J-Y Chaufray
email: chaufray@latmos.ipsl.fr

J-L Bertaux

E Quémerais

F Leblanc

LOCAL TIME VARIATIONS OF THE HYDROGEN CORONA OBSERVED BY SPICAV-UV/VEX

Introduction:

As all the terrestrial planets, Venus is surrounded by an hydrogen corona coming from the photodissociation of the water vapor followed by its vertical transport at very high altitudes. From the UV observations of the resonant scattering Lyman-alpha emission, two components have been observed in this corona. A cold component corresponding to hydrogen population at equilibrium with the global atmosphere dominant below ~ 2000 km. A suprathermal component, produced by collisions between energetic protons with the cold component in the upper atmosphere. Due to its large energy, this hot population is able to reach very high altitudes, and escape and becomes dominant above ~4000 km (e.g. Bertaux et al. 1982).

Observations:

The hydrogen corona of Venus has been observed systematically from the UV spectrometer SPICAV aboard Venus Express (Bertaux et al. 2007). It has been observed at dayside, confirming most of the results obtained by past studies, and for the first time at the nightside. As shown in Fig. 1, the two components corona is seen through the two scale heights profile obtained at limb above the dayside (LT = 12H). The nightside profiles are very different due to the low illumination of the shadow by multiple scattering. 2012) have analyzed the first profiles obtained at the dayside and derive a cold hydrogen density of ~1-2x10 5 cm -3 and an exospheric temperature ~ 250-300 K at 250 km. A larger brightness was observed at the morning terminator (LT = 6h) compared to the evening terminator (LT=18h), confirming an asymmetry observed from the mass spectrometer aboard Pioneer Venus Orbiter (PVO), but the hydrogen density needed to reproduce the profile at the morning terminator was lower than the hydrogen density derived by this instrument.

At higher altitudes, the brightness was dominated by the interplanetary emission making difficult an accurate retrieval of the hot hydrogen density. The hydrogen density derived was better constrained at the middle of the observed altitude range (~ 5000 km) and the hot hydrogen density estimated to ~50 cm -3 .

More recently, Chaufray et al. ( 2015) reproduce the first brightness profiles at the nightside evening terminator (LT = 20H), using a radiative transfer model including both cold and hot hydrogen populations as well as the interplanetary emission partly scattered by the Venusian hydrogen corona.

The cold hydrogen density and temperature of the cold hydrogen population derived at the exobase was 4x10 6 cm -3 and temperature between 175-225 K, confirming a cooler and denser nightside corona compared to the dayside corona. The hot hydrogen density derived at 5000 km was ~ 100 -200 cm -3 larger than the derived hot hydrogen density at the dayside and presenting a very short variability of a factor 2 in only few days. This variabilty could be driven by a variation of the dayside ionosphere.

In this presentation, we will summarize these recent results and present other observations obtained at the nightside morning side (LT = 4H) (Fig; 1 ), confirming the large variability of the hydrogen density with local time at the nightside.

.

Bibliography:

Bertaux, J-L., V.M. Lepine, V.G. Kurt, and A.S. Smirnov, 1982, Icarus, 52, 221-224 Bertaux, J-L. et al., 2007, Planet. Space Sci., 55, 1673-1700 Chaufray, J-Y., J-L. Bertaux, E. Quémerais, E. Villard, and F. Leblanc, 2012, Icarus, 217, 767-778 Chaufray, J-Y., J-L. Bertaux, E. Quémerais, F. Leblanc, and S. Sulis, 2015, Icarus, 262, 1-8

Fig. 1

 1 Fig. 1 Altitude profile of the Lyman-α brightness at different local times. Results: Chaufray et al. (2012) have analyzed the first profiles obtained at the dayside and derive a cold hydrogen density of ~1-2x10 5 cm -3 and an exospheric temperature ~ 250-300 K at 250 km. A larger brightness was observed at the morning terminator (LT = 6h) compared to the evening terminator (LT=18h),


LATMOS/IPSL Anni Määttänen
email: anni.maattanen@latmos.ipsl.fr

Sabrina Guilbon

Aurélien Stolzenbach

Slimane Bekki

Franck Montmessin

Franck Montmessin The

The LATMOS Venus cloud model VenLA : Status report

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

Introduction

The clouds of Venus and the aerosols in the Earth's stratosphere are close relatives: both are mostly composed of sulphuric acid droplets. Venus' clouds are optically thick and absorb most of the insolation arriving at Venus, letting only few percent of sunlight reach the surface and having an important climatic effect. The clouds on Venus are, based on the snapshot profile published by [6], divided in three layers that have different properties (particle size distributions, number densities, mass loads). Even though the upper cloud and upper haze can be directly studied with satellite instruments, only a handful of observations have acquired information on the properties of the lower cloud layers [6] and thus modeling is an important tool for studying the lower and middle cloud layers.

Methods

The LATMOS Venus cloud model VenLA (Venus Liquid Aerosols) is based on a terrestrial Polar Stratospheric Cloud (PSC) model [START_REF] Larsen | DMI Sci. Rep. 00-06[END_REF]. The PSC model [START_REF] Larsen | DMI Sci. Rep. 00-06[END_REF] is a sectional microphysical model that can describe a multimodal particle size distribution on a radius grid discretized in tens or hundreds of bins (radius intervals). In its original configuration the PCS model includes all of the microphysical processes relevant to the PSCs, including the multiple phase transitions related to the particle types including liquid and solid phases of water, sulfuric acid, nitric acid and their mixtures, and sedimentation of the particles.

The PSC model went through several modifications when becoming VenLA. The major ones include: removal of nitrous species and related cloud particle types and inclusion of the condensation nucleus particle type, addition of homogeneous and heterogeneous nucleation parameterizations, accounting for both intra-type and inter-type particle coagulation, and adding a parametrization of vertical mixing via eddy diffusion. Because of the extreme dryness of the Venus atmosphere, we also needed to add an iteration of the calculation of the weight fraction of sulfuric acid in the droplet in order to correctly account for the change in total water content.

VenLA describes the formation, growth and decay of sulfuric acid -water droplets, and when used in onedimensional (vertical profile) version it also accounts for sedimentation and mixing of particles and vapors via eddy diffusion. Homogeneous nucleation is described with the parameterization of [14] and heterogeneous nucleation with a simple parameterization as in [START_REF] James | [END_REF]. Condensation and evaporation are treated in two steps: simple (fast) equilibration whenever a droplet experiences a change in environmental conditions (temperature,partial pressure of water vapor) causing a change in the equilibrium composition, and (slow) condensation/evaporation during which the droplet grows/shrinks conserving the equilibrium composition [9]. We account for Brownian and gravitational coagulation (coalescence) and we use the numerical method of [4]. The coagulation kernels are calculated as in [1,12] and the sum of the Brownian and gravitational kernels is corrected as in [10,11]. Vertical transport (sedimentation and eddy diffusion) is treated following the method of [13] and settling velocity is calculated using [9,1] and corrected to account for mixing. The model has undergone several updates, the latest of which focused on accounting for, in all microphysical processes, the condensation nuclei (CN) captured within the droplets. This required transforming the pure twocomponent solution droplet type into a "mixed" particle type that includes both volatile and CN masses.

The runs are initialized with profiles from VIRA [5] for temperature and pressure and from occultation data concerning the vapors, as in [START_REF] Mcgouldrick | [END_REF]. VenLA receives also as input the properties of the condensation nuclei (a lognormal size distribution defined in a given altitude range [START_REF] James | [END_REF]). A prescribed droplet distribution can also be used as an initial state. The vapors are consumed during nucleation and condensation and replenished when the droplets evaporate or when mixing brings in vapor-rich air. In these simulations the temperature and pressure profiles are not changed and thus the simulated clouds are considered as formed in average conditions and do not reflect effects of large-scale dynamics.

Results

We will focus on finalizing the reference version of the model and reproducing the [6] in-situ observations of the cloud properties. We will present results of reference runs and sensitivity tests. We compare the results to observations on cloud droplet number densities and sizes, and to other modeling studies. One of the main sensitivity tests will be the effect of CN on the cloud properties. The nucleation pathway may prove significant in the simulations since it defines the number of formed particles. This regulates the particle size for a constant condensible mass. In our preliminary test runs, when using only the homogeneous nucleation parameterization, we reach the observed condensed mass load, but the droplet number concentrations are too low and consequently the droplets are too large. Using heterogeneous CN activation it is much easier to attain observed number concentrations and sizes, however, the used initial CN concentration profile dictates the development of the cloud.

Summary and Conclusions

We have developed a microphysical model for Venus' sulfuric acid clouds. The VenLA cloud model and reference run and sensitivity test results will be presented, with a particular focus on the role of CN. The results will be compared with other modeling studies and observations. The VenLA model defines the baseline for a parallel project on development of a moment method scheme to be used in a global climate model (see abstract Guilbon et al., [START_REF] Guilbon | Comparison of sectional and modal cloud microphysics representations for Venus: VenLA vs[END_REF]).

Acknowledgements

We acknowledge the support of the French Planetology program (Programme National de Planétologie, AT-MARVEN project).


Hans Geisler

Johann-Mattis List

Beautiful Trees on Unstable Ground Notes on the Data Problem in Lexicostatistics

Introduction

While lexicostatistics and glottochronology had been suffering a lack of prestige for a long time, the integration of stochastic methods taken from genetics has initiated an unexpected revival of these scorned disciplines. The proponents of these "new quantitative methods" in historical linguistics claim that the procedures are relatively robust regarding errors in the data (wrong cognate judgments, undetected borrowings, or wrong translations). In order to check this claim, we have investigated the differences and errors in two large lexicostatistical datasets and tested their influence on the topologies of computed family trees. Our results show clearly that the shortcomings of lexicostatistics and glottochronology have not been overcome by these new computation methods: the main problems of lexicostatistics and glottochronology, the translation of basic concepts into individual languages, and the execution of cognate judgments are still so grave that no reliable results can be drawn from these methods.

Lexicostatistics

Basic Assumptions of Lexicostatistics

Various authors have tried to summarize the basic assumptions of lexicostatistics in a consistent manner. Yet when turning to the more popular accounts on the basic assumptions of the method which are, e. g., given in the work of Arapov & Herz (1983: 17-20), [START_REF] Gudschinsky | Three disturbing questions concerning lexicostatistics[END_REF] and Sankoff (1969: 2f), one realizes that these accounts all differ to a certain degree. We propose that the core of lexicostatistical theory can be summarized in the following two basic assumptions:

1: The lexicon of every human language contains words which are relatively resistant to borrowing and relatively stable over time due to the meaning they express: these words constitute the basic vocabulary of languages. 2: Shared retentions in the basic vocabulary of different languages reflect their degree of genetic relationship, i.e. they are representative for the reconstruction of language phylogenies.

These two basic assumptions introduce the two main ideas of lexicostatistics as they were first proposed by Morris Swadesh in his early papers at the begin of the 1950ies (cf. [START_REF] Swadesh | Salish internal relationships[END_REF][START_REF] Swadesh | Lexico-statistic dating of prehistoric ethnic contacts: With special reference to North American Indians and Eskimos[END_REF][START_REF] Swadesh | Towards greater accuracy in lexicostatistic dating[END_REF], namely the idea of basic vocabulary as a specific set of concepts which are expressed in all languages and the idea that shared cognates within the realm of basic vocabulary reflect the degree of genetic closeness among languages. In our opinion, all methods for phylogenetic reconstruction which are based on these two basic assumptions can be classified as lexicostatistical approaches.

The Lexicostatistical Working Procedure

In contrast do Dyen et al. (1992: 95-98), who explicitly divide the lexicostatistical working procedure into four steps, we distinguish five steps. This is due to the fact that in many recent and old applications of lexicostatistics, the actual lists of basic vocabulary items were not solely based on one of the two original meaning lists proposed by [START_REF] Swadesh | Lexico-statistic dating of prehistoric ethnic contacts: With special reference to North American Indians and Eskimos[END_REF][START_REF] Swadesh | Towards greater accuracy in lexicostatistic dating[END_REF]. Therefore, the selection or compilation of an appropriate list of basic concepts should be included in a description of the lexicostatistical working procedure. Thus, the lexicostatistical working procedure can be characterized by the following five steps:

Step 1: Compilation: Compile a list of basic vocabulary items (a Swadesh-list).

Step 2: Translation: Translate the items into the languages that shall be investigated. 1Step 3: Cognate Judgments: Search the language entries for cognates.

Step 4: Coding: Convert the cognate information into a numerical format.

Step 5: Computation: Perform a computational analysis (cluster analysis, tree calculation) of the numerical data, which allows to make conclusions regarding the phylogeny of the languages under investigation.

Main Critics Regarding Lexicostatistics

Soon after Morris Swadesh established lexicostatistics as a new method in historical linguistics, the method was criticized in many publications for all its obvious shortcomings. Table 1 lists a few of the most crucial points which have been discussed so far, along with a reply by modern practitioners of lexicostatistics.

Critic Reply

Distances don't tell us anything about language history (cf. e.g. [START_REF] Blust | Why lexicostatistics does'nt work. The 'universal constant' hypothesis and the Austronesian languages[END_REF].

Our methods are character-based [START_REF] Atkinson | How old is the Indo-European language family? Illumination or more moths to the flame? in: Phylogenetic methods and the prehistory of languages[END_REF]).

Borrowing will make the results unreliable (cf. e.g. [START_REF] Bergsland | On the validity of glottochronology[END_REF] Not within basic vocabulary [START_REF] Atkinson | How old is the Indo-European language family? Illumination or more moths to the flame? in: Phylogenetic methods and the prehistory of languages[END_REF]).

Basic vocabulary is not resistant to borrowing (cf. e.g. Sagart & Lee 2008).

In most cases it still is [START_REF] Sergej | O dokozatel'stve jazykovogo rodstva (On the proof of genetic relationship of languages), in: Tipologija i teorija jazyka (Typology and language theory)[END_REF].

The method and its data basis is subjective and inconsistent (cf. e.g. [START_REF] Hoijer | Lexicostatistics: A critique[END_REF][START_REF] Rea | The Romance data of pilot studies for glottochronology, in: Diachronic, areal and typological linguistics[END_REF].

NO REPLY SO FAR

Table 1: Some critics regarding lexicostatistics

In recent applications of lexicostatistics, most of these critics are explicitly mentioned and commented by Swadesh's new followers, as Table 1 shows. Yet it is interesting to note, that -to our knowledge -the last point of criticism has not yet been explicitly addressed in the recent lexicostatistical literature. This coincides well with a general tendency in studies concerning lexicostatistics (even the critical ones) to underestimate the importance of the data basis for lexicostatistical analyses, safely assuming that possible errors in translation and coding won't turn out to be statistically significant.

Problems of Data Handling

Let us start with some general considerations regarding possible shortcomings of lexicostatistical datasets. Due to the fact that parts of the lexicostatistical working procedure are based on individual decisions which might be prone to subjectivism, we expect to find the greatest problems within Step 2 (Translation) and Step 3 (Cognate Judgments) of the lexicostatistical working procedure. We can distinguish two kinds of possible errors in these two steps: methodological errors, i.e. errors provoked by shortcomings of the method, and individual errors, i.e. errors provoked by shortcomings of individual scholars applying the method.

Regarding

Step 2 of the working procedure, we identify the following methodological sources of errors:

1: Concept Fuzziness: The basic concept is defined in a way that makes it difficult to find a unique, best match for the translation into the target language. Cf. e.g. the basic concept KNOW for which it is very difficult to decide which of the possible German equivalents kennen "know something", wissen "know facts" would match it best. 2: Synonymous Differentiation: The target language offers more than one translation for the basic concept due to language specific differentiation. Cf. e.g. the two possible translations for the basic concept BIRD in Spanish, where pájaro refers to small birds, while ave refers to big birds. 3: Linguistic Diversity: The target language offers different translations for the basic concept, due to dialectal or sociolinguistic variation. Cf. e.g. the two possible translations for the basic concept KILL in German, where we have umbringen as a colloquial and töten as a literal variant.

As individual sources of errors, we identify the following two:

1: Lack of Competence: If the researcher doesn't have a sufficient knowledge of the target language, which is necessarily the case when -as [START_REF] Dyen | Comparative Indoeuropean database: File IE-data1[END_REF] did -a handful of researchers tries to analyze a set of 95 languages, many of which are only sparsely documented, errors in the coding will be unavoidable. 2: Use of Low-Quality References: Errors will likewise increase, if the references which are taken into account when translating the basic concepts into the target languages are of low quality or out-dated.

Regarding possible problems of cognate judgments (Step 3), a specific problem in lexicostatistics is that the question of reconstruction depth has never been solved sufficiently. What should count as cognate: Language entries which can be matched completely, i.e. the few examples which we have in historical linguistics, where regular sound changes took place without the slightest exception? Or should we base the cognate judgments on root-identity, as it is the usual practice in many lexicostatistical applications? But what does the fact, that items do not match, tell us then? The fundamental idea of lexicostatistics is that replacements of word forms in certain meaning slots of the basic part of the lexicon constitute a regular process. If we consider the forms for the basic item "give" in Figure 1, it is obvious that we are dealing with a real replacement of the form Latin dare "give" in Provencal and French, since the etymological connection between Latin dōnare "give as a present" and dare "give" was surely not transparent for the Romans. From a root-perspective, however, we have to count all forms as cognates: they all go back to the PIE root *deh 3 -"give" (cf. Meiser 1999).

Figure 1: The problem of reconstruction depth

To sum up: The lexicostatistical working procedure and its above-mentioned shortcomings lead to datasets where we are dealing with an arbitrary selection of language variants with arbitrary assignments of cognacy.

Comparison of Datasets for Lexicostatistics

Our Data

To check to which degree the problems of methodological and individual errors in lexicostatistical datasets may influence the results of computer analyses, we have compared of two large lexicostatistical databases for Indo-European, namely the Dyen database (cf. [START_REF] Dyen | Comparative Indoeuropean database: File IE-data1[END_REF]) and the Tower of Babel database (cf. [START_REF] Starostin | Tower of Babel: An etymological database project[END_REF]. In order to have two independent test lists provided by different scholars which are maximally comparable we extracted a set of 46 languages and 103 basic vocabulary items which occur in both datasets. The cognate judgments for the Dyen database are based on the application of [START_REF] Gray | Language tree divergence times support the Anatolian theory of Indo-European origin[END_REF] which we further compared with the cognate judgments displayed in the original dataset. The cognate judgments for the Tower of Babel dataset were provided by the Tower of Babel team.

In order to make the datasets comparable, we applied the following steps:

1: Intersection of both datasets: We chose only those languages and basic vocabulary items which would overlap in both datasets. This was the primary reason for the selection of basic vocabulary items and languages. 2: Making the coding similar: Both loans and gaps were coded by assigning negative numbers to the respective translated entries (this is the usual practice in the STARLING software package, cf. [START_REF] Sergej | Rabočaja sreda dlja lingvista (Working environment for a linguist), in: Bazy dannyh po istorii Evrazii v srednie veka[END_REF]), which we used for part of our calculations. 3: Excluding "singletons": All singletons, i.e. all translated entries which are not cognate with any other entries, were excluded from the analysis. 4: Restricting cognate judgments to item identity: Tower of Babel assigns the same cognate ID to all etymologically related words, such that e.g. English what and who are given the same ID. Since the Dyen database was not coded in this way, we changed the coding of the Tower of Babel database.

Table 2 gives an overview over the way we coded both databases in order to make them comparable.

Database

Coding Problems in the Dyen Database

The trouble with the encoding in the Dyen database is that the problem of multiple language entries was not solved properly. Figure 2 gives an example on the way the data is coded in this database. Instead of allowing to list multiple entries separately, [START_REF] Dyen | Comparative Indoeuropean database: File IE-data1[END_REF] applied a strange method of assigning relation codes (codes preceded by "c" in Figure 2) to pseudo cognate sets (all language entries listed under a specific cognate header, preceded by "b" in Figure 2), which in turn lead to non-transitive cognate judgments: The cognate sets going back to two distinct Latin words denoting two distinct concepts (avis "bird" and passer "sparrow") are interlinked by the "c"-lines, only because there are two entries in Spanish, each corresponding to one of the two Latin roots. These cognate judgments are very hard to check on their correctness. In order to compile the data for the biological software packages, one has to untangle the "networks of cognacy" proposed by the authors, which is a task that, unfortunately, cannot be done in a consistent way. The result is a confusing network of inter-cognate relationships.

The Coding of the Tower of Babel Database

The Tower of Babel project created a special way of encoding lexicostatistical wordlists which is implemented in the STARLING software package (cf. [START_REF] Sergej | Rabočaja sreda dlja lingvista (Working environment for a linguist), in: Bazy dannyh po istorii Evrazii v srednie veka[END_REF]. The idea is to simply assign the same number to related, i.e. cognate, entries and to link these entries with proto-forms, which makes these databases to complete etymological dictionaries.

Figure 3: Coding of the Tower of Babel dataset

This system, which is reflected in Figure 3, is exemplary, both in transparency of cognate judgments and applicability.

Detailed Comparison of the Datasets

In order to get a first impression regarding the differences in the datasets which can be explained by the sources of errors we identified, we carried out a closer examination of the Romance partition of both datasets. As an example, Table 3 gives a detailed comparison of the entries for BIRD in Tower of Babel and the Dyen database. In this case, there is only a difference in one item, namely the additional entry for BIRD in Portuguese in the Tower of Babel dataset. These apparently minor differences, however, sum up to about 10 percent in the whole Romance partition of both databases. This clearly shows that item translation is a huge problem of lexicostatistics. If the datasets which different scholars use in order to draw their conclusions differ to such a great extent, it is almost impossible to compare their results and map them to "real" historical scenarios of language development.

While differences in item translation can surely be considered as an inherent problem of lexicostatistical methodology and thus belonging to our category of methodological errors, the many cases of undetected borrowings which we could identify in both datasets (although the Dyen database performed worse), clearly belong to the latter category of individual errors. How do the differences we identified in the two datasets surface when applying Step 5 of the lexicostatistical working procedure and computing family trees out of the coded data? In order to test this, we applied several methods of tree conversion, using distanceand character-based approaches. In order to have a first rough approximation of differences, we measured the split-differences between the trees, using the TOPD-software (cf. [START_REF] Puigbò | Topd/fmts: A new software to compare phylogenetic trees[END_REF]. Table 5 lists the results of these tests for different methods we applied for the data analysis.

Method

Split-Difference (%) Uncorrected distances (Neighbor-Joining) 39.53 Cosine distances (Neighbor-Joining) 32.56 Matching distance (Neighbor-Joining) 41.86 MrBayes (Bayesian approach) 30.23

Table 5: Split differences between Dyen and Tower of Babel

These comparisons reveal that all computed tree topologies differ by 30 -40% regarding their splits. Note that -for the Romance partition of both datasets, where our analysis revealed about 10 percent differences in item translation and cognate judgmentsthe tree topologies in both analyses are the same. Thus, the differences which we identified even do not show up in the tree topologies, suggesting that the differences in the rest of the datasets are even greater than in the Romance part. The results for the Bayesian analyses 3 , which performed best, showing split differences of only about 30%, are given in Figure 4. A closer comparison of these two figures clearly shows that the differences between the two trees are so great that they cannot be simply ignored. These differences occur in all parts of the trees, showing conflicts in higher phylogenies and in the subgrouping of closer related languages. Note that these differences are only due to differences in cognate judgments and item translations. Both datasets contain the same number of items and the same number of languages, so actuallyassuming that lexicostatistics is a valid method -there should be no differences at all.

3

The analysis was made using the MrBayes software package (cf. [START_REF] Ronquist | MrBayes 3: Bayesian phylogenetic inference under mixed models[END_REF] with Albanian as outgroup. 1.5 million trees of both datasets were created (by this time, both datasets had reached convergence), of which we sampled 1000 for the consensus trees.

Conclusion: Back to the Roots?

What is left to say? Our analysis clearly shows that differences in item translation and cognate judgments have a great impact on the topology of the trees calculated from lexicostatistical datasets. The impression that -due to the large amount of data employedthese differences would not show up in the calculations has proven to be problematic. This shows clearly that the main problem of lexicostatistics lies not in its basic assumptions, which most scholars still see as the most problematic aspect of the method, but in its working procedure which is prone to subjectivism and errors. Given these facts, we may ask whether lexicostatistics has a future after all, or whether John Rea was right in his pessimistic résumé, stated about forty years earlier:

If, as Lees and Chrétien feel, the mathematics are inadequate; if, as Hall, Bergsland and Vogt, Arndt, O'Neill, Coseriu, Fodor, I and others have found, the results of the method do not correspond to known facts; if now, the Romance wordlists and scorings that formed the basis of the method are in fact full of indeterminacies, inconsistencies and errors, what then remains? (Rea 1973: 361) We think that lexicostatistics in its current form does not have a future, but we do not think that, because of this failure of one particular method, all quantitative approaches to genetic language classification should be given up at once. We especially hope that rootbased approaches which are closer to the traditional methodology of historical linguistics (cf. e.g. [START_REF] Sergej | Comparative-historical linguistics and lexicostatistics[END_REF][START_REF] Hans | Genealogy of the main Indo-European branches applying the separation base method[END_REF] will produce datasets which are less prone to subjective judgments and individual errors. Datasets encoded in this way can then further used for phylogenetic calculations, and we hope that they will provide a more objective basis for stochastic calculations on linguistic datasets and may reveal interesting aspects and new insights into the complexity of language history.

Figure 2 :

 2 Figure 2: Coding of the Dyen dataset

Figure 4 :

 4 Figure 4: Bayesian analysis for Dyen (left) and Tower of Babel (right)

Table 2 :

 2 The structure of the two datasets

		Dyen et al. 1997	Tower of Babel	Intersection
	Language family	Indo-European	Indo-European	Indo-European
	No. of languages	95	98	46
	No. of items	200	110	103

Table 3 :

 3 Comparison of BIRD in Dyen and Tower of Babel

Table 4 :

 4 Table 4 gives a non-exhaustive list of some of the most typical cases of undetected borrowings within the Romance partition of both datasets. 2 Undetected borrowings in Dyen and Tower of Babel Comparing the Computed Tree Topologies of the Datasets

	Author Item	Donor	Source		Recipient Languages
			Language	Lang.	Rom.	Italian Provencal French	Spanish
	Dyen	KILL	French	tuer		tua
		ROAD	Greek	drómos drum
		SKIN	Latin	cutis		cutis
		WALK	Old Franc.	marka		marcha	marcher
		WOMAN Greek	familia	femeie
	ToB	THIN	French	mince		mince
		WARM	Latin	calidus		calido
		WOMAN Greek	familia	femeie
		KILL	French	tuer		tuar

We use the term "translation" in this context, since it is traditionally used in the lexicostatistical literature for the process of finding a word in a certain language which expresses a given basic concept.

Rumanian femeie is misjudged in both datasets for being cognate to French femme, Sardinian femmina, etc. Only the ladder go back to Latin femina, whereas the Rumanian word is clearly related to Latin familia which was first borrowed into Turkish and changed meaning from "family" to "woman (in a harem)". The word migrated with his new meaning from Turkish to Greek and then to Rumanian.


come   L'archive ouverte pluridisciplinaire

1

Toward a Digital Hermeneutics

Alberto Romele

Review of Virtual Worlds as Philosophical Tools: How to Philosophize with a Digital Hammer, by Stefano Gualeni (Palgrave Macmillan, 2015). 194 pp., ISBN: 978-1137521774 For some years, academics have been discussing 'the end of the virtual.' According to some of them, this means that the old economic and political forces are succeeding into 'dividing and conquering' the 'spaceless space' of the Internet as Manuel Castells called it. Recent initiatives of the European Commission such as the 'Right to be forgotten' ruling demonstrate that the Internet is increasingly becoming regionalized. According to the ruling, people have the right, under certain conditions, to ask search engines like Google to remove results for queries that include their name.

As a consequence, today research results within European countries might always be different than those made within other states.

Moreover, people today are disposed to pay for services and products online that were considered free until few years ago. For instance, Google has recently released Google Contributor, an experimental service that allows users to pay in order to have less or no ads on their favorite websites. Music file sharing has been used in the past to show the dynamics of gift giving online; the current success of commercial music streaming services like Spotify is illustrative of the end of such a 'cyberutopia' [START_REF] Romele | The Economy of the Digital Gift. From Socialism to Sociality Online[END_REF]. Finally, the giants of the Internet are now able to collect, aggregate, and monetize all sorts of digital traces we leave behind us. In some cases, these traces are ceded to security agencies of nation states like the American NSA, as revealed by Edward Snowden in 2013.

According to other scholars, the end of the virtual has more to do with the emergence of an always already connected environment that Luciano Floridi has called 'infosphere.' In this environment, the frontiers between human intentions and their surroundings are softened. The Internet of things, the augmented reality, the diffused traceability, etc. are optimizing our relations with the others, the world, and ourselves. Let us consider, for example, the movement of the 'Quantified Self.' Ten, fifteen years ago, a series of ritual actions used to mediate access to the Internet: turn the computer on, wait, turn the modem on, wait, sit down on a chair in front of a computer's screen, wait, launch the browser, wait, etc. Thanks to all sorts of mobile devices and connected objects that characterize our present, which will certainly be part of our future, we are spending most of our life online. 'Onlife' is another of Floridi's fancy expressions [START_REF] Floridi | The Onlife Manifesto. Being Human in a Hyperconnected Era[END_REF]. In this sense, it is not the 'real' that conquered the 'virtual,' but the other way round.

Virtual Worlds as Living Metaphors

Compared with these two perspectives (balkanization of the Internet on the one hand, digitalization of our lives on the other hand), Stefano Gualeni takes what at first glance might be considered a half step back. Indeed, he implicitly defends the idea that the frontiers between the 'real' and the 'virtual,' or between actual and virtual digital worlds in his terminology, are permeable, but nonetheless they must be maintained. This is mainly due to the fact that the author, who is both a philosopher and a computer designer, limits his analysis to the domain of non-immersive video games, in which the screen and the input devices still represent rather solid barriers between real and virtual worlds. In reality, as I will suggest below, Gualeni takes a step forward, toward a hermeneutical approach to digital technologies that might be extended to the experiences of telepresence, as he calls them, i.e. those technologies enabling information exchanges and different degrees of agency (43)(44).

The main thesis of the book is that computer games, albeit without radically subverting human experiences and thoughts, can cause their 'distortion, extension, and fragmentation.' In other words, the virtual digital worlds exert a power of 'reconfiguration' over human ways of being in the world, with the others, and with oneself. The term 'reconfiguration' refers to the theories of the French philosopher Paul Ricoeur on the heuristic function of metaphor and narrative. In The Rule of Metaphor [START_REF] Ricoeur | The Rule of Metaphor[END_REF], he refused both the more classic 'cosmetic' idea according to which metaphors just have the function of embellishing stories; and the Nietzschean and postmodern idea for which there is nothing but metaphors, and that the reality itself, together with its concepts, is a 'white mythology,' that is to say a metaphor whose nature has been forgotten. In the first volume of Time and Narrative [START_REF] Ricoeur | Time and Narrative[END_REF]), thanks to the notion of threefold mimesis, Ricoeur discusses the impact of stories, fictional and historical, told and read, on the temporal character of human experience. Finally, the stories become fully effective through the concept of narrative identity, developed in the third volume of Time and Narrative and in the fifth and sixth study of Oneself as Another [START_REF] Ricoeur | Oneself as Another[END_REF]): since human beings constitute a part of their self in relation to the stories they tell and read, narrations have a relevance that go far beyond entertainment and mere distraction. It is not by chance then that Gualeni abundantly refers to Ricoeur in chapter VII of the book, when he defines the virtual digital worlds as metaphors that 'have the power to disrupt and change fundamental attitudes and beliefs about the world and can thus be used persuasively in the pursuit of institutional as well as artistic, philosophical, critical, and personal goals' (133). He also refers to Lakoff and Johnson's notion of metaphor's 'ontological function,' i.e. 'its formative role in shaping individual thought and framing social interaction' (136).

In Gualeni's opinion, as he argues in the central chapters (III-IV-V), computer games go even further in their heuristic function than the more classic cultural objects such as books. Firstly, because their semantics is not confined to the spoken and written words; they are multimedial, i.e. they combine words with moving images, and sounds. Secondly, in terms of automation and immersion, computer games have popularized and improved multilinearity and interactivity made by literary and artistic avant-gardes during the last century such as Raymond Queneau's 1961 book A Hundred Thousand Billion Poems, Surrealist collages, and Dada assemblages. Finally, in the traditional media, virtual worlds, that is to say those worlds bursting into the continuum of our 'native world,' are experienced 'on the basis of subjective imagination and interpretation.'

Computer games, by contrast, provide 'experiences that emerge from establishing relationships with an objective world' (62); 'traditional media cannot provide the effective materialization of worlds and, as such, cannot be expected ever to engage a subject at the ontological level' (67).

It is noteworthy that Gualeni distinguishes here four levels on which computer games have or might have an effect on human existence. First, they affect the practices and cognitions of the users. Second, they influence the practices and the cognitions of the game designers themselves.

Incidentally, this point has often been neglected in the philosophical hermeneutic tradition. Third, they help in concretizing and broadly diffusing those philosophical concepts that otherwise would remain too abstract. As examples, he takes two 'philosophical video games' he personally designed and developed, Gua-Le-Ni and Necessary Evil. The former aims to playfully negotiate David Hume's notion of complex ideas; the latter offers a critique of 'player-centrism,' which is an integral feature of classic video games. It wants 'to make the player experience the feeling of marginality and to reveal experientially what a virtual world feels like when this world is designed around someone else's point of view and someone else's goals and desires' (89). Fourth, virtual digital worlds can make accessible to humans those experiences that are radically non-human. In response to Thomas Nagel's argument, according to which human beings cannot share non-human experiences such as those of bats, Gualeni created Haerfest, a video game, whose objective is precisely to show, at least in part, what it is like to be a bat for a bat.

Philosophical Heritages

Gualeni's reflections are based on a twofold philosophical heritage. First of all, as he makes explicit in chapter I, they have a source of inspiration in Don Ihde's and Peter-Paul Verbeek's 'postphenomenology' or 'material hermeneutics.' Postphenomenology generally argues that technological artifacts have a mediating role in the relation between human beings and the world.

Moreover, it claims that the subject and the world are not given a priori, but they constitute themselves at the precise moment of the relation. From this, one can infer that the technological artifacts, both when they are conceived and forged, and when they are used, have a central role in the constitution of the subjects and the world. The designer realizes in the objects her own ethos and sensitivity. The user finds in the artifacts an occasion for thinking and acting differently. Gualeni applies postphenomenology to the computer games. Following Ihde's distinction between four Itechnology-world relations, one might say that computer games establish 'alterity relations' that become 'hermeneutic relations' when the designer or the player starts to reinterpret herself and her own actual world in the light of the possibilities offered by digital simulations. For Gualeni, a sort of 'caring society' between players and designers exists, '[a] community of players-explorersdesigners-makers that is willing to play, discuss, and participate in the refinement of an experience' (78). The designer, then, is not a 'demiurge, but rather an earthly scenographer, someone who is responsible for setting up constraints and affordances that will be freely appropriated by the actors (the players) during the play' (96). Like all postphenomenologists, Gualeni attributes great importance, especially in chapter II, to Heidegger's philosophy of technology. In What Things Do (2005), Verbeek criticized the later Heidegger's writings on technology for being too abstract and monolithic, although he has also censured those critics of Heidegger who have been too abstract and monolithic in their own critiques. Verbeek proposes to turn the attention toward the early Heidegger's considerations on the technical artifacts. Gualeni claims, by contrast, that 'the second phase of Heidegger's thought is -at least in a general sense -more promising than the first in terms of its less monolithic approach to the projectual possibilities of our technically-mediated being-in-the-word' (38). First, since for the later Heidegger human artifacts can establish new worlds and the emergence of different worldviews. Second, because the German philosopher recognized the 'possibilities for overcoming Western thought as latent in the depth of the technological mindset' ( 39). Yet, according to Gualeni, the overcoming of the classic ontologies can be concretely pursued, and not, as the later Heidegger did, simply prophesized. Furthermore, the fact remains that the second phase of Heidegger's philosophy is deeply anti-humanist. For this reason, and this is the second philosophical heritage of Gualeni's book, the author refers to Helmuth Plessner's anthropology in chapter VI. He shares with Plessner the idea that human beings are 'artificial by nature.' He also uses Plessner's distinction between three levels of organic. Human beings are characterized, compared to plants and animals, by an 'eccentric positionality,' i.e. the coexistence of two connected nuclei, one within the body, and the other, that makes self-reflection possible, outside. The author integrates this theory with the insight offered by the Dutch philosopher Jos de Mul, according to which the structural hybridization of human biology and interactive digital technologies capable of displacing human cognition cause the emergence of an additional positional form: 'Poly(ec)centric positionality,' an expression indicating that digital technologies not only displace the human intentional boundary-realization, but also multiply it (115).

Transductions

As I said, Gualeni's book might be considered as the first step toward a digital hermeneutics. With this term, I propose to indicate an approach characterized by three elements. First of all, a problematization of the presumed homology between the world and its digital representations -a position that has been defended, for instance, by Bruno Latour and his collaborators on several occasions (e.g. [START_REF] Latour | The Whole is Always Smaller than Its Parts. A Digital Test of Gabriel Tarde's Monads[END_REF]. Another French philosopher, who is experiencing an increasing posthumous recognition, Gilbert Simondon, refers to 'transduction' as a process of thinking consisting of establishing similarities among relations. According to him, however, this process cannot be assimilated to translation -which, incidentally, is an important concept for actor-network theory -since it is not based on identity, but rather on the differences it aims to explain (Simondon 2005, 108). In these terms, digital hermeneutics would deal with analogies and differences between actual and virtual digital worlds, with (the limits of) their mutual effectiveness.

In order to do this, and this is the second element characterizing a hermeneutic approach toward digital technologies, it is necessary to overcome the ruinous alternative between truth and method in the field of the digital studies. Behind the unifying etiquette of 'digital humanities,' there is often either a technically-mediated approach to some cultural objects, or a sort of humanist critique to digital technologies -'le numérique,' as French academics commonly subjectivize the adjective 'digital.' Digital hermeneutics should instead articulate an object-oriented attitude toward specific digital objects with an interest for the existential and ontological consequences of their production and use.

Both these elements are well presented in Gualeni's book. He considers the mutual interactions between actual and virtual digital worlds, but he does not confuse them; he develops existential and ontological reflections on the basis of his technical competencies and his passion for computer games. Considering all this, it is such a pity that Gualeni limits his analysis to the context of video games, without considering other digital technologies such as social media. Facebook, for instance, has a great reconfiguration power over the narrative identities of its users [START_REF] Romele | Narrative Identity and Social Networking Sites[END_REF]).

Yet digital hermeneutics should be also made of a third element, which seems to be missing, at least in great part, from Gualeni's reflections. I refer to a 'pharmacology' of digital technologies, i.e. an analysis revealing both their benefits and risks. This term has been recently used by Bernard Stiegler, who borrowed it from Jacques Derrida. Interestingly, before Ihde and Verbeek, the Hungarian philologist Peter Szondi had already used the term 'material hermeneutics' for defining his approach to literary texts. On the one hand, he wanted to stress the necessity of an objectoriented research on specific texts, conducted with the most rigorous methodologies. On the other hand, he aimed to highlight the importance of a critique of ideology of their context of production and fruition. Szondi had in mind the thesis of the Frankfurt School's representatives Theodor W.

Adorno and Walter Benjamin, plus the thought of his compatriot György Lukács. Now, it is precisely this critical attitude that Gualeni seems almost entirely to neglect; an attitude that, in my opinion, must not necessarily be influenced by the theories of the Frankfurt School.

Gualeni refers to game designers and users as members of a (potentially) enlightened community, which in the end risks being no less exclusive than Plato's Academy. He forgets then to discuss the risks related to any form of elitism and communitarianism. He also neglects the fact that most of the computer games are not created for liberation purposes, but for economic interests. He strongly believes in the democratic force of virtual digital worlds. He is partly right in claiming that video games have popularized experiences that were reserved until thirty years ago for the cultural elites. But he does not consider the fact that computer games also generate new types of divides, between elderly and young people, between rich and poor, etc. Paradoxically, since most of human contemporary cultures are still writing-based, classic forms of mediation might be considered more 'democratic' than the new digital ones. Such a critique would be all the more urgent when one considers other digital technologies like social media. Indeed, most of them do not promote any sort of informed use, but rather the opposite in this case. Gualeni counterbalances his optimism in some passages, as when he claims that 'videogames, like any form of mediation, can disclose reality in specific ways that are always both revealing and concealing' (94), which are nonetheless too few and too short. Moreover, Gualeni seems to implicitly believe that philosophy is critical per se, and always bearer of positive changes and values. Unfortunately, in the course of history, philosophy has often been used for maintaining the status quo as well.

Finally, the statement according to which only digital technologies provide 'effective materializations of worlds' is rather problematic. He does not consider, for instance, the virtual analogic worlds created by cinema, which are no less concrete, although certainly less interactive.

He does not reflect on the fact that literary worlds overcome the limits of 'subjective imagination and interpretation' as long as they are the objects of public and social debates, as long as they are part of a specific literary genre, and of a socially shared tradition, which can be defended or contested.

As I said, Virtual Worlds as Philosophical Tools has the merit to pave the way for a hermeneutic approach to digital technologies. It is now the task of Gualeni himself, or of someone else's, to walk this path. This means both to approach also different kind of digital technologies, and to definitely renounce to any kind of romanticism.


Cristanel Razafimandimby

Valeria Loscri
email: valeria.loscri@inria.fr

Anna Maria Vegni
email: annamaria.vegni@uniroma3.it

A neural network and IoT based scheme for performance assessment in Internet of Robotic Things

Keywords: IoT-based, connectivity maintenance, coverage, IoRT, neural network

Internet of Robotic Things (IoRT) is a new concept introduced for the first time by ABI Research. Unlike the Internet of Things (IoT), IoRT provides an active sensorization and is considered as the new evolution of IoT. This new concept will bring new opportunities and challenges, while providing new business ideas for IoT and robotics' entrepreneurs. In this paper, we will focus particularly on two issues: (i) connectivity maintenance among multiple IoRT robots, and (ii) their collective coverage. We will propose (i) IoRT-based, and (ii) a neural network control scheme to efficiently maintain the global connectivity among multiple mobile robots to a desired quality-ofservice (QoS) level. The proposed approaches will try to find a trade-off between collective coverage and communication quality. The IoT-based approach is based on the computation of the algebraic connectivity and the use of virtual force algorithm. The neural network controller, in turn, is completely distributed and mimics perfectly the IoT-based approach. Results show that our approaches are efficient, in terms of convergence, connectivity, and energy consumption.

I. INTRODUCTION

Nowadays, Internet of Things (IoT) technology begins to take an important place in economic systems and in society daily life [START_REF]Internet of things council[END_REF]. It has got a large success in several application areas, ranging from smart city applications [START_REF] Aloi | Stemnet: an evolutionary network architecture for smart and sustainable cities[END_REF] [START_REF] Petrolo | Towards a smart city based on cloud of thoings[END_REF], smart grid [START_REF] Qinghai | Application of internet of things in smart grid power transmission[END_REF], etc. However, sensors constituting IoT paradigm are only passive so far. Later, adding an active role for sensors will be needed, in order to optimize the systems where they are present.

Robotic systems match very well to this new need, since robots can sense and interact with their environment. That is why ABI Research introduced a new concept called Internet of Robotic Things (IoRT) [START_REF]Internet of robotic things[END_REF]. IoRT was defined as an intelligent set of devices that can monitor events, fuse sensor data from a variety of sources, use local and distributed intelligence to determine a best course of action, and then act to control or manipulate objects in the physical world [START_REF]Internet of robotic things[END_REF]. This new concept is expected to be the evolution of IoT and robotics.

In various IoRT applications (e.g: smart agriculture, smart environment monitoring, smart exploration, smart disaster rescue, etc), the use of mobile robots' teams brings many advantages over one powerful IoRT robot. As a matter of fact, a team of robots can accomplish tasks more efficiently, faster and more reliable than a single robot [START_REF] Uny Cao | Cooperative mobile robotics: Antecedents and directions[END_REF][14] [START_REF] Arai | Editorial: Advances in multi-robot systems[END_REF]. To carry out cooperative tasks, IoRT team members need to communicate with each other, often via a wireless link (i.e. Wifi, Bluetooth). Maintaining communication among multiple mobile IoRT robots is therefore a crucial issue.

Many approaches have been designed to maintain the connectivity of multi-robot and multi-agent systems. These approaches can be classified into two groups i.e. (i) local and (ii) global connectivity maintenance. With the local connectivity maintenance, the initial set of edges which define the graph connectivity must be always preserved over time. Unlike local connectivity maintenance, global connectivity maintenance allows suppression and creation of some edges, as long as the overall connectivity of the graph is conserved. Different examples and results related to these approaches can be found in [START_REF] Carmela | Decentralized control of connectivity for multi-agent systems[END_REF][20] [START_REF] Bouraqadi | Making networked robots connectivity-aware[END_REF][21] [START_REF] Hsieh | Maintaining network connectivity and performance in robot teams[END_REF] [START_REF] Casteigts | Biconnecting a network of mobile robots using virtual angular forces[END_REF].

In Multi-Robot Systems (MRS), global connectivity maintenance is often used since the local connectivity maintenance presents some restrictions. Besides connectivity maintenance, the major problematic in global connectivity maintenance approaches is how to maximize the network connectivity. Maximizing the connectivity is important to ensure reliable communication between any pair of IoRT robots. Many works based on graph theory were proposed in the literature to face this problematic. These works are extensively used in multi-agent systems and are based on the maximization of the algebraic connectivity. In this paper, we try to migrate some of these ideas in IoRT applications. Precisely, we will use the graph connectivity metric to maintain the global connectivity of IoRT robots' team, when they are in mobility. This paper addresses also the coverage issue. In general, coverage issue aims to determine how well the sensing field is monitored or tracked by sensors. In literature, Virtual Force Algorithm (VFA) was widely used to formulate this problem [START_REF] Zou | Sensor deployment and target localization based on virtual forces[END_REF]. However, these methods have limitations since there are situations that do not allow the systems to converge in a stable state [START_REF] Chen | Novel deployment schemes for mobile sensor networks[END_REF]. We will present a new solution to this problem later in this paper.

To summarize, in this paper we address two problems i.e. (i) connectivity maintenance, and (ii) collective coverage. However, it is interesting to mention that maximizing these two parameters simultaneously is difficult (if not impossible).

Maximize the collective coverage may lead poor communication quality and conversely (i.e. a very good communication may lead poor coverage). It follows that our goal is to capture the trade-off between collective coverage and communication quality. Leveraging on the above motivations, in this paper, we propose two motion control strategies which maintain global connectivity between IoRT robots to a desired QoS level. The first approach is an IoT-based while the second in a distributed trained neural network controller.

The main contribution of this paper is the design of two approaches that have the following properties:

• The first approach is IoT-based, IoRT robots works with a central object which has high computation capability for network connectivity computing/monitoring and for the robot motion decision;

• Our both approaches converge to the desired communication quality level;

• Connectivity between any pair of IoRT robots is kept all along the deployment procedure;

• Our approaches use a distributed virtual force algorithm when the access to the central object is available and a distributed trained neural network controller otherwise. Both strategies are computed locally and based only on the local neighborhood information.

The rest of this paper is organized as follows. Section 2 provides some backgrounds which include information on algebraic graph theory and neural networks. Section 3 describes the IoT-based approach, while Section 4 details the neural network approach. Section 5 provides the simulation results. Finally, Section 6 is dedicated to the conclusions.

II. BACKGROUNDS

A. Graph representation and Eigenvalues

Multi-Robot Systems (MRS) can be represented by a graph G(V, E) where V is the set of vertices representing each IoRT robot and E ⊆ V 2 is the set of edges. E can be be defined as : where d(i,j) is the euclidean distance between i-th and j-th IoRT robots and R is the communication range. Following the above definition, let N i be the one-hop neighborhood of the i-th IoRT robot. Thus, N i is the set of IoRT robots which can exchange information with IoRT robot i. N i can be defined as follow :

E = (i, j) ∈ V 2 | i = j ∧ d(i, j) ≤ R ,
N i = {j ∈ V | d(i, j) ≤ R} (1)
Definition 1. An undireted graph G is connected if there exists a path between each pair of vertices.

In this paper, the graph G may evolve over time due to the IoRT robots motion but has to be always connected. Definition 2. Let define a matrix A ∈ R n×n . The scalar λ is an eigenvalue of A if there exists a non-zero vector w such that

A.w = λ.w (2)
The vector w is called eigenvector of A corresponding to λ.

B. Laplacian matrix and algebraic connectivity

Given a undirected graph G, its Laplacian matrix L is defined as:

L(G) = Ψ(G) -A(G) (3)
where:

• A(G) is the weighted adjacency matrix of graph G whose entries A ij is defined as in [START_REF] Carmela | Decentralized control of connectivity for multi-agent systems[END_REF]:

A ij=      1 d(i, j) < D th e -5(d(i,j)-D th ) R-D th D th ≤ d(i, j) ≤ R 0 d(i, j) > R (4)
• Ψ(G) is a diagonal matrix such as the components

Ψ i = n i=1 A ij along the diagonal • D th is the desired distance between each pair of IoRT robots.
The Laplacian matrix L(G) holds some interesting properties:

1) Let 1 be the column vector of all ones. Then, L1 = 0. 2) Let λ i , i = 1, ..., n the eigenvalues of the Laplacian matrix L(G).

• The eigenvalues of L(G) can be ordered such that

0 = λ 1 ≤ λ 2 ≤ λ 3 ≤ ... ≤ λ n (5)
• λ 2 > 0 if and if only the graph G is connected. The second-smallest eigenvalue λ 2 is called also algebraic connectivity of the graph G. The value of λ 2 indicates how weel connected the graph is.

Further details on graph theory and proof can be found in [START_REF] Fiedler | Algebraic connectivity of graphs[END_REF].

C. Artificial Neural Networks

Artificial Neural Networks (ANN) was inspired by the human brain and was designed as a computational model to solve specific problems [START_REF] Abraham | Artificial neural networks. handbook of measuring system design[END_REF]. It's architecture is defined by (i) a basic processing elements called artificial neurons, and (ii) the way in which they are interconnected. The output value of a neuron is given by:

output = f ( i w i x i + b) = f (W T X + b) (6)
where

• x i : the inputs
• w i : connections' weights between x i and the neuron

• W : weights' vector

• X: inputs' vector • b: the bias • f : the activation function
The basic architecture of ANN contains three neuron layers: input layer, hidden layer and output layer. In this case, the outputs of one layer become the inputs of next layer [START_REF] Abraham | Artificial neural networks. handbook of measuring system design[END_REF]. A typical artificial neuron and a basic ANN are illustrated in Figure 1. A key element of an artificial neural network is its ability to learn. This meant that ANN has to learn from a data set in order to match the inputs to the desired output. During the learning process, weights and biases are adjusted till the desired output will be reached. There are several learning algorithm but in this paper we will use the backpropagation algorithm [START_REF] Riedmiller | Advanced supervised learning in multi-layer perceptronsfrom backpropagation to adaptive learning algorithms[END_REF].

III. IOT-BASED APPROACH

As we saw in the previous section, an undirected graph is connected if and only if λ 2 > 0. Therefore, any strategy which maintiens λ 2 at positive values guarantees global connectivity among multi-robot systems.

In this section, we present an IoT-based approach which is capable of maintaining desired wireless communication coverage among neighboring robots.

The proposed approach uses a Central Object (CO) with high computation capability to compute and monitor the connectivity of the overall multi-robot system. We assume that each IoRT robot knows its own position by using GPS or other localisation system. Beacon messages are used to allow IoRT robots exchange their positions with their one-hop neighbors. Each IoRT robot in the system applies a distributed virtual force algorithm to control its movement. This computation is only based on the local neighborhood information. In order to keep the desired distance and hence the desired connectivity quality with its neighbor, the i -th IoRT robot should move away from the IoRT robot j ∈ N i if d(i, j) < D th and should move close if d(i, j) > D th . D th is the desired distance between each pair of IoRT robots. This simple control law generates a vector position -→ P ij such that the i -th IoRT robot keeps the line of sight of the IoRT robot j.

-→ P ij is defined as :

-→ P ij = (0.1 × k × error, θ ij ) if d(i, j) > D th and error > (k × error, θ ji ) if d(i, j) < D th and error > ( 7
)
where :

• error =| d(i, j) -D th | (7)
• θ ij is the orientation of the line segment from robots i to j;

• k is the damping coefficient

• is a lower bound of error. It will be used in order to avoid useless small movements.

In order to overcome the problem in the original VFA, we set the attractive coefficient w a to one tenth of repulsive coefficient k (w a = 0.1 × k).

When the i -th IoRT robot has more than one neighbor, its new position is calculated as the summation of the position decisions with respect to all the neighbors :

-→

P i = j∈Ni -→ P ij ( 8
)
After calculating their new positions, each IoRT robot sends the computed position to the Central Object (CO). Then, CO computes the algebraic connectivity λ 2 of the IoRT robots network according to the formula (3). The central object CO allows each IoRT robot to move to their new positions if and only if λ 2 > 0. This guarantees that global connectivity is always kept all along the deployment procedure. It is important to note that IoRT robots and CO can communicate to each other through an IoT platform.

The following algorithm summarizes our approach: As we mentioned before, the connection to the central object is not always possible. For example, a rescue operation may be difficult after a disaster when the access to the central node is not available. An approach which easily adapts to any type of situation and environment is more than necessary.

To meet this need, we provide an ANN-based technique which can perfectly mimic the behaviors of IoT-based approach. The ANN-based approach is completely distributed and is trained from a set of data. The data set is obtained by using the IoT-based approach and we use backpropagation algorithm to train ANN. The trained ANN is constituted by 2 input units and 1 output unit. The 2 input units are d(i, j) and θ ij , while the output is -→ P ij . Therefore, the trained ANN is executed locally for each IoRT robot to control its movement according to its neighbor's distance d(i, j) and angle θ ij . When the position -→ P ij is estimated, the new position -→ P i of the IoRT robot is computed by using the formula [START_REF]Internet of things council[END_REF]. Then, the collective movement of all IoRT robots will allow our trained ANN converge to the desired distance D th . The global connectivity will also keep if our ANN is well trained (i.e. if training error equals zero or near to zero). The algorithm below illustrates our ANN-based approach: Algorithm 2 ANN approach (runs every t units of time) Phase I: Neighbor Discovery MyNeighbor = FindNeighbor(RobotId)

Phase II: Estimate the position -→ P ij between two robots

-→ P ij = trained ann(d(i, j), θ ij )
Phase III: Compute the new position -→ P i

Compute

-→ P i using Formula ( 8)

Phase IV: Deployment move to -→ P i V. EVALUATION & DISCUSSION OF THE RESULTS
In this section we first describe the simulation parameters and then provide the simulation results of our approaches. We are interested in studying how our approaches converge to the desired distance D th between any pair of IoRT robot (hence to the desired communication quality matching D th ). We will see also how the density of IoRT robots influences the traveled distance of a robot. The importance of taking account the algebraic connectivity before taking a movement decision will be also highlighted. Our approaches will be compared to the approach described in [START_REF] Li | An extended virtual force-based approach to distributed self-deployment in mobile sensor networks[END_REF] called hereafter EVFA (Extended Virtual Force-Based Approach). EVFA was designed by its authors to overcome the connectivity maintenance and nodes stacking problems in the traditional Virtual Force Algorithm (VFA). Unlike our approaches, EVFA is based only on the orientation force and the judgment of distance force between node and its one-hop neighbors.

We assess our techniques w.r.t. (i) the algebraic connectivity, (ii) the robot traveled distance, (iii) the average distance, and (iv) the QoS level expressed in terms of RSSI (Received Signal Strength Indicator). Simulations have beeen carried out for a variable number of robots (i.e. from 5 to 50 robots) in an area of 3x3 km.

A. Simulation parameters

All the algorithms in this paper were implemented in version 2.29 of Network Simulator with patch from [START_REF] Fiore | Ns-2.29 wireless update patch[END_REF] that reflect a realistic channel propagation and error model. The patch is used in order to provide the effect of interference and different thermal noises to compute the signal to noise plus interference ratio (SINR) and accounting for different bit error rate (BER) to SINR curves for the various codings Table I: Simulation parameters employed [START_REF] Del | Link adaptation strategy for ieee 802.11 wlan via received signal strength measurement[END_REF]. Table 1 summarizes the parameters used in the simulations.

B. Simulation results

All of the following results are the average of 100 times simulations and we assume that the topology is totally connected at the beginning of the simulation.

We can observe in the Figures [START_REF] Arai | Editorial: Advances in multi-robot systems[END_REF][START_REF] Bouraqadi | Making networked robots connectivity-aware[END_REF][START_REF] Uny Cao | Cooperative mobile robotics: Antecedents and directions[END_REF][START_REF] Casteigts | Biconnecting a network of mobile robots using virtual angular forces[END_REF](a) that IoT-based approach always kept the global connectivity since it always take account the algebraic connectivity constraint. Unlike IoTbased, EVFA has a connectivity problem when the robots density is low and this can explain why EVFA traveled a lot when the number of robot is less than 15 (see Figures 2(a)). The goodness of connectivity is observed in EVFA when the robots density is higher (i.e. > 15 robots). However, as we mentioned before our goal is not to maximize the algebraic connectivity but just to keep it always greater than zero. This condition is enough to keep the global connectivity.

Figures [START_REF] Arai | Editorial: Advances in multi-robot systems[END_REF][START_REF] Bouraqadi | Making networked robots connectivity-aware[END_REF][START_REF] Uny Cao | Cooperative mobile robotics: Antecedents and directions[END_REF][START_REF] Casteigts | Biconnecting a network of mobile robots using virtual angular forces[END_REF](c) and [START_REF] Arai | Editorial: Advances in multi-robot systems[END_REF][START_REF] Bouraqadi | Making networked robots connectivity-aware[END_REF][START_REF] Uny Cao | Cooperative mobile robotics: Antecedents and directions[END_REF][START_REF] Casteigts | Biconnecting a network of mobile robots using virtual angular forces[END_REF](d) illustrate the convergence of our algorithms to the desired distance and the desired communication quality (RSSI) throughout the simulation. We can notice that our approaches converge quickly to the aforementioned parameters which is not always the case for EVFA. We can see also that ANN mimics perfectly the behaviours of the IoT-based approach. This is due to the fact that our neural network has been well trained.

Figures [START_REF] Arai | Editorial: Advances in multi-robot systems[END_REF][START_REF] Bouraqadi | Making networked robots connectivity-aware[END_REF][START_REF] Uny Cao | Cooperative mobile robotics: Antecedents and directions[END_REF][START_REF] Casteigts | Biconnecting a network of mobile robots using virtual angular forces[END_REF](b) depict the distance traveled by a robot during the simulation time. By considering the relationship between energy and traveled distance, we can say that our approaches are energy efficient as compared to EVFA. However, it is observed that ANN consumes a bit more than Iot-based approach. This is because ANN has made a bit more step 1 to converge (see Figures 2(b)).

As a conclusion, it is worth to say that the global connectivity is reached with ANN approach since it was well trained and inherited the characteristics of IoT-based approach.

It should be noted that the coverage rate strongly depends on the initial network topology. If initially the robots are very close to each other, the convergence to the desired distance enlarges the collective coverage. Else, if the distances between robots are initially bigger than the desired distance, the coverage rate will decrease but the communication quality will improved. This has been proven but we omit it in this paper for lack of space. In this paper, we implemented a IoT-based and an ANN control scheme to maintain global connectivity among multiple IoRT robots. The proposed approaches tried to capture the trade-off between network coverage and communication quality expressed as RSSI level. The proposed algorithms allow the whole IoRT robot network converges to the desired distance, and hence the desired communication quality. Through extensive simulation we showed that our approaches outperform the EVFA approach proposed in [START_REF] Li | An extended virtual force-based approach to distributed self-deployment in mobile sensor networks[END_REF], in terms of traveled distance and convergence time. Moreover, Our proposed methods always maintain the global connectivity throughout the simulation.

Figure 1 :

 1 Figure 1: Architecture of an artificial neuron and a multilayered neural network

Figure 2 :

 2 Figure 2: Traveled distance and robot step according to the robots number

Figure 3 :

 3 Figure 3: Simulation results obtained with 5 robots moving in 3x3 km area

Figure 4 :

 4 Figure 4: Simulation results obtained with 10 robots moving in 3x3 km area

Figure 5 :

 5 Figure 5: Simulation results obtained with 25 robots moving in 3x3 km area

Figure 6 :

 6 Figure 6: Simulation results obtained with 50 robots moving in 3x3 km area

Each robot increments its counter when it decides to move. In this paper, robot step is defined as the average of the maximum counter value achieved by one robot during the simulation.

ACKNOWLEDGMENT

This work was partially supported by a grant from CPER Nord-Pas-de-Calais/FEDER Campus Intelligence Ambiante.