution before and after treatment. With TOC, it is possible to calculate the mineralization rate (degradation of the organic compounds in the liquid to CO2).

Results and Discussion

Influence of the oxide nature

The effects of different oxides coupled with plasma were evaluated in terms of paracetamol conversion and mineralization rates. The conversion and mineralization rates were calculated with the following equations (1) and (2), respectively. C0, Ct are the concentrations of paracetamol and TOC0, TOCt the concentrations of organic carbon in the solution, at the beginning (t = 0) and at the end of the treatment (t).

𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 (%) =

𝐶 0 -𝐶 𝑡 𝐶 0 × 100 (1)

𝑚𝑖𝑛𝑒𝑟𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 (%) = 𝑇𝑂𝐶 0 -𝑇𝑂𝐶 𝑡 𝑇𝑂𝐶 0 × 100 (2)
According to the results shown in Fig. 2, we observed an increase of the paracetamol conversion and mineralization with all the tested oxides coupled with plasma. The beneficial effects of the catalysts are as follow for conversion and mineralization: The least important improvement is obtained with MnO2 oxide. MnO2 is well known for ozone decomposition [START_REF] Long | Room Temperature Catalytic Ozonation of Toluene over MnO2/Al2O3[END_REF], but the formed ozone in gas phase can have difficulties to reach MnO2

MnO2/Al2O3/GF < Al2O3/GF < Fe2O3/Al2O3/GF
surface because it has a very low solubility in water and there is a competition between water and ozone adsorption on the active sites of MnO2. Moreover, it seems that this oxide does not allow to improve H2O2 conversion (Table 1). H2O2 concentrations are similar after treatment with plasma alone and with plasma + MnO2/Al2O3/GF. The Al2O3/GF catalyst, in turn, seems act like a Fenton Catalyst (FC), an improvement of the H2O2 conversion was observed (Table 1) and thus conversion and mineralization rates significantly increase. With the Fe2O3/Al2O3/GF catalyst, the best results were observed. This catalyst seems really efficient to form hydroxyl radicals, according to the equation ( 3), which quickly react with the pollutant or by-products.

FC + H2O2  FC + + OH• + OH - (3)
According to the results shown in Table 1, we observed a slight decrease of the pH after each treatment due to the formation of nitrates and carboxylic acids (observed by HRMS analysis).

With catalysts, more nitrates were still formed compared to plasma alone. Indeed, with catalysts more reactive species are formed, thereby improving the paracetamol conversion and mineralization rates but also the formation of nitrates. The conductivity of the solution is also very important after treatment with catalysts. In the following section, a study of the paracetamol degradation as a function of treatment duration was presented with Fe2O3/Al2O3/GF catalyst. This catalyst was chosen because it showed better results coupled to plasma than other catalysts.

Study of the paracetamol degradation as a function of the treatment time

In this part, the paracetamol conversion and mineralization rates were determined as a function of the treatment duration. The non-thermal plasma was combined with the Fe2O3/Al2O3/GF catalyst for this study and the results were compared with those obtained by plasma alone.

Better results were obtained with the presence of the catalyst. After 1h of treatment, a total conversion of the paracetamol and a mineralization rate of 84 % were obtained with catalyst (Figure 3).

The energy yield was also calculated according to the equation (3). C0, Ct (g.L -1 ) are the concentrations of pollutant in the solution at the beginning and at the end of the time interval Δt (h), V is the volume of the treated solution (L) ant P the consumed power (kW).

EY (g.kWh

-1 )= (𝐶 0 -𝐶 𝑡 )×𝑉 𝛥𝑡×𝑃 (3)
An improvement of the energy yield was observed in presence of the catalyst (Figure 3a) during the paracetamol treatment. For 45 and 60 min of treatment, the gap between plasma alone and plasma + catalyst is however lower. Indeed, the more the treatment time increases, the less it remains of paracetamol to be treated. But more by-products were oxidized as can be seen with the rate of mineralization (Figure 3b). From 45 min of treatment, the mineralization rate increases. HRMS analysis confirm these results. By-products with important molar mass were observed after treatment by plasma alone, but with catalyst lighter by-products were observed, and for 45 and 60 min of treatment you can see there's not much left in there.

Conclusion

In this study, non-thermal plasma coupled to catalysis was used for the degradation of paracetamol. Various heterogeneous catalysts were developed and tested. Until now, the coupling of plasma and heterogeneous catalyst was studied little. But according to this study, the combination of non-thermal plasma and heterogeneous catalysis shows a great interest.

Indeed, the degradation of the paracetamol was highly improved with their presences, and the conversion, mineralization rates but also energy yield were improved greatly. The best results in terms of conversion and mineralization were achieved with the iron-based catalyst (Fe2O3/Al2O3/GF). Coupling with this catalyst to non-thermal plasma, the paracetamol conversion is 100% with 84% mineralization after 60 min of treatment, against 64% and 4% respectively with plasma alone (without catalyst).

Fig. 1

 1 Fig. 1 Scheme of the multiple needle-to-plate reactor

Fig. 2

 2 Fig. 2 Paracetamol conversion and mineralization rates after treatment with plasma alone and with plasma coupled with different oxide based catalysts (U = ± 5,6 kV, treatment time : 30 min, gas : 100 sccm air )

Fig. 3

 3 Fig. 3 Paracetamol degradation for different treatment duration with and without catalyst, (a) Conversion rates and energy yields, (b)Mineralization rates (Catalyst : Fe2O3/Al2O3/GF, U = ± 5,6 kV, gas : 100 sccm air)

Table 1

 1 Concentration of NO3 -, H2O2, pH and conductivity before and after the different treatment (U = ± 5,6 kV, treatment

	time t : 30 min, gas : 100 sccm air)
	[NO3 -]t mg.L -1	[H2O2]t mg.L -1	pH0  pHt	λ0  λt µS.cm -1
	Plasma alone	25	3	6.5  5	18  37
	Plasma + Al2O3/GF	56	<1	8.5  8.2	75  227
	Plasma + MnO2/Al2O3/GF	62	3	8  6.5	63  192
	Plasma + Fe2O3/Al2O3/GF	56	<1	9  8	70  196

Acknowledgments

We gratefully acknowledge the financial support provided to the PIVOTS project by the Région Centre -Val de Loire.