Siyang Liu
email: siyang.liu@centralesupelec.fr

Raul De Lacerda
email: raul.delacerda@centralesupelec.fr

Jocelyn Fiorina
email: jocelyn.fiorina@centralesupelec.fr

WKNN indoor Wi-Fi localization method using k-means clustering based radio mapping

Keywords: Indoor localization, WiFi fingerprinting, RSS, k-means clustering, WKNN

Wifi fingerprinting using received signal strength has been widely studied for indoor localization. Classic similaritybased methods like weighted K-nearest neighbor (WKNN) localize targets by searching the best matching fingerprint in the dataset. Performance of these methods suffers from RSS variance and they are slow under a large size of fingerprint dataset. In this paper, we propose a WKNN localization strategy using k-means clustering radio mapping to improve localization precision while mitigating computational complexity.

I. INTRODUCTION

With rapid development of Internet of Things (IoT), the need of location based services such as asset management, routing, and equipment positioning has also grown overtime. Global Positioning System (GPS), which supports a large number of location based applications is not adapted for indoor environments due to signal attenuation and scattering caused by walls and other obstacles [START_REF] Wang | Csi-based fingerprinting for indoor localization: A deep learning approach[END_REF]. Therefore, indoor localization system becomes an area of interest.

Localization can be performed using fingerprinting approach which exploits the mapping between measurements and positions [START_REF] Wang | Csi-based fingerprinting for indoor localization: A deep learning approach[END_REF], [START_REF] Bhatti | Machine learning based localization in largescale wireless sensor networks[END_REF]. The process of fingerprinting includes an offline training phase and an online localization phase.

Received signal strength (RSS) is a commonly used feature for fingerprinting. However, it is easily affected by environment factors and it fluctuates even in the same position [START_REF] Tian | Performance analysis of rss fingerprinting based indoor localization[END_REF]. One way to address RSS variance problem is to use probabilistic approach. A. Haeberlen et al. [START_REF] Haeberlen | Practical robust localization over large-scale 802.11 wireless networks[END_REF] proposed a Gaussian fit sensor model, which is robust against untrained fluctuations. Another way to compensate is to sample multiple times in the same reference point (RP) over a long period of time. With redundant measurements, M. Adriano et al. [START_REF] Moreira | Wi-fi fingerprinting in the real world -rtls@um at the evaal competition[END_REF] proposed to only use the minimum feature distance between test sample and all RSS samples at the same RP for WKNN which ensures that each RP will only contribute with the best similarity value.

Even though sampling RSS multiple times can provide more information for localization, a large fingerprint database not only results in high power consumption but also long processing time during online phase especially for similarity based methods like WKNN [START_REF] Cherif | Optimization of k-nn algorithm by clustering and reliability coefficients: Application to breastcancer diagnosis[END_REF]. Improving accuracy and reducing computational complexity are two important directions of current localization studies [START_REF] Wang | An improved wifi positioning method based on fingerprint clustering and signal weighted euclidean distance[END_REF].

Many methods are proposed to reduce the dataset used for similarity comparison mainly by reducing the number of fingerprints or the dimension of each sample. Radio mapping methods compress radio database during the offline phase. A. Arya et al. [START_REF] Arya | A hierarchical clustering technique for radio map compression in location fingerprinting systems[END_REF] used hierarchical clustering on the entire dataset taking into account both the location and the radio components of samples. S. G. Lee et al. used k-means clustering to reduce redundant measurements on each RP [START_REF] Lee | Developing an improved fingerprint positioning radio map using the k-means clustering algorithm[END_REF]. Clustering methods divide the entire radio map into clusters during offline phase and localize the TP inside the most relevant cluster [START_REF] Wang | An improved wifi positioning method based on fingerprint clustering and signal weighted euclidean distance[END_REF]. Reduction of dataset can also take place during the online phase by filtering the radio map for relevant RPs [START_REF] Kushki | Kernel-based positioning in wireless local area networks[END_REF]. AP selection and data quantisation use prior knowledge to reduce sample dimension [START_REF] Kushki | Kernel-based positioning in wireless local area networks[END_REF], [START_REF] Khandker | Analysis of received signal strength quantization in fingerprinting localization[END_REF]. Feature selection methods like Principle Component Analysis (PCA) technique recover the low-rank matrix from a noisy RSS matrix [START_REF] Zhang | Fingerprint database reconstruction based on robust pca for indoor localization[END_REF]. Deep neural network such as auto-encoder can also be used to reduce the dimension of feature vectors [START_REF] Xiao | 3-d ble indoor localization based on denoising autoencoder[END_REF].

In this paper, a strategy combining radio mapping based on k-means clustering and WKNN algorithm is proposed aiming to improve localization efficiency while maintaining accuracy. To further reduce fingerprint data size, a variant of the proposed method is also introduced, adding an extra spatial filtering step. The remainder of the paper is organized as follows: Section II presents notations and system model. The proposed improved WiFi fingerprinting method and its variant are presented in Section III. Section IV presents numerical results for performance evaluation, and Section V concludes the paper.

II. SYSTEM MODEL

We consider an Area of Interest (AoI) with R fixed reference points {RP r } R r=1 with known coordinates (x r , y r ) and M fixed access points {AP m } M m=1 whose positions are not specified. A RSS sample of an arbitrary point on the AOI would be a vector of size M × 1 constituted by the Received Signal Strength Indicator (RSSI) of all M APs. Let's assume that at each RP several measurements were taken, where the number of measurements are represented by {N r } R r=1 and we define the total number of RP measurements as N = N r . At test point q, RSS sample is taken forming a vector of size M . Sample distance between samples i and j is given by:

ds i,j = M m=1 (RSSI m j -RSSI m i ) 2 . (1)
Based on the fact that for each RP r has N r RSS samples, similarity is employed to identify the smallest distance between all N r RSS samples and the given test sample:

s r,q = min{ds i,q } Nr i=1 . (2)
Similarity-based localization algorithms search the best matching fingerprint on the training set. For each test sample, K RPs with highest similarity are selected whose coordinates denotes as (x k , y k ) (k = 1, ..., K). WKNN algorithm estimates TP coordinates as a weighted average of these selected RPs. The weight is chosen as a decreasing function of similarity assuming that RP with higher similarity is closer to the TP. In this paper, the weight of RP k is chosen as:

w k = 1 s 2 k,q (k = 1, ..., K). (3)
The estimated TP coordinates are obtained as:

xq = K k=1 w k x k K k=1 w k ŷq = K k=1 w k y k K k=1 w k . ( 4
)
The number of K should be chosen considering the tradeoff between accuracy and complexity. Assuming the true coordinates of T P q is (x q , y q ) ∈ AOI, then we can obtain the error of localization as:

err q = (x q -x q ) 2 + (ŷ q -y q ) 2 .
(5)

III. METHODOLOGY

In this section, a radio mapping scheme aiming to improve localization efficiency by reducing the number of fingerprint samples and details of the localization strategy are presented. A block diagram of the proposed fingerprinting method and its variant in dashed line is shown as Fig. 1.

First, fingerprint samples measured at the same RP are put into the same group. Then using k-means algorithm each group of samples is divided into a certain number of non-overlapping clusters. For each cluster, one representative sample will be obtained, forming a new fingerprint set that is smaller and more robust to noise and signal fluctuation.

For k-means algorithm, the number of clusters kc is a parameter that should be determined before using. Choosing kc is often a decision based on prior knowledge, assumptions, and practical experience which is difficult when the data has many dimensions [START_REF] Hamerly | Learning the k in k-means[END_REF]. Given a certain value of kc, a global silhouette index S r,kc for RP r is defined to evaluate the quality of clustering [START_REF] Desgraupes | Clustering indices[END_REF]. First, we consider a RSS sample i in the p-th cluster C p with n p samples. Using sample distance definition (1), a(i) is defined as the mean distance between this sample and other samples in the same cluster shown as:

a(i) = 1 n p -1 np i =i ds i,i f or i, i ∈ C p . (6)
Then we define the mean distance between sample i and another cluster C p of the same reference point with n p samples shown as:

dc(i, C p ) = 1 n p n p j=1 ds i,j for i ∈ C p and j ∈ C p . ( 7
)
Let us also denote by b(i) the smallest of these distances:

b(i) = min p =p dc(i, C p ) (8)
The cluster C p that presents the lowest distance represents the most probable cluster to consider the RSS sample i other than cluster C p . A silhouette index is defined to describe relative similarity between sample i and its closest other cluster:

S(i) = b(i) -a(i) max(a(i), b(i)) (9)
A global silhouette index S r,kc for RP r is defined as the mean value of S(i) considering all RSS samples of this RP. A large S r,kc indicates that samples are well clustered.

To determine the optimal value of cluster number kc, inspired by [START_REF] Lee | Developing an improved fingerprint positioning radio map using the k-means clustering algorithm[END_REF] we perform k-means clustering on each RP with kc as an integer value that varies from 2 to 6 and then the final cluster number of RP r is chosen as the one that maximizes S r,kc . Once cluster number kc for a RP is determined, kc representative samples can be obtained from these clusters as weighted centres and silhouette index S(i) serves as the weight. A weighted average allows well classified samples in the cluster to contribute more to representative samples.

After radio mapping, N (2R < N < 6R) number of representative samples are generated. Since N depends only on the RP number R and the range of kc we set, using this representative sample set with limited size, the complexity of WKNN is also limited.

A step of spatial filtering is added before WKNN localization as a variant of the proposed method to further reduce the size of fingerprint dataset. For each test sample, spatial filtering selects a subset of RPs that are spatially relevant to the TP using AP coverage information. A binary AP coverage vector is generated for each point as I = [I 1 ...I M ], where I m = 1 if the RSS reading from AP m is greater than receiver sensitivity for at least 90% of the time [START_REF] Kushki | Kernel-based positioning in wireless local area networks[END_REF]. Hamming distance is then computed for AP vector of all RPs and TPs. For a TP, only RPs with distance smaller than a threshold αM (0 ≤ α ≤ 1) are taken for localization.

IV. PERFORMANCE EVALUATION

In this section, two datasets are used for performance evaluation, a simulated fingerprinting dataset and an open access dataset UjiIndoorLoc. Two other localization methods as well as another radio mapping method are taken for comparison.

A. Datasets for simulation

A simulated dataset is generated based on Friis Radiation Propagation model noted as dataset 1. 9 APs with fixed position are deployed evenly on the surface of 200 * 200 meters. 1600 reference points are spread in a grid of 5 meters and for each RP 10 RSS samples are generated. To evaluate the localization method, 500 test points are randomly selected on the surface, each with one RSS sample. A Gaussian white noise with SNR of 100dBm is added to both training and test set.

Dataset 2 is a public assess localization database UjiIndoor-Loc with 520 APs over 3 buildings [START_REF] Torres-Sospedra | Ujiindoorloc: A new multi-building and multifloor database for wlan fingerprint-based indoor localization problems[END_REF]. RSSI is represented as negative integer values ranging from -104dBm (extremely poor signal) to 0dBm. In this dataset positive default value 100 is used to denote when an AP was not detected. This value does not reflect the received signal strength or distance to the AP but it will greatly affect the calculation of similarity. A range of other values are considered as replacement [START_REF] Moreira | Wi-fi fingerprinting in the real world -rtls@um at the evaal competition[END_REF] and for the proposed method (k = 3 for WKNN) the best results are achieved with -95 as shown in Table I. Noted that in this dataset, position information of each point is given as longitude, latitude, floor and building ID. To calculate positioning error, the vertical axis is normalized considering a floor height of 4 meters.

B. Comparison to prior work

In this section, performance of the proposed method and its variant is compared to other radio mapping and localization methods. WKNN proposed in [START_REF] Moreira | Wi-fi fingerprinting in the real world -rtls@um at the evaal competition[END_REF] is applied to the entire original fingerprint dataset. Method proposed in [START_REF] Lee | Developing an improved fingerprint positioning radio map using the k-means clustering algorithm[END_REF] use k-means clustering method to produce representative samples for each RP then use NN for localization. Average linkage hierarchical clustering is used as comparison for radio mapping which is suggested to outperform k-means clustering under big cluster number [START_REF] Arya | A hierarchical clustering technique for radio map compression in location fingerprinting systems[END_REF]. Noted that k-means radio mapping in the proposed method is different from the one compared in [START_REF] Arya | A hierarchical clustering technique for radio map compression in location fingerprinting systems[END_REF]. The former one is conducted on samples of the same RP whereas the latter one is used directly on the entire fingerprint dataset. Variant of the proposed method adds a step of spatial filtering after radio mapping to further reduce sample number for localization.

Comparative methods as well as their computation complexity zuo2008kernel, [START_REF] Xu | A comprehensive survey of clustering algorithms[END_REF] are shown in Table II. Note that M is the number of APs while N , N and N ( N > N > N ) corresponds to the number of original RSS samples, generated representative samples and filtered samples. K is the parameter for WKNN. k h is the number of clusters for hierarchical clustering. kc and L is the number of clusters and iterations preset for the k-means.

Table II COMPARATIVE METHODS

Method

Computational complexity Offline Online WKNN [START_REF] Moreira | Wi-fi fingerprinting in the real world -rtls@um at the evaal competition[END_REF] -

O(M N + KN ) k-means+NN [9] O(M N Lkc ) O(M N + N ) Hierarchical clustering+NN [8] O(M N 2 k h ) O(M N + N ) Proposed method O(M N Lkc ) O(M N + KN ) Proposed method' O(M N Lkc ) O(N + M N + KN )
By taking more neighbor RPs into account, WKNN has slightly higher complexity than NN. From the expression of complexity we can see that reducing data size has a direct impact on WKNN efficiency for the online phase. For the proposed method, given a defined range of cluster number kc, for example, from two to six, the size of representative fingerprint set 2R < N < 6R gives maximum complexity of the WKNN as O(M 6R + K6R). N depends on RP number R as well as the preset range of kc and it does not grow with the number samples taken at the same RP making the gain on localization efficiency more significant with more samples taken at each RP. By adding spatial filtering step, complexity for WKNN is further reduced with the cost of some extra operations for filtering during the online phase. The overall complexity for proposed method' is smaller than the proposed method if the size reduction of filtering is big enough.

C. Simulation results

For the proposed method and its variant, parameter k for WKNN and spatial filtering threshold α need to be tuned first to achieve better performance.

Localization performance of WKNN with and without kmeans radio mapping under different value of k is shown in Fig. 2 in which average error 1 corresponds to the mean error of all the samples in the validation set whereas average error 2 considers only the error of samples who are correctly classify for buildings and floors. On both datasets, when k is small, the localization error reduces as k increases. On dataset 2, localization error increases after a certain value of k which is different from dataset 1 where the radio map is more ideal. To balance between accuracy and complexity, k = 3 is chosen for further simulations. Also, the performance of both methods are quite close if the value of k is well chosen meaning that using k-means clustering can the complexity for WKNN without compromising the performance too much. Spatial filtering parameter α affects the number of samples filtered for localization. With a larger value of α, more fingerprints will pass through the filter and α = 1 corresponds to no filtering. Since spatial filtering depends on AP coverage information and all samples in dataset 1 have the same AP coverage, proposed method' is only applied on dataset 2.

Table III presents impact of α on localization performance in which the ratio of filtering is defined as the ratio of sample number after and before filtration. As the the value of α increases, more survey points are kept after the filtering step and hence smaller localization error. Since dataset 2 is quite sparse, a small value of α already lets a large percentage of samples pass the filter but if the value is below 0.05, all points are filtered out and it is unable to perform localization. In this section, α = 0.06 is chosen for simulations. Then performance of the proposed and comparative methods is compared on both datasets. Mean error, building and floor classification accuracy as well as data size for localization are shown in Table .IV while Fig. 3 presents the distribution of localization error. For comparison, the maximum cluster number for hierarchical clustering is set to be the same as the number of representative samples generated using k-means clustering. As we can see, in both datasets, adding a radio mapping step effectively reduces the data size for localization by 40% and 78%, respectively. Besides the gain in efficiency, radio mapping step does not improve localization performance. Adding k-means clustering, mean localization error only increase slightly comparing to only using NN or WKNN. Hierarchical clustering on the other hand, results in a significant decrease in terms of performance and it is also with high complexity as shown in TableII above. Results on both datasets also show an improvement of localization error using WKNN instead of NN. On dataset 1, mean error is reduced by 1 meter using WKNN. Comparing the proposed method to k-means+NN, the use of WKNN for localization leads to a mean error that is 0.6 meter smaller.

By combining k-means radio mapping with WKNN, the proposed method finds a way to balance between efficiency

Figure 1 .

 1 Figure 1. Block diagram for the proposed localization method

Figure 2 .

 2 Figure 2. Performance of k-means+WKNN and WKNN

Table I IMPACT

 I OF DEFAULT RSS VALUE ON THE PROPOSED METHOD

	def RSS(dbM)	Building acc(%) Floor acc(%) Position error(m)
	100	99.19	75.52	13.51
	-85	98.47	91.18	13.49
	-95	99.46	91.27	8.62
	-105	99.82	89.83	9.01
	-115	99.82	88.12	9.89

Table IV PERFORMANCE

 IV OF THE PROPOSED AND COMPARATIVE METHODS

		Mean error(m)	Building(%)	Floor (%)	Data size
			Dataset 1
	NN	2.44	-	-	16000
	WKNN	1.45	-	-	16000
	k-means+NN	2.44	-	-	9557
	HC+NN	2.44	-	-	9557
	Proposed method	1.45	-		9557
			Dataset 2
	NN	8.82	99.64	91.18	19861
	WKNN	8.39	99.64	91.18	19861
	k-means+NN	9.15	99.55	91.09	4202
	HC+NN	15.10	74.62	54.28	4202
	Proposed method	8.54	99.55	91.09	4202
	Proposed method'	8.73	99.64	91.18	1775

and accuracy. Adding a spatial filtering step in proposed method' further reduces the average data size for localization by 57% with a small increase in localization error.

V. CONCLUSION AND FUTURE WORK

In this paper, we propose a WKNN localization strategy with limited complexity using k-means clustering based radio mapping to improve efficiency of localization without sacrificing performance too much. This mapping scheme reduces the complexity of WKNN by producing a new dataset with fewer and limited number of representative samples. Simulations on two datasets show that this mapping scheme does not improve localization accuracy but with well chosen parameters the increase of mean error is minor and therefore, this strategy finds a balance between precision and efficiency.

As future work, reducing complexity can be investigated for example by using neural network to extract feature with smaller dimension or using clustering methods to further divide the feature space into smaller subareas.


Yu Liu

Shenle Pan

Pauline Folz

Fano Ramparany

Sébastien Bolle

Eric Ballot

Thierry Coupaye

Connected Freight Parking in Smart City Logistics

Keywords: City Logistics, Smart Cities, Freight Parking Management, Sustainability, Digital Twin, Property Graph, Ontology, Semantic Web

Overview and motivation

. These unnecessary and inefficient goods and vehicles movements, in turn, exacerbate congestion and air pollutant emissions. Motivated by that, this work investigates how the new technologies and paradigms (such as Smart Cities, Digital Twins, Internet of Things, Semantic Web) can help improve the performance of city logistics via better management of freight parking areas.

Methodology, results and main contributions

Generally, Smart City Logistics is supported by a set of technical systems for the identification, localization, and condition monitoring of different objects or systems in logistics from freight to vehicles until the infrastructure, for goods distribution in the urban area [START_REF] Kirch | RFID in logistics and production--Applications, research and visions for smart logistics zones[END_REF]. Such technologies could further enable the interconnection of objects (or of systems), in order to share the logistics resources, assets, or services, such as in Smart Cities. To this end, we first propose an architectural framework to describe the modeling of Smart City Logistics in the context of Smart Cities and the Web of Things (WoT) [START_REF]Web of Things[END_REF] (see Figure 1).

In Layer 1 Physical Logistics System, smart objects used in logistics systems are present, which are objects with sensors or tagged products. Moving up to Layer 2 Cyber Logistics System, objects and their connection are modeled with Property Graph (PG) to shape their informational representation, namely Digital Twins or avatars of physical entities [START_REF]Beyond IoT: Digital Twins and Cyber-Physical Systems -Hello Future Orange[END_REF]. In this layer, the objects are connected while their relationships are displayed and registered. Realtime data source (in Layer 1) related to each avatar will be injected and updated to make sure it is living. Layer 1 and 2 together can be seen as Cyber-Physical Logistics System (CPLS) in logistics. In Layer 3 Semantic Logistics System, Web Ontology Language (OWL) is used to define the objects and concepts to describe the domain (and the knowledge) of the logistics system. Since Ontology is defined as a formal, explicit specification of a shared vocabulary [START_REF] Studer | Knowledge Engineering: Principles and methods[END_REF], the CPLS modeled is able to communicate with other existing systems or objects in this level, i.e., the context including shared infrastructures or assets, stakeholders' systems, etc. [START_REF] Liu | Digital Twin-Driven Approach for Smart City Logistics: The Case of Freight Parking Management[END_REF]. This layer is of foremost importance in the context of Smart Cities where WoT is present, and to enable the Plug-and-Play and interoperability of systems. A query language like SPARQL can be used to query the ontology in Layer 3. The results will be injected into Layer 4 Logistics Web Application, where decisions (e.g., scheduling of vans and drivers, route planning) will be made based on the more comprehensive information and knowledge on the whole system and its context. Decisions will then be communicated to the corresponding avatars located in Layer 2. After the status of the digital twins is synchronized, the action of the physical objects in the first layer will be determined.

Figure 1 .

 1 Figure 1. Architectural framework of Smart City Logistics


Sulian Thual
email: sthual@cerfacs.fr

Boris Dewitte

The role of spatial shifting in El Niño/Southern Oscillation complexity

Keywords: El-Niño Southern Oscillation, Walker Circulation, Conceptual Models

 The present paradigm of spatial shifting participates towards a more unified understanding of the ENSO, with potentially far reaching implications down the lines of modelling and prediction.

Introduction

The El Niño-Southern Oscillation (ENSO), which refers collectively to the alternation between El Niño and La Niña events in the equatorial Pacific, affects extreme weather, populations and ecosystems worldwide. [START_REF] Ropelewski | Global and regional scale precipitation patterns associated with the El Niño Southern Oscillation[END_REF][START_REF] Mcphaden | ENSO as an integrating concept in earth science[END_REF] Its impacts are however highly variable and unpredictable due to a considerable diversity in characteristics from one event to the next. Although most El Niño events are characterized by modest sea surface temperature (SST) warming in the central Pacific, a few of them stand out by a strong SST warming in the eastern Pacific with much more severe impacts. [START_REF] Kug | Two types of El Niño events: cold tongue El Niño and warm pool El Niño[END_REF][START_REF] Kao | Contrasting eastern-Pacific and central-Pacific types of ENSO[END_REF] For instance, the record eastern Pacific El Niño of 1997-98 induced catastrophic floods along the western coasts of both North and South America, droughts over the maritime continent in Southeast Asia as well as an increased tropical cyclone activity over the Pacific. [START_REF] Mcphaden | Genesis and evolution of the 1997-98 El Niño[END_REF] La Niña events, characterized by moderate cooling in the central to eastern Pacific, tend to yield similar although spatially displaced climate impacts. [START_REF] Ropelewski | Global and regional scale precipitation patterns associated with the El Niño Southern Oscillation[END_REF] Beyond disrupting the global atmospheric and oceanic structures, major ENSO events can be highly detrimental to both populations and ecosystems in terms of fisheries, tropical diseases spread, coral reef bleaching, and so on. [START_REF] Mcphaden | ENSO as an integrating concept in earth science[END_REF] Understanding and predicting the ENSO's event-to-event diversity is thus a fundamental yet unreached goal in climate sciences. [START_REF] Barnston | Skill of real-time seasonal ENSO model predictions during 2002-11: Is our capability increasing?[END_REF] Despite the primary importance of the ENSO and the decades of research progress, presentday general circulation models with full-physics still tend to represent it with some bias as regards it amplitude, spatial pattern or evolution, among others. [START_REF] Bellenger | ENSO representation in climate models: From CMIP3 to CMIP5[END_REF][START_REF] Ham | How well do current climate models simulate two types of El Niño?[END_REF] Similar issues arise in models of decreased complexity that, despite reasonably depicting the ENSO in terms of coupled interactions between the atmosphere and ocean, differ in terms of the processes invoked for its more advanced features. [START_REF] Neelin | ENSO theory[END_REF][START_REF] Jin | Simple ENSO Models[END_REF][START_REF] Guilyardi | ENSO Modeling: History, Progress and Challenges[END_REF] A major reason for these shortcomings is, generally speaking, a lack of consensus for understanding the ENSO's nonlinear dynamics. For example, even though El Niño events are commonly classified into the central Pacific or eastern Pacific type, which is referred to as ENSO diversity, it is still debated whether these stem from a continuum or from separate modes of variability. [START_REF] Capotondi | Understanding ENSO diversity[END_REF][START_REF] Takahashi | Strong and moderate nonlinear El Niño regimes[END_REF][START_REF] Xie | Two leading ENSO modes and El Niño types in the Zebiak-Cane model[END_REF] Another lack of consensus regards the processes by which El Niño events may reach larger amplitudes yet shorter durations than La Niña events, which is referred to as ENSO asymmetry or non-normality. [START_REF] An | ENSO Irregularity and Asymmetry[END_REF][START_REF] Timmermann | A nonlinear theory for El Niño bursting[END_REF][START_REF] An | Nonlinearity and asymmetry of ENSO[END_REF] Although significant progress has been made, there is no generally accepted theory that provides a complete and comprehensive picture of the ENSO space-time complexity. [START_REF] Timmermann | El Niño-Southern Oscillation complexity[END_REF] Here we propose a model that captures the essential ingredients of ENSO complexity discussed above such as its diversity and asymmetry in spatial patterns and evolution (Fig. 1). The present model manages to do so in extremely simple fashion: it is a minimal oscillator with only two core variables and one source of randomized forcing, that extends commonly accepted recharge-discharge theory 8 but does not introduce any sophisticated mechanism. Its novelty consists in reframing the main geometry of the ENSO, which simplifies the problem but also questions the ENSO's generally accepted degree of complexity. Hereafter we detail the model's rationale and properties as well as the broader implications for predicting ENSO variability and impacts.

Model Geometry

The formulation of the present oscillator model starts by proposing an idealized geometry for the general circulation of the equatorial Pacific, commonly referred to as the Walker circulation (Fig. 2a). [START_REF] Bjerknes | Atmospheric teleconnections from the equatorial Pacific[END_REF][START_REF] Dijkstra | Oceanatmosphere interaction and the tropical climatology. Part II: Why the Pacific cold tongue is in the east[END_REF][START_REF] Xie | Ocean-atmosphere interaction in the making of the Walker circulation and equatorial cold tongue[END_REF] We consider a longitudinal strip at the equator that represents the circulation in terms of two regions with distinct properties, the so-called warm pool and cold tongue regions. For simplicity, our representation is limited to zonal wind stress and SST at the ocean's surface as well as thermocline depth that roughly measures the amount of heat stored below the surface. Such a representation is compelling here in that it is amenable to detailed analysis yet compares reasonably well with observations (Extended Data Fig. 1).

The Walker circulation is not static and its evolution is in fact what constitutes ENSO variability (Fig. 2b,c). The novelty of the present approach consists in representing such an evolution in rather simple terms, by directly shifting the entire Walker circulation back and forth in the longitudinal (i.e. zonal) direction. This generates La Niña events when the circulation shifts westward which expands the cold tongue region, and conversely El Niño events when the circulation shifts eastward which expands the warm pool region. Such a behavior is observed in nature in the form of general and coherent movements that follow the warm pool edge and that involve both the atmosphere and ocean (Extended Data Fig. 2, Supplementary Information Video 1).

Generally speaking, the Walker circulation can be decomposed into a mean state, representative of average (or seasonal) conditions, and anomalies, representative of departures i.e. of ENSO variability (Fig. 1). Conventional ENSO models typically simplify the problem by prescribing the mean state to focus on the ENSO anomalies. [START_REF] Neelin | ENSO theory[END_REF] This however, adds an unexpected layer of complexity as it accounts rather indirectly for the spatial movements of the total circulation. [START_REF] Schopf | A simple mechanism for ENSO residuals and asymmetry[END_REF] In order to circumvent this difficulty, our representation focuses explicitly on the total circulation (minus seasonal effects) from which the mean state and anomalies are deduced but not prescribed.

Model Dynamics

Although fundamental, the process of Walker circulation shifting discussed above hasn't yet found a firm standing in ENSO theory with the exception of a few attempts at modelling the warm pool's edge position. [START_REF] Picaut | An advective-reflective conceptual model for the oscillatory nature of the ENSO[END_REF][START_REF] Clarke | A simple warm-pool displacement ENSO model[END_REF] Here we encapsulate the process in a minimal oscillator with concise ENSO dynamics, which is achieved by extending a well proven and widely-used 9 theoretical framework, the so-called recharge-discharge oscillator. [START_REF] Jin | An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model[END_REF] As detailed in the methods section, a general form The cold tongue is characterized by trade winds blowing west that gradually shallow the thermocline and cool the SST. b,c, The present approach consists in shifting the circulation as a whole during La Niña and El Niño while conserving its general geometrical features. This results in opposite contractions and expansions of each region as described by the variable extents χ and µ. of the resulting system can be expressed as:

dµ/dt = -a 1 µ -b 1 h M + c 1 -d 1 µ 2 dh M /dt = -a 2 h M + b 2 µ + c 2 + ζ ( 1
)
where t is time, µ is the extent of the cold tongue region, h M is basin-wide heat content, [START_REF] Jin | An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model[END_REF][START_REF] Meinen | Observations of warm water volume changes in the equatorial Pacific and their relationship to El Niño and La Niña[END_REF] ζ is a stochastic (i.e. randomized) forcing, [START_REF] Jin | Ensemble-mean dynamics of the ENSO recharge oscillator under state-dependent stochastic forcing[END_REF] and the remainder consists of constant parameters. The above system generates ENSO-like oscillations that are irregular due to the stochastic forcing and that occasionally exhibit strong El Niño events as in nature (Fig. 3a,b).

The main novelty compared to conventional recharge-discharge theory is that, instead of fixing the domain of the cold tongue, we allow it to expand and contract by solving for its extent µ (Fig. 2). This allows capturing all major ENSO patterns as a single continuum: [START_REF] Capotondi | Understanding ENSO diversity[END_REF] La Niña (µ large), central Pacific El Niño (µ moderately small) and eastern Pacific El Niño (µ very small) (Fig. 1,2). Such a modification nevertheless conserves the original recharge-discharge mechanism responsible for the ENSO's reversal of conditions, that is: the more expanded the cold tongue, the more the trade winds recharge heat content (term b 2 µ) which in turns warms the surface and rebalances the Walker circulation (term -b 1 h M ), and conversely (Extended Data Fig. 3).

Another novel addition is a quadratic nonlinearity (term -d 1 µ 2 ) that stems directly from the Walker circulation's geometry as detailed hereafter. Such a nonlinearity here shapes the dynamics such as to generate an asymmetry in amplitude and duration between El Niño and La Niña, as in nature [START_REF] An | ENSO Irregularity and Asymmetry[END_REF] (Extended Data Fig. 4). Meanwhile, the remainder of the system is more conventional: ζ in particular is an ad-hoc stochastic forcing that mimics the effect of random fluctuations in nature (e.g. wind bursts [START_REF] Vecchi | Tropical pacific sea surface temperature anomalies, El Niño, and equatorial westerly wind events[END_REF][START_REF] Jin | Ensemble-mean dynamics of the ENSO recharge oscillator under state-dependent stochastic forcing[END_REF] ) and excites the otherwise dissipated system.

Model Nonlinearities

Our representation of the Walker circulation's spatial shifting movements offers new perspectives for interpreting the multi-faceted aspects of ENSO nonlinearity and non-normality. [START_REF] An | ENSO Irregularity and Asymmetry[END_REF] We provide an overview of this interplay in the form of spatial averages over various regions of the equatorial Pacific including the warm pool and cold tongue regions of variable extents (Extended Data Fig. 5). The relationships between these spatial averages and spatial shifting are nonlinear for the most part as per the model's formulation (see methods), yet all of them hold reasonably well in observations (Fig. 3c-q). Importantly, the present model nonlinearities all stem from the general geometry of the problem rather than details of local processes (e.g. starting budgets), which differs from other rationales proposed in the literature. [START_REF] Timmermann | A nonlinear theory for El Niño bursting[END_REF][START_REF] An | Nonlinearity and asymmetry of ENSO[END_REF][START_REF] Jin | Ensemble-mean dynamics of the ENSO recharge oscillator under state-dependent stochastic forcing[END_REF] For example, the thermocline's response to spatial shifting is geometrically quadratic (Fig. 3e,j), which in turn generates ENSO asymmetry as it mitigates La Niña development but amplifies El Niño development (Extended Data Fig. 6). As another example, the central to eastern Pacific is overlapped back and forth by either the warm pool or cold tongue which mixes nonlinearly saturating and sloping SST characteristics (Fig. 3g,l,q). This, in turn, provides a simple source of non-normality (e.g. skewness) for the resulting statistics [START_REF] Jin | Ensemble-mean dynamics of the ENSO recharge oscillator under state-dependent stochastic forcing[END_REF][START_REF] Chen | A multiscale model for el Niño complexity[END_REF] (Extended Data Tab. 1).

Principal Component Analysis

The first principal components (PCs) of SST in the equatorial Pacific deduce the leading ENSO patterns in terms of data covariance (see methods), but their interpretation still lacks consensus. [START_REF] Takahashi | ENSO regimes: Reinterpreting the canonical and Modoki El Niño[END_REF][START_REF] Dommenget | Analysis of the non-linearity in the pattern and time evolution of El Niño Southern Oscillation[END_REF] Here we reproduce the PC's overall characteristics for the first time with a minimal model (Fig. 4): this is not only achieved in terms of spatial structures but also in terms of a nonlinear quadratic relationship between PCs. [START_REF] Karamperidou | The importance of ENSO nonlinearities in tropical Pacific response to external forcing[END_REF][START_REF] Cai | Increased variability of eastern Pacific el Niño under greenhouse warming[END_REF] The Walker circulation's longitudinal movements can in fact explain the PC's characteristics in reasonably simple terms. The first PC captures the cold tongue's movements over the eastern Pacific and approximately no variability from the warm pool's saturating SSTs over the western Pacific (Fig. 4a). The second PC captures a central Pacific variability (Fig. 4b) that stems from a spatial shifting nonlinearity mentionned earlier. As the central Pacific is overlapped back and forth by either the warm pool or cold tongue, it mixes saturating and sloping SST characteristics (Fig. 3q). The resulting characteristics have approximately a quadratic shape that is necessarily captured by a joint contribution of the first and second PCs, thus tying those together nonlinearly (Fig. 4c, Extended Data Fig. 7). Although our results suggest that the first PCs predominantly capture spatial shifting, they do not exclude the potential imprint of other phenomena from the literature. [START_REF] Stuecker | A combination mode of the annual cycle and the El Niño Southern Oscillation[END_REF][START_REF] Martinez-Villalobos | An analytical framework for understanding tropical meridional modes[END_REF]

Outlook

Here we have shown that the spatial shifting movements of the Walker circulation shape the ENSO variability in a major way. [START_REF] Bjerknes | Atmospheric teleconnections from the equatorial Pacific[END_REF] This allows reinterpreting some of the phenomenon's most complex and elusive features 7, 5 using simple geometrical principles, as encapsulated in a minimal oscillator model. Our discovery suggests that the ENSO's nonlinear dynamics are simpler than previously considered to some extent, thus hopefully more predictable. [START_REF] Barnston | Skill of real-time seasonal ENSO model predictions during 2002-11: Is our capability increasing?[END_REF] Beyond improving ENSO understanding, the seminal concepts proposed here may shed a new light on other major aspects of the phenomenon. First and foremost, the present spatial shifting paradigm should be combined and reconciled with other rationales for complexity, nonlinearity and mean state interactions proposed in the literature, including in more realistic setups. [START_REF] Jin | Simple ENSO Models[END_REF][START_REF] An | ENSO Irregularity and Asymmetry[END_REF][START_REF] Fedorov | ENSO Low-Frequency Modulation and Mean State Interactions[END_REF] Far reaching implications extend to the study of teleconnections considering that the Walker circulation's movements are tied to pan-tropical as well as extra-tropical variability. [START_REF] Cai | Pantropical climate interactions[END_REF][START_REF] Yun | Synchronized spatial shifts of Hadley and Walker circulations[END_REF] In fact, these interactions bridge not only ENSO-induced climate disruptions across the planet, but also remote influences on El Niño or La Niña onset. [START_REF] Ropelewski | Global and regional scale precipitation patterns associated with the El Niño Southern Oscillation[END_REF][START_REF] Mcphaden | ENSO as an integrating concept in earth science[END_REF][START_REF] Klein | Remote sea surface temperature variations during ENSO: Evidence for a tropical atmospheric bridge[END_REF] Conjointly, our representation provides novel geometrical guidelines for the diagnosis of general circulation models, e.g. to infer core convective or dynamical feedbacks. [START_REF] Ham | How well do current climate models simulate two types of El Niño?[END_REF][START_REF] Jin | A coupled-stability index for ENSO[END_REF][START_REF] Vijayeta | An evaluation of ENSO dynamics in CMIP simulations in the framework of the recharge oscillator model[END_REF] This, in turn, may help further understand how El Niño's strength and flavor are modulated by decadal variability and climate change. [START_REF] Cai | Increased variability of eastern Pacific el Niño under greenhouse warming[END_REF][START_REF] Fedorov | A stability analysis of tropical ocean-atmosphere interactions: Bridging measurements and theory for El Niño[END_REF][START_REF] Wittenberg | Are historical records sufficient to constrain ENSO simulations?[END_REF] Acknowledgments. The research of S.

Methods

Idealized Walker Circulation. Consider nondimensional fields of SST T , thermocline depth h and zonal wind stress τ x in a zonal strip representative of the equatorial Pacific (120 • E to 80 • W, averages 5 • N to 5 • S). Let the fields describe the evolution of an idealized Walker circulation (Fig. 2, Extended Data Fig. 1) that reads:

if x < χ(t)      τ x (x, t) = 0 T (x, t) = T W h(x, t) = h W (t) if x ≥ χ(t)      τ x (x, t) = τ E T (x, t) = T W -2s(x -χ) h(x, t) = h W (t) -2a(x -χ)
(2) where x is zonal position (with 0 ≤ x ≤ 1) and t is time. The circulation is centered on the warm pool edge of position χ (pronounced "ki") that separates the warm pool region (x < χ) from the cold tongue region (x ≥ χ) with distinct properties.

The structure of such a circulation results from a complex balance between the atmosphere and ocean in nature that is summarized here in its essential terms. [START_REF] Bjerknes | Atmospheric teleconnections from the equatorial Pacific[END_REF][START_REF] Dijkstra | Oceanatmosphere interaction and the tropical climatology. Part II: Why the Pacific cold tongue is in the east[END_REF][START_REF] Xie | Ocean-atmosphere interaction in the making of the Walker circulation and equatorial cold tongue[END_REF][START_REF] Neelin | ENSO theory[END_REF] Trade winds (oriented westward) span the cold tongue region with constant intensity τ E < 0 where they induce SST as well as thermocline depth to slope at rates 2s and 2a, respectively. Meanwhile, SSTs saturate at T W = 29 • C over the warm pool region. In fact, SSTs nearing that threshold significantly increase convective activity in the atmosphere, which in turn captures excess heating. Convective activity reinforces the trade winds over the cold tongue through large scale convergence but also approximately breaks them down over the warm pool through the buildup of smaller scales fluctuations (e.g. wind bursts [START_REF] Vecchi | Tropical pacific sea surface temperature anomalies, El Niño, and equatorial westerly wind events[END_REF] ).

The above circulation may vary in terms of the warm pool edge position χ(t), which consists of a spatial shifting movement of its entire structure in the longitudinal direction (Fig. 2, Extended Data Fig. 2, Supplementary Information Video 1). The rationale for this is simply that, from one state to another, the atmosphere and ocean approximately rebalance according to the same arguments discussed above. Such a process can be seen as a reinterpretation of the so-called Bjerknes hypothesis, that broadly speaking refers to mutual reinforcements between the Walker circulation's atmosphere and SSTs. [START_REF] Bjerknes | Atmospheric teleconnections from the equatorial Pacific[END_REF] The circulation may also vary in terms of h W (t) that relates to the overall ocean heat content as detailed hereafter.

Regions averages. Let χ from Eq. 2 be the variable extent of the warm pool region with 0 ≤ χ ≤ 1. Similarly, let µ (pronounced "mu") be the variable extent of the cold tongue region with 0 ≤ µ ≤ 1. Longitudinal (i.e. zonal) shifting results in opposite contractions and expansions of each region as encapsulated by χ + µ = 1. Here χ denotes interchangeably warm pool extent or warm pool edge position ranging from 0 to 1 in non-dimensional units: these are however distinct in dimensional units ranging respectively from 0 • to 160 • longitude and from 120 • E to 80 • W.

For a more concise representation, we introduce new indices:

T W (t) = χ -1 χ 0 T (x, t)dx T E (t) = µ -1 1 χ T (x, t)dx T M (t) = 1 0 T (x, t)dx = χT W + µT E (3)
that represent spatial averages of SST at a given time respectively over the warm pool and cold tongue regions of variable extent and over the entire basin (Extended Data Fig. 5). Similar indices are defined for zonal wind stress (τ W , τ E , τ M ) and for thermocline depth (h W , h E , h M ). With this, the geometrical relationships from Eq. 2 can be expressed more simply as:

τ M = µτ E T E = T W -sµ h E = h W -aµ (4)
which encapsulates the trade winds span over the cold tongue region as well as the sloping of SST and thermocline depth. Combining the above with the definitions of basin-wide averages (Eq. 3), we obtain nonlinear quadratic relationships:

T W = T M + sµ 2 T E = T M -sχµ h W = h M + aµ 2 h E = h M -aχµ (5)
where we recall that T W is constant. We can also deduce spatial averages over any given region of the equatorial Pacific (e.g. conventional regions Niño 4, 3.4 or 3) from Eq. 2.

The relationships in Eq. 2-5 infer the Walker circulation's geometrical response to given dynamical constraints as discussed hereafter (Fig. 3, Extended Data Fig. 6, Extended Data Tab. 1). The characteristics of the Walker circulation at a given time are set entirely by χ (or equivalently µ) and h M , from which we deduce other variables. h M is the spatial average of thermocline depth over the basin, also referred to as basin-wide heat content or warm water volume in the literature. [START_REF] Meinen | Observations of warm water volume changes in the equatorial Pacific and their relationship to El Niño and La Niña[END_REF] Model Derivation. Consider a thermodynamical budget for the cold tongue SST and a dynamical budget for the basin-wide heat content:

dT E /dt = -ξ(T E -T W ) + ηh E -Q -q * dh M /dt = -σh M + γτ M + F + ζ (6)
with relaxation parameters (ξ, σ), thermocline feedback (η), wind stress forcing (γ) and optional stochastic forcing ζ as in conventional rechargedischarge theory. [START_REF] Jin | An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model[END_REF] Modifications to this theory consist here in adding constant external sources F , Q that set equilibrium conditions (as we are working with field totals instead of anomalies), in addition to a flux q * = (T E -T W )µ -1 (dµ/dt) as we allow the cold tongue region to expand and contract (Leibniz integral rule). With the exception of q * , the present starting budgets are linear as model nonlinearities will be introduced hereafter from the geometry of the problem. We also approximately omit seasonal effects for the sake of brevity. Other relationships invoked in rechargedischarge theory (e.g. atmospheric response 8 ) are here disregarded: instead, we close the above budgets with the Walker circulation's geometry (Eq. 4-5).

Combining the above relationships, we obtain a minimal oscillator for the ENSO:

2s(dµ/dt) = -ξsµ + aη(µ -µ 2 ) -ηh M + Q dh M /dt = -σh M + bµ + F + ζ (7)
where we note b = -γτ E for brevity. The above model is nicknamed Contraction-Recharge-Expansion-Discharge Oscillator (CREDO) in reference to the original Recharge-Discharge Oscillator (RDO). [START_REF] Jin | An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model[END_REF] This is because the warm pool consecutively contracts, recharges, expands then discharges during an ENSO cycle (Extended Data Fig. 3). The model represents all major ENSO patterns as a single dynamical continuum: [START_REF] Capotondi | Understanding ENSO diversity[END_REF] La Niña (µ large), central Pacific El Niño (µ moderately small) and eastern Pacific El Niño (µ very small) (Fig. 1,2).

Model Details. In order to sustain ENSO variability, we include ad-hoc stochastic forcing in the otherwise dissipated system from Eq. 7 in the form of: dζ/dt = -eζ + r Ẇ (8) where ζ accounts for random fluctuations in nature (e.g. wind bursts [START_REF] Vecchi | Tropical pacific sea surface temperature anomalies, El Niño, and equatorial westerly wind events[END_REF] ) as driven by a white noise source Ẇ with standard normal distribution [START_REF] Jin | Ensemble-mean dynamics of the ENSO recharge oscillator under state-dependent stochastic forcing[END_REF] (Extended Data Fig. 5e).

In practice, the external sources F , Q are deduced such as to obtain a model equilibrium µ 0 , h M 0 that is comparable to observed temporal averages. [START_REF] Timmermann | A nonlinear theory for El Niño bursting[END_REF] This reads:

F = -bµ 0 + σh M 0 Q = ξsµ 0 -aη(µ 0 -µ 2 0 ) + ηh M 0 (9)
where µ 0 , h M 0 are imposed. These external sources here maintain the cold tongue and control its average extent. For lower values of F and Q, it is in fact possible to obtain µ 0 = 0 for which the cold tongue collapses and the equatorial Pacific is overlapped entirely by the warm pool. While these external sources may stem from a wide range of processes, [START_REF] Dijkstra | Oceanatmosphere interaction and the tropical climatology. Part II: Why the Pacific cold tongue is in the east[END_REF][START_REF] Xie | Ocean-atmosphere interaction in the making of the Walker circulation and equatorial cold tongue[END_REF] we leave their discussion for future work. The model's linear solutions around the present equilibrium consists in an oscillatory mode with period around 2.5 years and decay time around 5 months.

Extended Tab. 2 details model units and parameters. As regard numerics, we integrate the model using a simple Euler scheme in time with a timestep 0.1 mth. We constrain 0 ≤ µ ≤ 1 each timestep to deal with potential region collapses even though none occurs during the present simulation (Fig. 3a).

Potential Model Modifications. The present model is in no way a definitive theory for ENSO space-time complexity and may be extended in future work through different avenues. Building upon the existing body of work from the literature, the present framework could be combined with seasonal effects, statedependent noise, zonal advection of SST or other SST feedbacks, and so on. [START_REF] Jin | Simple ENSO Models[END_REF] These modifications might help reconcile spatial shifting with other rationales for complexity, nonlinearity and mean state interactions from the literature. [START_REF] An | ENSO Irregularity and Asymmetry[END_REF][START_REF] Timmermann | A nonlinear theory for El Niño bursting[END_REF][START_REF] An | Nonlinearity and asymmetry of ENSO[END_REF][START_REF] Jin | Ensemble-mean dynamics of the ENSO recharge oscillator under state-dependent stochastic forcing[END_REF][START_REF] Chen | A multiscale model for el Niño complexity[END_REF] As a proof of concept, we have kept the model's complexity to a minimum. Suitable modifications may improve detailed yet important features of ENSO variability (Supplementary Information Video 1). For example, some central Pacific El Niños exhibit a localized SST warming just west of the warm pool edge that overshoots the warm pool saturation level 29 • C imposed here. Some eastern Pacific El Niños exhibit a lingering of warm SSTs in their trail that isn't grasped by the present idealized geometry. The model representation may also be refined to account for the gradual trade winds decays towards the South American coasts, the thermocline sloping in the western Pacific, and so on.

Principal Components Reconstruction. Principal component (PC) analysis is a statistical method based on covariance that is widely used in climate sciences to deduce dominant patterns from data [START_REF] Takahashi | ENSO regimes: Reinterpreting the canonical and Modoki El Niño[END_REF][START_REF] Dommenget | Analysis of the non-linearity in the pattern and time evolution of El Niño Southern Oscillation[END_REF][START_REF] Stuecker | A combination mode of the annual cycle and the El Niño Southern Oscillation[END_REF][START_REF] Karamperidou | The importance of ENSO nonlinearities in tropical Pacific response to external forcing[END_REF][START_REF] Cai | Increased variability of eastern Pacific el Niño under greenhouse warming[END_REF] (among other applications). Here SST in the equatorial Pacific may be reconstructed for example from its first PC or from its first and second PCs as:

R1(x, t) = PC1(t)EOF1(x) + T R1&2(x, t) = R1 + PC2(t)EOF2(x) (10)
with associated empirical orthogonal functions (EOFs, Fig. 4a,b), where we denote here PC1 and PC2 as PC timeseries (Fig. 4c) and where T is temporal mean. The first PC alone (R1) reasonably reconstructs SST variability in the eastern and western Pacific but is severely biased in the central Pacific (Extended Data Fig. 7). In the present reconstruction R1&2, the first and second PC timeseries are approximately tied by a quadratic relationship with general form:

PC2 = a 2 PC1 2 + b 2 PC1 + c 2 (11)
that reasonably holds in observations and the proposed oscillator model (Fig. 4c, Extended Data Fig. 7). Such a relationship has received recent focus in order to diagnose ENSO nonlinearity. [START_REF] Karamperidou | The importance of ENSO nonlinearities in tropical Pacific response to external forcing[END_REF][START_REF] Cai | Increased variability of eastern Pacific el Niño under greenhouse warming[END_REF] Observational Data. Observational data used in this paper is from the NCEP Global Ocean Data Assimilation System (GODAS), [START_REF] Behringer | ) Extended Data Fig. 5 Indices timeseries. Timeseries from observations of warm pool edge position (a), SST spatial averages (b), thermocline depth spatial averages (c), and[END_REF] provided by the NOAA/OAR/ESRL PSL, Boulder, Colorado, USA, from their Web site at https://www.psl.noaa.gov/data/gridded/data. godas.html. Data is monthly over 1982-2017 and includes fields of zonal wind stress (N.m -2 ), thermocline depth (m, measured as the 20 • C isotherm) and SST ( • C). All fields span the equatorial Pacific 120 • E-80 • W, are meridionaly averaged within 5 • N-5 • S and have their seasonal variations around temporal averages removed (which we refer to as totals in the present paper with a slight abuse in terminology).

The indice χ that measures the warm pool edge position in observations (Fig. 1,3, Extended Data Fig. 2,3) is defined as:

χ(t) = 1 0 bool(T > 28.5 • C)dx + ∆ c ( 12
)
where T (x, t) is observed SST, the equatorial Pacific spans 0 ≤ x ≤ 1 (120 • E-80 • W in dimensional units), the bool function maps 1 if the boolean condition is true and zero otherwise, and ∆ c is a constant. The estimation method is meant to delineate robustly the 29 • C isotherm at which warm pool SSTs approximately saturate, but requires additional workarounds to minimize thresholding sensitivity. First, we measure the index on data without seasonal variations which simplifies the delineation. Second, a threshold value 28.5 • C is chosen that, in order to allow delineation, must be slightly below the actual saturation value 29 • C. In order to grasp the saturation value slightly more west, we add an empirical correction ∆ c (-10 degrees • E in dimensional units). Third, occasional cooling below 28.5

Fig. 1

 1 Fig. 1 Observed and modelled ENSO variability. a,b, Time-longitude hovmollers of sea surface temperatures anomalies (SSTA) and thermocline depth anomalies (TDA) in the equatorial Pacific, as computed from observations (averaged 5 • N-5 • S with seasonal variations removed). Solid lines in each panel indicate the longitudinal position of the warm pool edge (i.e. 29 • C SST isotherm, see methods). c,d, Hovmollers repeated for solutions generated by a minimal oscillator model, displayed over a hand-picked period with time relative to the beginning of numerical simulation. The model reasonably reproduces all major ENSO patterns: El Niños with strong eastern Pacific warming (EP), with moderate central to eastern Pacific warming (CP), and La Niñas with moderate and lingering cooling that extends further westward (LN).

Fig. 2

 2 Fig. 2 Idealized Walker circulation. a, The equatorial Pacific is represented by a longitudinal strip divided into a warm pool region and a cold tongue region. The warm pool is characterized by saturating sea surface temperatures (SST), a deep thermocline and increased convection.The cold tongue is characterized by trade winds blowing west that gradually shallow the thermocline and cool the SST. b,c, The present approach consists in shifting the circulation as a whole during La Niña and El Niño while conserving its general geometrical features. This results in opposite contractions and expansions of each region as described by the variable extents χ and µ.

Fig. 3

 3 Fig. 3 Evolution of spatial averages. a,b, Timeseries of warm pool extent χ and basin-wide heat content h M obtained from a numerical integration of the oscillator model (Eq. 1), and which represents ENSO variability. χ within 0-1 corresponds to a warm pool edge within 120 • E-80 • W (Fig. 1, 2). c-q, Scatterplots between spatial averages (or combinations of them) and warm pool extent χ as measured in either model outputs (red) or observations (black). The indices T W , T E , T M (h W , h E , h M ) averages SST (thermocline depth) conditions respectively over the warm pool, cold tongue and entire basin (120 • E-80 • W). The conventional indices Niño 4, 3.4 and 3 SST average conditions over the central (160 • E-150 • W), central-eastern (170 • W-120 • W) and eastern (150 • W-90 • W) Pacific. All averages are within the equatorial band (5 • N-5 • S). The ENSO-like oscillations from panels a,b are encapsulated in panel h. The model solutions reasonably match observations for relationships that are either linear (d,n,o,p), nonlinear quadratic (e,f,i,j,k), nonlinear saturating (g,l,q) or nonlinear oscillatory (c,h,m). The Niño SST indices (g,l,q) saturate at around 29 • C when the warm pool region overlaps their domain entirely.

Fig. 4

 4 Fig. 4 Principal component analysis of SST. a,b, First and second Empirical Orthogonal Functions (EOFs) as computed from either model outputs (red) or observations (black), with explained variance indicated (%). c, Scatterplot between first and second principal component (PC) timeseries as computed from model outputs (red) or observations (black). The model solutions compare reasonably well with observations in terms of EOFs, explained variance and a quadratic relationship between PC timeseries (as highlighted in observations by a second order polynomial fit, green line). The first PC timeserie strongly correlates with spatial shifting (χ) in both the model (r=0.99) and observations (r=0.91). SST represent 5 • N-5 • S averages in the equatorial Pacific.

  T. is supported by ANR (Grant ANR-18-CE01-0012). B.D. acknowledges support from ANID (Concurso de Fortalecimiento al Desarrollo Científico de Centros Regionales 2020-R20F0008-CEAZA, Eclipse FSEQ210017 and COPAS COASTAL FB210021) and ANR (Grant ANR-18-CE01-0012). The authors thank O.Thual for discussions. Competing interests. The authors declare no conflict of interest. Authors' contributions. S.T. designed and performed research. S.T. and B.D. discussed research and wrote the paper.

Extended Data Fig. 1

 1 Walker circulation structure. Zonal profiles of zonal wind stresses (ZWS, a), sea surface temperatures (SST, b) and thermocline depth (TD, c) in a longitudinal strip spanning the equatorial Pacific (black lines and fillings). The circulation can only vary in terms of its warm pool edge position χ, except for thermocline depth that can additionally vary in terms of its basin-wide average h M (blue dashed lines). As a proof of concept we adjust these variables in the figure in order to match observed temporal averages of ZWS, SST and TD (purple dashed lines).Extended Data Fig.2Time-longitude hovmollers for totals. a,b,c, Time-longitude hovmollers of zonal wind stress (ZWS), sea surface temperature (SST) and thermocline depth (TD) in the equatorial Pacific, as computed from observations (averaged 5 • N-5 • S with seasonal variations removed). d,e,f, Analysis repeated for the outputs of the oscillator model (displayed over a hand-picked period). Solid lines in each panel indicate the longitudinal position of the warm pool edge (i.e. 29 • C SST isotherm, see methods). The spatial shifting of the Walker circulation consists of a general and coherent longitudinal movement of the atmospheric and oceanic structures that follows the warm pool edge, as found in observations and as reproduced qualitatively by the oscillator model. The movement is less apparent on thermocline depth that also varies significantly in terms of its basin-wide average. Extended Data Fig.3ENSO cycle in the oscillator model. a-d, Sketch of the Walker circulation at the four consecutive stages of one ENSO cycle: contracted (La Niña), recharged, expanded (El Niño) and discharged. This is shown for zonal wind stress (ZWS), sea surface temperatures (SST) and thermocline depth (TD) represented as in Extended Data Fig.1. The circulation is entirely determined by the warm pool extent χ and basin-wide heat content h M , indicated at each stage of the cycle (blue dashed lines) and for the entire cycle (red lines, years 132 to 135 in Fig.1)). e-h, Mean state of SST and TD (i.e. temporal averages computed over the entire simulation, green dashed lines) with total fields from a-d repeated (gray fillings). i-l, Sea surface temperature anomalies (SSTA) and thermocline depth anomalies (TDA) at each stage as computed with respect to the mean state. The oscillator model generates ENSO cycles that follow a conventional rechargedischarge evolution of heat content but where SSTA and TDA patterns stem from the Walker circulation's movements.Extended Data Fig.4Phase space comparison. Kernel density estimates (contours) and individual realizations (black lines) in phase space of warm pool extent χ and basin-wide heat content h M , in either observations (a) or model solutions (b). For clarity, density estimates are shown only above 0.04% where they hide individual realizations that are too dense to visualize. Phase space is divided into El Niño or La Niña states as well as recharged or discharged states as defined here with respect to average conditions (white dashed lines). El Niño events may reach larger amplitudes than La Niña events but are more short-lived.Extended Data Fig.6Thermocline nonlinearity. Starting from either a La Niña state (a) or El Niño state (b), we apply a zonal shifting perturbation δχ (at constant basin-wide heat content h M ) that further develops the corresponding event (purple dashed lines). We then compare the original thermocline depth profile (gray filling) versus the modified one (green filling). The thermocline depth averaged over the cold tongue h E increases in both cases (dots and dashed lines). This generates asymmetry as it mitigates La Niña development but amplifies El Niño development. The relationship is encapsulated by h E = h M -a(χ -χ 2 ) in the oscillator model (see methods).Extended Data Fig.7Principal components reconstruction. a-e, Scatter plots between sea surface temperatures (SST) and first principal component timeserie (PC1) at different longitudes of the equatorial Pacific, as computed from observations. f-j, Analysis repeated for outputs of the oscillator model. Individual realizations are discriminated in terms of their belonging to the warm pool region (WP, red) or cold tongue region (CT, blue), with total occurrences indicated in %. We show SST reconstructed from first principal component (R1, black lines), as well as SST reconstructed from first and second principal components (R1&2, green lines) for which PC2 approximately depends on PC1 through a quadratic relationship (Fig.4and methods). First principal component alone (R1) captures well "pure" WP or CT characteristics in the western and eastern Pacific, but fails to capture nonlinearly mixed WP-CT characteristics in the central Pacific. These mixed WP-CT characteristics have approximately a quadratic shape that is captured instead by a joint reconstruction from first and second principal components (R1&2).

  • C in the far western Pacific can bias the estimation, and to remedy this we set bool= 1 west of the measured χ and recompute it once. Indices statistics.

	Extended Data Tab. 2 Model units and parameters.
	Parameter Value	Scaling	Definition
	[x] Extended Data Tab. 1 Indice 1 [t] 1	18000 km Mean 1 month	unit zonal position Std Skewness unit time
	[h] [T ]	1 1	20 m Model Obs Model Obs Model Obs unit thermocline depth 1 • C unit SST
	[τ x ] L T W s a ξ σ b η Q F µ 0 h M 0 e	χ (1000 km) 1 τ W (10 -3 N.m -2 ) 0.01 N.m -2 6.61 6.56 0 -10 1 18 000 km τ M -22 -26 29 29 • C τ E -35 -35 4.5 0.25 • C.(1000 km) -1 sloping rate SST (halved) 2.43 1.96 0.92 unit zonal wind stress 1.44 0 7.8 0 equatorial Pacific length 0.45 4.7 5.8 0.92 saturation level SST 0.09 0 0.6 0 0.27 h W (m) 165 165 12.8 12.5 5 5.56 m.(1000 km) -1 sloping rate thermocline (halved) -1.1 -0.63 h M 124 125 8.4 6.3 1/6 (6 mth) -1 relaxation SST -0.25 -0.85 h E 102 104 7.0 7.7 1/14 (14 mth) -1 relaxation thermocline -0.33 -0.22 T W ( • C) 29.0 29.4 0 0.25 0.7 7.8 10 -7 mth -1 trade winds constant 0 -0.24 T M 27.1 27.5 0.71 0.53 0.11 0.8 0.04 • C.m -1 .mth -1 thermocline feedback 0.34 T E 26.2 26.4 0.61 0.55 0.92 4.56 4.56 • C.mth -1 external cooling 0.98 Niño 4 SST • C 28.3 28.5 0.63 0.67 -1.6 10 -3 -0.37 m.yr -1 external forcing -0.89 -0.45 Niño 3.4 SST 27.4 27.5 0.88 0.81 -0.18 0.36 6480km equilibrium value of µ 0.06 Niño 3 SST 25.7 25.8 1.14 0.93 0.57 6.25 125m equilibrium value of h M 0.97 1/3 (3 mth) -1 stochastic forcing dissipation
	r	0.1	2 m.mth -2	stochastic forcing generation
	∆ c	-0.0625	-10 deg • E	correction for χ (in observations)

Supplementary Material Video 1 Evolution of the Idealized Walker Circulation. a,e,f, Idealized Walker circulation (black lines) compared to observations (purple dashed lines) in terms of zonal wind stresses (ZWS), SST and thermocline depth (TD), where each animated frame corresponds to a given month of the record. The idealized Walker circulation is entirely determined by warm pool edge position and zonal mean thermocline depth (blue dashed lines), which values here match the ones from observations. b,c,d, longitude-time hovmollers of ZWS, SST and TD, with indication of warm pool edge position (blue dashed lines) and time of current frame (purple dashed lines). The idealized circulation's geometry compares reasonably to observations including for individual ENSO events.

File SI Video 1.mp4 or link https://drive.google.com/file/d/1BJmSKkDtvi60t9 u40Vck7-8d7i2KL1X/view?usp=sharing


C Briant

Alvarez

O Sublemontier

M Briant

C Alvarez-Ilamas

come

Laser-Induced Breakdown Spectroscopy for atmospheric monitoring of selected fine and ultrafine particles O. Sublemontier Air quality monitoring is a major challenge for this decade. One of the most important and difficult issues concerns the monitoring of fine particles (1 µm or less), and in particular ultrafine particles (100 nm or less). In mid-2018, ANSES published a report recommending strengthening the monitoring of ultrafine particles, classified as priority pollutants in the air [START_REF]Polluants « émergents » dans l'air ambiant : Identification, catégorisation et hiérarchisation de polluants actuellement non réglementés pour la surveillance de la qualité de l'air[END_REF]. In addition, access to the number concentration of fine and ultrafine particles of a given elementary composition is crucial for the following reasons:

-Ultrafine particles typically make up less than 1% of the mass of aerosols, but more than 80% of the total number of particles in the atmosphere. -Ultrafine particles remain suspended in the air for a very long time, unlike micrometric particles. -The health risks due to ultrafine particles by inhalation are high and linked to their chemical composition since they penetrate the respiratory system and can pass into the blood.

Here, we propose to discuss a method that should makes it possible to obtain the number and mass concentrations, in real time and in situ, of particles of a given elementary composition, without limitation in the type of particle. The size range considered is from few tens of nm to 1000 nm, covering as much as possible the domain of fine and ultrafine particles [START_REF] Picard | [END_REF][START_REF] Sublemontier | Dispositif de caractérisation de particules dans un jet de particules sous vide[END_REF].

The process is based on Laser-Induced Breakdown Spectroscopy (LIBS) applied to aerosols. It differs from previous works [START_REF] Amodeo | [END_REF] by an interaction taking place under vacuum between a focused high-speed pulsed laser and a jet of particles produced by an aerodynamic lens system (SLA) [5]. The interaction with the laser therefore takes place only with the particulate phase without interaction with the gaseous phase, and continuously. The SLA makes it possible to produce a very fine and very dense jet of particles under vacuum while avoiding contamination by particle deposition of the optical elements. This deposit is indeed a major limitation of the online analysis of aerosols by optical technique.

The advantages of the presented technique compared to conventional ones at ambient pressure are:

-Zero background noise from the surrounding gas plasma.

-Highly increased sensitivity thanks to SLA concentration effect.

-Detection of individual particles, allowing counting, connected to the number concentration of particles in the air. -More efficient detection of elements emitting in the far UV, even down to VUV.

  , M. Briant and C. Alvarez-Ilamas, Université Paris-Saclay, CEA, CNRS, NIMBE, 91191, Gif sur Yvette, France


Brigitte Bigi
email: brigitte.bigi@lpl-aix.fr

Béatrice Priego-Valverde
email: beatrice.priego-valverde@univ-amu.fr

The automatic search for sounding segments of SPPAS: application to Cheese! corpus

Keywords: speech, IPUs, segmentation, silence, corpus, conversation

The development of corpora inevitably involves the need for segmentation. For most of the corpora, the first segmentation to operate consist in determining silences vs Inter-Pausal Units -IPUs, i.e. sounding segments. This paper presents the "Search for IPUs" feature included in SPPAS -the automatic annotation and analysis of speech software tool distributed under the terms of public licenses. Particularly, this paper is focusing on its evaluation on Cheese! corpus, a corpus of reading then conversational speech between two participants. The paper reports the number of manual actions which was performed manually by the annotators in order to obtain the expected segmentation: add new IPUs, ignore irrelevant ones, split an IPU, merge two consecutive ones and move boundaries. The evaluation shows that the proposed fully automatic method is relevant.

Introduction

Corpus Linguistics is a Computational Linguistics field which aims to study the language as expressed in corpora. Nowadays, Annotation, Abstraction and Analysis (the 3A from [START_REF] Wallis | Knowledge discovery in grammatically analysed corpora[END_REF]) is a common perspective in this field. Annotation consists of the application of a scheme to recordings (text, audio, video, ...). Abstraction is the mapping of terms in the scheme to terms in a theoretically motivated model or dataset. Analysis consists of statistically probing, manipulating and generalizing from the dataset. Within these definitions, this paper focuses on annotation which "can be defined as the practice of adding interpretative, linguistic information to an electronic corpus of spoken and/or written language data. 'Annotation' can also refer to the end-product of this process" [START_REF] Leech | Introducing corpus annotation[END_REF]. Annotating corpora is of crucial importance in Corpus Linguistics. More and more annotated corpora are now available, and so are tools to annotate automatically and/or manually. Large multimodal corpora are now annotated with detailed information at various linguistic levels. The temporal information makes it possible to describe behaviour or actions of different subjects that happen at the same time.

An orthographic transcription is often the minimum requirement for a speech corpus. It is often at the top of the annotation procedure, and it is the entry point for most of the other annotations and analysis. However, in the specific annotation context of a multimodal corpus, the time synchronization of the transcription is of crucial importance.

In recent years, SPPAS [START_REF] Bigi | SPPAS -Multi-lingual Approaches to the Automatic Annotation of Speech[END_REF] has been developped by the first author to automatically produce time-aligned annotations and to analyze annotated data. The SPPAS software tool is multi-platform (Linux, MacOS and Windows) and open source issued under the terms of the GNU General Public License. It is specifically designed to be used directly by linguists. As a main functionality, SPPAS allows to perform all the automatic annotations that are required to obtain the speech segmentation at the word and phoneme level of a recorded speech audio and its orthographic transcription [START_REF] Bigi | Automatic segmentation of spontaneous speech[END_REF].

Figure 1 describes the full process of this method in order to annotate a multimodal corpus and to get time-synchronized annotations, including the speech segmentation. The audio signal is analyzed at the top-level of this procedure in order to search for the Inter-Pausal Units. IPUs are defined as sounding segments surrounded by silent pauses of more than X ms. They are time-aligned on the speech signal. IPUs are widely used for large corpora in order to facilitate speech alignments and for the analyses of speech, like prosody in (Peshkov et al., 2012). The orthographic transcription is performed manually at the second stage and is done inside the IPUs. We applied this annotation method to the conversational French multimodal corpus 'Cheese!' [START_REF] Priego-Valverde | Is smiling during humor so obvious? A cross-cultural comparison of smiling behavior in humorous sequences in american english and french interactions[END_REF][START_REF] Priego-Valverde | Cheese!": a Corpus of Face-to-face French Interactions. A Case Study for Analyzing Smiling and Conversational Humor[END_REF]. "Cheese!" is made of 11 face-to-face dyadic interactions, lasting around 15 min each. This paper presents the automatic annotation "Search for IPUs" of the SP-PAS software tool. Given a speech recording of Cheese!, the goal was to generate an annotation file in which the sounding segments between silences are marked. This paper describes the method we propose for a fully automatic search for IPUs. The second section of this paper briefly presents Cheese!. We then propose a user-oriented evaluation method based on the amounts of manual interventions which were required to obtain the final IPUs annotation. Finally, the results are presented as appropriate for the intended use of the task and accompagnied by a qualitative discussion about the errors.

2 The method to search automatically for IPUs

Algorithm and settings

The search for IPUs is performed on a recorded audio file made of only one channel (mono) and lossless.

Evaluation of a threshold value:

The method is using the Root-Mean-Square (rms), a measure of the power in an audio signal. The rms can be evaluated on the whole audio channel or on a fragment of n of its samples. It is estimated as follow:

rms = n i (S 2 i ) n (1)
At a first stage, the search for IPUs method estimates the rms value of each fragment of the audio channel. The duration of these fragment windows is fixed by default to 20 ms and can be configured by the user.

The statistical distribution of the obtained rms values is then analyzed. Let min be the minimum rms value, µ the mean and σ the coefficient of variation. Actually, if the audio is not as good as it is expected, the detected outliers values are replaced by µ and the analysis is performed on this new normalized distribution.

A threshold value Θ is fixed automatically from the obtained statistical distribution. The estimation of Θ is of great importance: it is used to decide whether each window of the audio signal is a silence or a sounding segment:

silence: rms < Θ; sounding segment: rms ≥ Θ We fixed the value of Θ as follow:

Θ = min + µ -δ (2)
The δ value of equation ( 2) was fixed to 1.5σ. All these parameters were empirically fixed by the author of SPPAS from her past experience on several corpora and from the feedback of the users.

It has to be noticed that Θ strongly depends on the quality of the recording. The value fixed automatically may not be appropriate on some recordings, particularly if they are of low-quality. By default it is estimated automatically but it can optionnally be turned off and the user can fix it manually.

Get silence vs sounding fragment intervals:

The rms of each fragment window is compared to Θ and the windows below and above the threshold are identified respectively as silence and sounding. The neighboring silent and neighboring sounding windows are grouped into intervals. At this stage, we then have identified intervals of silences and intervals with "sounds". However, their duration can be very short and a filtering/grouping system must be applied to get intervals of a significant duration.

Because the focus is on the sounding segments, the resulting silent intervals with a too small duration are removed first (see the discussion section below). The minimum duration is fixed to 200 ms by default. This is relevant for French, however it should be changed to 250 ms for English language. This difference is mainly due to the English voiceless velar plosive /k/ in which the silence before the plosion could be longest than the duration fixed by default.

Construction of the IPUs:

The next step of the algorithm starts by re-grouping neighboring sounding intervals that resulted because of the removal of the too short silences. At this stage, the new resulting sounding intervals with a too small duration are removed. This minimum duration is fixed to 300 ms by default. This value has to be adapted to the recording conditions and the speech style: in read speech of isolated words, it has to be lowered (200 ms for example), in read speech of sentences it could be higher but it's not necessary to increase it too much. In spontaneous speech like in conversationnal speech, it has to be lowered mainly because of some isolated feedback items, often mono-syllabic, like 'mh' or 'ah'.

The algorithm finally re-groups neighboring silent intervals that resulted because of the removal of the too short sounding ones. It then make the Inter-Pausal Units it searched for. Silent intervals are marked with the symbol '#' and IPUs are marked with 'ipus ' followed by its number.

The algorithm and its settings in a nutshell:

1. fix a window length to estimate rms (default is 20 ms); 2. estimate rms values on the windows and their statistical distribution; 3. fix automatically a threshold value to mark windows as sounding or silentthis value can be fixed manually if necessary; 4. fix a minimum duration for silences and remove too short silent intervals (default is 200 ms); 5. fix a minimum duration for IPUs and remove too short sounding intervals (default is 300 ms); 6. tag the resulting intervals with # or ipu i.

Optional settings

From our past experience of distributing this tool, we received users' feedback. They allowed us to improve the values to be fixed by default this paper mentioned in the previous section. These feedbacks also resulted in adding the following two options:

move systematically the boundary of the begin of all IPUs (default is 20 ms); move systematically the boundary of the end of all IPUs (default is 20 ms).

A duration must be fixed to each of the two options: a positive value implies to increase the duration of the IPUs and a negative to reduce them. The motivation behind these options comes from the need to never miss aso unding part. To illustrate how this might work, one of the users fixed the first value to 100 ms because his study focused on the plosives at the beginning of isolated words.

Figure 2 shows the full list of required parameters and optional settings when using the Graphical User Interface. The same parameters have to be fixed when using the Command-Line User Interface named searchipus.py.

Discussion

If the search for IPUs algorithm is as generic as possible, some of its parameters have to be verified by the user. It was attempted to fix the default values as relevant as possible. However, most of them highly depend on the recordings. They also depend on the language and the speech-style. It is strongly recommended to the users to check these values: special care and attention should be given to each of them.

Another issue that has to be addressed in this paper concerns the fact that the algorithm removes silence intervals first then sounding ones instead of doing it in the other way around. This choice is to be explained by the concern to identify IPUs as a priority: the problem we are facing with is to search for sounding segments between silences, but not the contrary. Removing short intensity bursts first instead of short silences results in possibly removing some sounding segments with for example a low intensity, or an isolated plosive, or the beginning of an isolated truncated word, i.e. any kind of short sounding event that we are interested in. However, removing short silences first like we do results in possibly assigning a sounding interval to a silent segment.

It has to be noticed that implementing a "Search for silences" would be very easyand-fast but at this time none of the users of SPPAS asked for.

3 Cheese! corpus

Description

"Cheese!" is a conversational corpus recorded in 2016 at the LPL -Laboratoire Parole et Langage, Aix-en-Provence, France. The primary goal of such data was a crosscultural comparison on speaker-hearer smiling behavior in humorous and non-humorous segments of conversations in American English and French. For this reason, "Cheese!" has been recorded in respect with the American protocol [START_REF] Attardo | Prosodic and multimodal markers of humor in conversation[END_REF], as far as possible.

"Cheese!" is made of 11 face-to-face dyadic interactions, lasting around 15 min each. It has been audio and video recorded in the anechoic room of the LPL. The participants were recorded with two headset microphones (AKG-C520) connected by XLR to the RME Fireface UC, which is connected with a USB cable to a PC using Audacity software. Two cameras were placed behind each of them in such a way each participant was shown from the front. A video editing software was used to merge the two videos into a single one (Figure 3) and to embed the high quality sound of the microphones.

The 22 participants were students in Linguistics at Aix-Marseille University. The participants of each pair knew each other because they were in the same class. All were French native students, and all signed a written consent form before the recordings. None of them knew the scope of the recordings.

Two tasks were delivered to the participants: they were asked to read each other a canned joke chosen by the researchers, before conversing as freely as they wished for the rest of the interaction. Consequently, although the setting played a role on some occasions, the participants regularly forgot that they were being recorded, to the extent that sometimes they reminded each other that they were being recorded when one of the participants started talking about quite an intimate topic.

In a previous study based on 4 dialogues of Cheese! [START_REF] Bigi | Automatic segmentation of spontaneous speech[END_REF], we observed a larger amount of laughter compared to other corpora: 3.32% of the IPUs of the read part contain

The IPUs of Cheese!

All the 11 dialogues were annotated by using the audio files re-sampled at 16,000Hz. For each of the speakers, the "Search for IPUs" automatic annotation of SPPAS was performed automatically with the following settings:

minimum silence duration: 200 ms because it's French language; minimum IPUs duration: 100 ms because it's conversationnal speech; shift begin: 20 ms; shift end: 20 ms.

The IPUs were manually verified with Praat [START_REF] Boersma | Praat: Doing phonetics by computer[END_REF]. Five dialogs were verified by 2 annotators and 6 by only one.

Table 1 reports the minimum (min), mean (µ), median, σ of the statistical distribution of the rms values. The second last column indicates the resulting automatically estimated Θ. The last column indicates if the rms values were normalized. This table shows that even with the same recording conditions, the recorded rms values are ranging from very different values depending on the speaker. It confirms the need to fix a specific threshold value for each recorded file in order to get the appropriate segmentation. Fixing automatically the Θ value is then important and a great advantage for users of the software tool.

It results in the following files:

-22 files with the IPUs SPPAS 4.1 created fully automatically; -22 files with the manually corrected IPUs.

Evaluation method

There are numerous methods and metrics to evaluate a segmentation task in the field of Computational Linguistics. Most of the methods are very useful to compare several systems and so to improve the quality of a system while developing it but their numerical result is often difficult to interpret. In this paper, we developped an evaluation method and a script that is distributed into the SPPAS package. It evaluates the number of manual "actions" the users had to operate in order to get the expected IPUs. We divided these manual actions into several categories described below. For a user who is going to read this paper, it will be easy to know what to expect while using this software on a conversational corpus, and to get an idea of the amount of work to do to get the expected IPUs segmentation.

In the following, the manually corrected IPUs segmentation is called "reference" and the automatic one is considered the "hypothesis". The evaluation reports the number of IPUs in the reference and in the hypothesis and the following "actions" to perform manually to transform the hypothesis into the reference: add : number of times an IPU of the reference does not match any IPU of the hypothesis. The user had to add the missing IPUs; merge : number of times an IPU of the reference matches with several IPUs of the hypothesis. The user had to merge two or more consecutive IPUs; split : number of times an IPU of the hypothesis matches with several IPUs of the reference. The user had to split an IPU into several ones; ignore : number of times an IPU of the hypothesis doesn't match any IPU of the reference. The user had to ignore a silence which was assigned to an IPU; move b : number of times the begin of an IPU must be adjusted; move e : number of times the end of an IPU must be adjusted.

The add action is probably the most important result to take into account. In fact, if add is too high it means the system failed to find some IPUs. It is critical because it means the user have to listen the whole content of the audio file to add such missing IPUs which is time consuming. If none of the IPUs is missed by the system, the user had only to listen the IPUs the system found and to check them by merging, splitting or ignoring them and by adjusting the boundaries.

In order to be exhaustive, this paper presents the ignore action. However, from our past experience in checking IPUs, we don't really consider this result an action to do. In practice, the user is checking IPUs at the same time of the orthographic transcription. If there's nothing interesting to transcribe, the interval is ignored: there's nothing specific to do. Moreover, we developed a plugin to SPPAS which deletes automatically these un-transcribed IPUs.

Quantitative evaluation

We applied the evaluation method presented in the previous section on the 11 dialogs of Cheese! corpus. The evaluated actions are reported into a percentage according to the 6922 IPUs in the reference for add, merge, move b, move e or according to the 7343 IPUs in the hypothesis for split and ignore:

-add: 54 (0.79% of the IPUs in the reference) -merge: 104 (1.51% of the IPUs in the reference) -split: 273 (3.72% of the IPUs in the hypothesis) -ignore: 724 (9.86% of the IPUs in the hypothesis are false positives) -move b: 497 (7.23% of the IPUs in reference) -move e: 788 (11.46% of the IPUs in reference)

Reducing the number of missed IPUs was one of the main objective while developping the algorithm and we can see in the evaluation results that the number of IPUs to add is very small: it represents only 0.78% of the IPUs of the reference. It means that the user can be confident with the tool: the sounding segments are found.

The same holds true for the merge action: only concerned which is very good because it's relatively time-consuming to do it manually. However, the number of IPUs to split is relatively high which is also relatively time-consuming to do manually.

Finally, the highest number of actions to perform is to move boundaries of the IPUs but this action is done very easyly and fastly with Praat.

Qualitative evaluation

We observed the durations of the added and ignored IPUs. It is interesting to mention that the duration of the IPUs to add and the IPUs to ignore are less than the average. Actually, the duration of the IPUs of the reference is 1.46 seconds in average but the 39 IPUs we added are only 0.93 seconds in average. This difference is even more important for the IPUs we ignored: their duration is 0.315 seconds in average.

Another interesting aspect is related to the speech style of the corpus: 14.11% of the IPUs contain a laughter or a sequence of speech while laughing. These events have a major consequence on the results of the system. Most of the actions to do contain a high proportion of IPUs with a laughter or a laughing sequence:

-11 of the 39 IPUs to add (28.21%); -86 of the 171 IPUs to merge (50.29%); -5 of the 7 IPUs to split (71.42%). This analysis clearly indicates that laugher, or laughing while speaking, is responsible for a lot of the errors of the system, particularly for the actions to split and to merge. Figure 4 illustrates this problem: the first tier is the manually corrected one -the reference, and the second tier is the system output -the hypothesis.

In this scope of analyzing the errors, we also used the filtering system of SPPAS [START_REF] Bigi | Searching and retrieving multi-levels annotated data[END_REF] that allowed us to create various tiers with: (1) the first phoneme of each IPU of the reference; (2) the first phoneme of each IPU of the reference for which a "move begin" -/Z/ is starting 2.72% IPUs of the reference but 3.81% of the move b ones; Moreover, we observed that 10.6% of the move b actions concern a laughter item. We finally have done the same analysis for the last phoneme of the IPUs of the reference versus the last phoneme of IPUs with the move e actions:

-/s/ is ending 2.67% IPUs in the reference but 7.11% in the move e ones;

-/E/ is ending 9.08% IPUs in the reference but 6.85% in the move e ones; -/a/ is ending 10.42% IPUs in the reference but 6.72% in the move e ones; -/R/ is ending 5.72% IPUs in the reference but 6.32% in the move e ones; -/t/ is ending 3.88% IPUs in the reference but 6.19% in the move e ones; Like for the beginning, the /s/ and /t/ are relatively more frequent in the "move end" action than in the reference. And we observed that 17.26% of the move e actions concern a laughter item which makes it the most frequently required "move end" action; but it's also the most frequent one to end an IPU with 11.11% in the reference.

Figure 5 illustrates the two actions move b and move e on the same IPU even if this situation is quite rare. In this example, the first phoneme is /s/ and the last one is /k/.

Conclusion

This paper described a method to search for inter-pausal units. This program is part of SPPAS software tool. The program has been evaluated on the 11 dialogues of about 15 minutes each of Cheese! corpus, a corpus made of both read speech (1 minute) and spontaneous speech.

We observed that the program allowed to find properly the IPUs, even on this particularly difficult corpus of conversations. To check the output of this automatic system, we had to perform the following actions on the IPUs the system found: to add new ones, to merge, to split, to ignore; and to perform the following actions on their boundaries: to move the beginning, to move the end. The analysis of the results showed that laughter are responsible for a large share of the errors. This is mainly because a laughter is a linguistic unit but acoustically it's often an outcome of alternate sounding and silence segments (Figure 4).

Fig. 1 .

 1 Fig. 1. Annotation process method

Fig. 2 .

 2 Fig. 2. Configuration with the Graphical User Interface

Fig. 3 .

 3 Fig. 3. Experimental design of Cheese!

Fig. 4 .

 4 Fig. 4. Example of merged IPUs: laughter items are often problematic

Fig. 5 .

 5 Fig. 5. Example of the move b and move e actions on an IPU with a low rms

Table 1 .

 1 Distribution of the rms and the threshold value Θ fixed automatically spk min µ median σ Θ Norm. spk min µ median σ Θ Norm.

	AA 12 548	58 177 295	OR 5 1009 19 160 773
	AC 6 818 371 209 510	MZ 5 1313 38 175 1056
	AW 7 595	96 164 355	CG 2 492	90 147 273
	CM 12 876 257 141 675	MCC 4 397	44 203 96
	ER 3 502	30 159 266	AG 8 328	38 168 84
	CB 4 753	63 174 495	FB 17 1058 89 194 783
	CL 3 1151 2918 15 256 x	JS	3 564	23 230 221
	LP 8 659	92 164 420	MA 3 672 123 152 446
	MA 3 608	24 178 343	PC 2 373	28 202 71
	AD 3 1680 3744 138 855 x	MD 10 844 164 199 555
	EM 4 1162 181 157 929	PR 12 427	61 188 156

Acknowledgments

We address special thanks to the Centre d'Expérimentation de la Parole (CEP), the shared experimental platform for the collection and analysis of data, at LPL.