Laïla Nehmé

DiCoNab, the Digital Corpus of Nabataean and Developing Arabic Inscriptions

). As such, it contains letter shapes which are still recognisable as Nabataean or closer to Nabataean than 1

they are to Arabic. It is the predecessor of "pre-Islamic Arabic" or "Palaeo-Arabic", most letter shapes of which are already recognisable as Arabic (fig. 2). Since the distinction between Nabataeo-Arabic and Palaeo-Arabic can be difficult because it is not based on a list of objective criteria, it has been decided to group the two under a single umbrella and make the distinction between them only when there is no ambiguity. The Developing Arabic inscriptions are dated to the interval between the last quarter of the 3rd and the early 7th century CE. Those which are written specifically in Nabataeo-Arabic are usually not later than the mid-fifth century CE. The number of Developing Arabic inscriptions does not, at present, exceed 250. The majority have been found in what is now Saudi Arabia, with a few examples in Syria and Jordan. Altogether, the countries in which inscriptions written in the Nabataean, Nabataeo-Arabic or Palaeo-Arabic scripts were found are Syria, Jordan, Saudi Arabia, Yemen, Egypt, and Israel. In a much lower proportion, and only in the Nabataean script, inscriptions were found in other countries, namely Greece, Italy, Lebanon, and Turkey. The DiCoNab project was launched in september 2022 and is based at the UMR 8167, the Orient & the Mediterranean laboratory of the French National Centre for Scientific Research (CNRS, https://www.orient-mediterranee.com/). It is undertaken under the aegis of the Académie des Inscriptions et Belles-Lettres, in the framework of the Corpus inscriptionum semiticarum (https://aibl.fr/travaux/le-cabinet-du-corpus-inscriptionum-semiticarum/). The academic director is Laïla Nehmé (CNRS), with the collaboration of Michael C.A. Macdonald (University of Oxford) and Jérôme Norris (University of Lorraine). It is hosted by Huma-Num (https://www.huma-num.fr/), a French infrastructure which provides support to research projects in the field of digital humanities. The initial development of the database was made thanks to the support given through Benjamin Suchard's research project on "Nabataean as a spoken language" [START_REF] Barkay | Coinage of the Nabataeans[END_REF]-2022, VI.Veni.191T.023, Dutch Research Council). 3 In its initial stages, it was also helped by the Maparabia project4 as well as by a remainder of the sponsorship given between 2019 and 2023 by the Total Foundation to the Madain Salih Archaeological Project.

Users

DiCoNab is of course addressed to epigraphists, archaeologists, and historians. It will make it easy to find much of the information they may need, from dated inscriptions to the mention of any word(s), names, etc., in the texts. This is normal and will not be more detailed. The aim is also to provide either Master/PhD students or academics in charge of the study or publication of corpus(es) of texts the possibility to enter in the database the texts they work,5 and thus benefit from its processing power to build indexes of all sorts and analyse the texts' contents from various perspectives. Surely, the internet pages of the texts entered as part of such studies or publications should not be visited by all users indiscriminately but only by those who are entering them and by the community of specialists. By putting the material on an online device, students and academics would thus benefit from the help of colleagues but the material would not be accessible by all users until the author decides to make it public. This is simply done clicking on either "Public" or "Private" in a dedicated field.

Technical aspects

*The database was developed by Matteo Gallo, a freelance developer from Pisa who has gained, with CSAI and other projects, a real and extremely valuable experience in academic databases, including in the field of Semitic studies. The database was developed using MySQL, an open source database management system. Each text is provided with a unique Uniform Resource Locator (URL) which allows to refer to it easily (e.g. https://diconab.humanum.fr/inscriptions/14).

Structure

The structure of DiCoNab is that of relational database. It includes three main enterable related tables: Sites, Inscriptions, and References (publications/bibliographical references). These are related either by 1 to N or by N to N links. 6 Thus, Sites are related to Inscriptions by a 1 to N link because one site can contain several inscriptions whereas one inscription cannot belong to more than one site. On the other hand, Inscriptions are related to References (publications) by an N to N link because one inscription can appear in one or more publication(s) and vice versa, one publication can contain one or more inscription(s). The link between the two is made through a fourth enterable table called "Editions and commentaries" in which the data relative to a specific inscription in a specific publication is entered. 7 This allows to build automatic indexes of references, as are often provided at the end of proper academic publications of epigraphic material. In addition, three always accessible utilities offer the significant advantage of being modifiable by the administrators of the database or by the standard users upon simple request to the administrators, without-and that is important-the help of a computer engineer. These are the List of values, the Word tags, and the Media resources.

The List of values utility concerns fields-such as Country, Script, Writing technique and several others-that are enterable through predefined values. For example, the field "Associated motif(s)" in the Inscriptions' table contains the following values: Betyl, Cavalryman, Dromedary, Eagle, Equid, etc.". Like all lists of values, they allow data to be entered in a fully consistent way. Word tags are the tags which can-and are highly recommended to-be entered at the end of each word in the transliteration of an inscription. Each word tag refers to a particular word category (substantives, verbs, proper nouns, particles, etc., see the list of word tags in Appendix 1). The Word tags are also mofiable by the administrators and since some tag values are not used, a few tags can be added if needed. The tagged version of a transliterated text (in Unicode)8 , here JSNab 16,9 looks as follows, where the tags always come immediately after the sign "*":

kprʾ dy ʿbdw kmkm brt wʾlt brt ḥrmw w klybt brth lnpšhm w ʾḥrhm byrḥ ṭbt šnt tšʿ lḥrtt mlk nbṭw rḥm {ʿ}mh w ylʿn dwšrʾ w mwtbh w ʾlt mn ʿmn{w} w mnwtw w qyšh mn yzbn kprʾ dnh ʾw mn yzbn ʾw yrh{n} ʾw {yn}tn yth ʾw ynpq mnh gt ʾw šlw ʾw mn yqbr bh ʿyr kmkm w brth w ʾḥrhm w mn dy lʾ yʿbd kdy ʿlʾ ktyb p ʾyty ʿmh ldwšrʾ w hblw w lmnwtw šmdyn 5 w lʾpklʾ qns slʿyn ʾlp ḥrty blʿd mn dy ynpq bydh ktb mn yd kmkm ʾw klybt brth bkprʾ hw pqym ktbʾ hw whbʾlhy br ʿbdʿbdt ʿbd.

Tagging a text immediately provides a list of all the words and nouns that appear in it (fig. 3). Finally, two additional non enterable tables (i.e. their contents is updated automatically and cannot be modified by the users) complete the structure of the database: Index and Attestations. The difference between the two is simple but very important. The Index contains one single entry for each different word or noun that appears in the inscriptions. For example, the conjunction ʾw, "or", will appear only once in the Index even if it attested a number of times in the Nabataean inscriptions. This table is thus more or less the equivalent of the entries of a potential dictionary. A simple click on the word then lists all the attestations/ occurrences in each text, in the order of appearance (fig. 4). One of the great assets of the system is that it takes into accound the presence of editorial signs such as the curly brackets { } for uncertain letter(s) and ffffffffthefsquare brackets [ ] for restored letters. Thus, if a word is attested only once and if this single attestation contains either uncertain or restored letters, it appears in red in the Index (fig. 5) in order to draw the user's attention to the fact that its existence in the corpus is not absolutely sure. In the example given fig. 5, the letters {yn}tn-of the verb ntn in the Prefix conjugation pʿl (G-stem), tag *32-are uncertain and the fact that yntn appears in red in the list shows that this derived form of ntn is not surely attested in Nabataean.11 All the attestations/occurrences of the words are entered automatically in the other non enterable table, Attestations. An asset of this table is the fact that the words always appear in their context, and whatever comes after the word is given in the Aramaic alphabetical order (fig. 6). This is particularly useful for personal names because it allows to find individuals who bear the same name and whose father's name (or even grandfather's name, etc.) is also the same, thus providing the means to trace the same individuals, particularly between epigraphic sites on the trade routes and between the major Nabataean cities and these trade routes.

In conclusion, lists of words and nouns, given with their grammatical or noun category and in their context, provide continuously updated versions of the Nabataean dictionaries and corpora of personal names 12 and may form the basis of a new grammar of Nabataean, which would add a lot of material and examples to the one by J. Cantineau published in 1930Cantineau published in -1932.

Other assets of DiCoNab

Sites

About 520 sites where Nabataean inscriptions were found are already entered in the database, along with their geographical coordinates. The overherlming majority of these sites were listed by J. Norris who has been collecting, for years, sites with epigraphic material of various sorts in the Middle East. Only those sites which have yielded inscriptions that are already published are made available to all users the database. The rest will be accessible only to the editors who have received a login and a password. The availability of coordinates will allow the production of distribution maps, especially since DiCoNab allows exports to be made towards the maps of the atlas of the MAPARABIA project, directed by J. Schiettecatte (http://ancient-arabia.aidns-ag3.eu/atlas).

Bibliographical references

All the bibliographical references known and checked by L. Nehmé which concern Nabataean and Nabataeo-Arabic epigraphy, Nabataean papyrology, numismatics, onomastics, as well as general works on the Nabataeans have also already been entered in the database with a siglum and a short title, using a Zotero export format designed especially for DicONab:

Media resources

Media resources are entered in a separate table and can be called whenever needed. This is particularly useful if a photograph contains more than one inscription and needs to be referred to for each one of them so that the photograph is uploaded only once. The media accepted are images, whether photographs or facsimiles, but also 3D models, videos, PDF documents, audios and fonts, the only limit being the space it occupies on the Huma-Num server.

It is hoped that DiCoNab will meet the needs of all those who are interested in Nabataean studies and in the development of the Nabataean to the Arabic script. Taking on the legacy of scholars such as Jean Starcky and Joseph Milik, who started to write in Latin and by hand the continuation of volume II of the Corpus Inscriptionum Semiticarum, needed at least an ambitious project such as DiCoNab, for the elaboration of which we have put a lot of the experience we gained in databases of Semitic inscriptions over almost thirty years.

  10 dnh*66 kprʾ*13 dy*64 ʿbdw*22 kmkm*82 brt*12 wʾlt*82 brt*12 ḥrmw*81_ w*72 klybt*82 brt*14 -h*62 l-*71 npš*14 -hm*63 w*72 ʾḥr*14 -hm*63 b-*71 yrḥ*12 ṭbt*91 šnt*11_ tšʿ*94 l-*71 ḥrtt*84 mlk*12 nbṭw*88 rḥm*43 {ʿ}m*14 -h*62 w*72 ylʿn*32 dwšrʾ*87_ w*72 mwtb*14 -h*62 w*72 ʾlt*87 mn*71 ʿmn{w}*89 w*72 mnwtw*87 w*72 qyš*14 -h*62 mn*65 yzbn*32_ kprʾ*13 dnh*66 ʾw*72 mn*65 yzbn*32 ʾw*72 yrh{n}*32 ʾw*72 {yn}tn*32 yt*78 -h*62 ʾw*72 ynpq*32_ mn*71 -h*62 gt*11 ʾw*72 šlw*11 ʾw*72 mn*65 yqbr*32 b-*71 -h*62 ʿyr*51 kmkm*82 w*72 brt*14 -h*62_ w*72 ʾḥr*14 -hm*63 w*72 mn*65 dy*64 lʾ*74 yʿbd*32 kdy*72 ʿlʾ*77 ktyb*45 p*72 ʾyty*77 ʿm*71 -h*62_ l-*71 dwšrʾ*87 w*72 hblw*87 w*72 l-*71 mnwtw*87 šmdyn*15 5*93 w*72 l-*71 ʾpklʾ*13 qns*11 slʿyn*15 ʾlp*94 ḥrty*51 blʿd*71 mn*65 dy*64 ynpq*32 b-*71 yd*14 -h*62 ktb*11 mn*71 yd*12_ kmkm*82 ʾw*72 klybt*82 brt*14 -h*62 b-*71 kprʾ*13 hw*66 p-*72 qym*45 ktbʾ*13 hw*66_ whbʾlhy*81 br*0 ʿbdʿbdt*81_ ʿbd*22 The non tagged version of the text is of course created automatically and looks as follows: dnh

Example of information available for each site:

	Present	Ancient	Country Region	Accuracy of	Origin of	Latitude	Longitude
	name	name			coordinates	coordinates
	Buṣrā	Bostra	Syria	Ḥawrān	Certain	Pointed on	32.51947	36.48257
						Google Earth
	Dūmat al-	Dūmat	Saudi	North-	Certain	Pointed on	29.8113	39.86904
	Jandal	(Adumatu)	Arabia	West		Google Earth
				Arabia
	Wādī	Iram	Jordan	Northern	Certain	Pointed on	29.57784	35.41457
	Ramm,			Ḥismā		Google Earth
	Temple of
	Allāt

13 Example of information available for each reference:

	KDIWM	Khairy 1981, PEQ 113	Khairy, Nabil I. 1981. "A New Dedicatory Nabataean Inscription
			from Wadi Musa. With an additional note by J.T. Milik."
			Palestine Exploration Quarterly 113: 19-26, pl. 3.
	ZGAK	Zayadine 1990, The God	Zayadine, F. 1990. "The God (ess) Aktab-Kutbay and his (her)
		(ess)	Iconography." In Petra and the Caravan Cities : Proceedings of
			the Symposium organised at Petra in September 1985 , edited by
			F. Zayadine, 37-51, pl. 1-7. Amman.
	Siglum	Short title	Complete reference
	JSNab	Jaussen & Savignac 1909-	Jaussen, Antonin, and Raphaël Savignac. 1909-1922. Mission
		1922, Mission en Arabie	archéologique en Arabie. Publications de la Société française des
			fouilles archéologiques 2. Paris.

12 Thus superseding those published by W.J. Jobling, S. al-Theeb, and A.

Negev. 13

875 references are available to all users.

The project's director is extremely grateful to B. Suchard for his immediate and unreserved positive answer to our request for support in order to set up the database.

(French) National Research Agency project ANR-18-CE27-0015: "Mapping Ancient Arabia for enhancing knowledge and shifting paradigms", director J. Schiettecatte.

All they need is to be given access by DiCoNab's administrator(s) through a login and a password which makes them "Editors" of the database rather than only "Standard users".

N represents an unknown and unlimited number of records.

Page, copy, photograph, squeeze, reading and translation categories.

Special user-friendly keyboards for Azerty and Qwerty and for both Apple and PC computers have been developed so that entering letters with diacritical marks (ʾ, ʿ, ḥ, ṣ, š, ṭ, etc.) is both quick and easy.

[START_REF] Jaussen | Mission archéologique en Arabie[END_REF] Savignac 1909-1922, Nabataean inscription no. 16.

Note that the underscore "_" marks a change of line and that enclitic personal pronouns are preceded by "space+hyphen" so that they can be tagged and indexed separately from the word to which they are attached. Thus, npš -hm line 2 is tagged npš*14 -hm*63 because npš here is a substantive singular suffixed and -hm is an enclitic personal pronoun plural.

This is of course only an example since {yn}tn is in fact widely attested in Nabataean!


Tristan Dupeux

Théophile Gaudin

Clémentine Marteau-Roussy

Jean-Marie Aubry

Véronique Nardello-Rataj

COSMO-RS as an Effective Tool for Predicting the Physicochemical Properties of Fragrance Raw Materials

Keywords: Fragrance, COSMO-RS, Modelling, Solubility, Polarity, Volatility

A predictive tool called COSMO-RS, Conductor-Like Screening Model for Real Solvents, based on quantum chemistry, dielectric continuum models, electrostatics surface interactions and statistical thermodynamics have been used to predict five key physicochemical properties of raw materials used in perfumery industries. The prediction of boiling point (BP), octanolwater partition coefficient (log P), vapor pressure (VP), water-solubility (WS) and Henry's law constant (HLC) of fragrance molecules has been validated with a reference data set of 166 organic compounds. Knowing these properties for a fragrance molecule is essential and being able to predict them precisely can be particularly useful in the development of new molecules or in the replacement of controversial molecules regarding safety issues without compromising the overall hedonic accord. Finally, mapping the vapor pressure versus the Henry's law constant and the octanol-water partition coefficient, consistently predicts the note class of the molecules useful for release comparison of captives.

Introduction

Each year, fragrance companies develop and patent two or three new molecules called captives. [START_REF] Burr | the Seductive Fragrance of Molecules Under Patent[END_REF] These molecules are created not only to entice consumers with unique notes for perfumery but also to decrease cost, allergic reactions, feedstock shortages or nonbiodegradability/non-renewability of previous raw materials. To launch two to three captives per year on the market, screening of hundreds or thousands of molecules is necessary. As such, fragrance design requires considerable experimental work of synthesis and characterization. Hence, predicting in silico the physicochemical properties of virtual candidates can significantly contribute to a faster development of new captives with targeted features.

According to the REACH regulation, [START_REF] Lewis | Integrating process safety with molecular modeling-based risk assessment of chemicals within the REACH regulatory framework: Benefits and future challenges[END_REF] 17 properties must be determined to bring a new molecule to the market (Table S1). However, measuring experimentally all these properties is not always realistic in terms of time, cost, feasibility at R&D level and safety (notably for hazardous compounds). Therefore, this implementation has motivated the development of alternative approaches to experimental testing with fast and reliable methods. [START_REF] Lewis | Integrating process safety with molecular modeling-based risk assessment of chemicals within the REACH regulatory framework: Benefits and future challenges[END_REF] As a consequence, thanks to improvements in computer hardware and software in the past decades, numerous tools to predict property values for large molecule sets have emerged.

Perfumery is typically a field of application in which prediction of physicochemical properties can be very useful. Indeed, vapor pressure (VP) and boiling point (BP) as well as Henry's law constant (HLC) which represents the mass transfer of molecules from liquid to air are essential data to describe and assess the volatility of scent molecules. [START_REF] Wagner | Densities, Vapor Pressures, and Surface Tensions of Selected Terpenes[END_REF][START_REF] Bhal | LogP-Making Sense of the Value[END_REF][START_REF] Klamt | COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids[END_REF][START_REF] Nieto-Draghi | A General Guidebook for the Theoretical Prediction of Physicochemical Properties of Chemicals for Regulatory Purposes[END_REF][START_REF] Panayiotou | Equation-of-State Models and Quantum Mechanics Calculations[END_REF] Likewise, watersolubility (WS) and octanol-water partition coefficient (log P) can bring valuable insights for the elaboration of aqueous formulations. [START_REF] Bhal | LogP-Making Sense of the Value[END_REF] Among the available predictive approaches, mainly five stand out for estimating chemical properties with their pros and cons. [START_REF] Klamt | COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids[END_REF][START_REF] Nieto-Draghi | A General Guidebook for the Theoretical Prediction of Physicochemical Properties of Chemicals for Regulatory Purposes[END_REF][START_REF] Panayiotou | Equation-of-State Models and Quantum Mechanics Calculations[END_REF][START_REF] Grensemann | Performance of a Conductor-Like Screening Model for Real Solvents Model in Comparison to Classical Group Contribution Methods[END_REF][START_REF] Hornig | COSMOfrag: A Novel Tool for High-Throughput ADME Property Prediction and Similarity Screening Based on Quantum Chemistry[END_REF][START_REF] Franke | A Case Study in the Pre-Calculation of Henry Coefficients[END_REF][START_REF] Wille | Effect of Electrolytes on Octanol-Water Partition Coefficients: Calculations with COSMO-RS[END_REF] The group contribution model (GC) or additive group method is an empirical method based on the division of molecule in blocks (functional groups). [START_REF] Van Speybroeck | The calculation of thermodynamic properties of molecules[END_REF][START_REF] Benson | Additivity rules for the estimation of thermochemical properties[END_REF][START_REF] Constantinou | New group contribution method for estimating properties of pure compounds[END_REF][START_REF] Joback | Estimation of pure-component properties from groupcontributions[END_REF] In most cases, the property is computed as a sum of contributions of each group, though nonlinear GC models are sometimes proposed. GC is easy to use but despite all the development to improve the methods, the lack of parameters to describe all the molecules, the non-unicity of breakdown schemes for some molecules, the impossibility to discriminate isomers or the bad accuracy in the prediction for chiral compounds does not fulfill all the expectations for some applications. Quantitative structure-property relationships (QSPR) models correlate chemical properties with molecular features encoded by a series of molecular descriptors. [START_REF] Dearden | In Silico Prediction of Physicochemical Properties[END_REF][START_REF] Katritzky | Quantitative Correlation of Physical and Chemical Properties with Chemical Structure: Utility for Prediction[END_REF][START_REF] Dearden | QSPR prediction of physico-chemical properties for REACH[END_REF] It is based on the assumption that "similar structures give similar properties". Though the QSPR approach can quickly generate predictions, descriptors (especially topological and quantum-chemical ones) are not always easy to calculate and interpret. Moreover, as a purely empirical model, a QSPR model is fundamentally limited in its applicability to molecules similar to the ones it has been trained for. The equation of state approach (EoS) takes advantage of thermodynamics and statistical mechanical principles. [START_REF] Valderrama | The State of the Cubic Equations of State[END_REF][START_REF] Michelsen | Fundanental s & Computational Aspects: Thermodynamics Models[END_REF][START_REF] Kontogeorgis | Thermodynamic Models for Industrial Applications: From Classical and Advanced Mixing Rules to Association Theories[END_REF] It is based on mathematical relationships which allow describing the state of matter under certain physical conditions such as pressure, volume or temperature. Different approaches are possible, and some empirical modifications can improve the accuracy. These approaches are often powerful to predict physicochemical properties at different pressures and temperatures given a few experimental (or even predicted) data points. However, by themselves, they are of limited use where no initial data are available for the calibration of the models. Molecular simulation relies on the explicit computation of inter-particle energies and motion over a large ensemble of particles. [START_REF] Haile | Molecular Dynamics Simulation: Elementary Methods[END_REF][START_REF] Gubbins | Molecular Modeling of Matter: Impact and Prospects in Engineering[END_REF][START_REF] Maginn | Historical Perspective and Current Outlook for Molecular Dynamics As a Chemical Engineering Tool[END_REF] Macroscopic properties can then be calculated based on statistical mechanics principles. The molecular dynamic based on the equation of motion and the Monte-Carlo method based on statistics are the two main methods. These techniques present complex simulation set-up and the calculation time is generally long compared to previous techniques. Furthermore, the force fields that model the intermolecular interactions should be carefully selected as a function of the problem, requiring substantial user expertise. To the end, COSMO-RS is an approach which combines quantum chemistry, dielectric continuum models, electrostatic surface interactions and statistical thermodynamics. [START_REF] Klamt | COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids[END_REF][START_REF] Klamt | Erratum to "COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids[END_REF][START_REF] Lin | A Priori Phase Equilibrium Prediction from a Segment Contribution Solvation Model[END_REF][START_REF] Lin | Prediction of Vapor Pressures and Enthalpies of Vaporization Using a COSMO Solvation Model[END_REF][START_REF] Wang | Application of the COSMO-SAC-BP Solvation Model to Predictions of Normal Boiling Temperatures for Environmentally Significant Substances[END_REF] It is a fast method to predict liquid phase properties for neutral molecules, ionic liquids and mixtures.

Note that though the method is highly suitable to predict properties in the liquid phase, if ever the solid phase becomes relevant (e.g., to calculate the solubility of solid solutes) the contribution of crystal packing must be supplied eternally.

In this article, we show how the COSMO-RS method can be wisely used to find new captives when no experimental information is available in the literature or even easily accessible experimentally. Indeed, physicochemical properties can be predicted with accuracy for existing or virtual candidates avoiding time-consuming experimental measurements and the use of solvent and other hazardous chemicals.

Herein, we have therefore focused on five essential physicochemical properties of fragrance molecules: log P, boiling point BP, vapor pressure VP, Henry's law constant HLC and watersolubility WS. Their value has been predicted and compared to experimental data for 166 organic compounds to validate the approach which has then been applied to a set of 16 common fragrance and flavor compounds. Finally, a 3D-mapping of the predicted properties has been built for a real perfume to show how such information could be beneficial to compare the potential release of captives and therefore to adjust the perfume composition.

Materials and methods

Reference data set and data set of flavor and fragrance molecules

Data of 166 organic raw materials were extracted from the Yaws' database. [START_REF] Yaws | Yaws' Handbook of Thermodynamic and Physical Properties of Chemical Compounds[END_REF] They were selected on the basis of their chemical structure. Indeed, only molecules with the C, N, O, H atoms were extracted as they constitute the majority of the fragrance molecules. In addition, we have taken care to cover the whole range of chemical functions of fragrance molecules (i.e. alcohols, aldehydes, ketones, acetates, esters, terpenes, phenols/aromatic derivatives and ethers) of the perfumer portfolio (see Figure S1).

COSMO molecular surfaces

The COSMO-RS model is a semi-explicit extension of an implicit solvation model, the COnductor-like Screening MOdel (COSMO). [START_REF] Klamt | From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design[END_REF][START_REF] Klamt | COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient[END_REF] In this model, solute-solvent interactions are represented by the polarization induced on the solvent by the charge distribution of the solute (Figure 1), in the form of polarization charge densities on the solute/solvent interface, i.e. the molecular surface of the solute (here named COSMO surface).

COSMO models the solvent as a conductor, and the extent to which this implicit solvent is polarized by the solute is entirely controlled by its dielectric constant. Though real solvents have a finite dielectric constant, an interesting reference state is reached for the perfect conductor, i.e. a fictitious solvent with infinite dielectric constant. COSMO-RS theory is based on COSMO surfaces at infinite dielectric constant (or in the perfect conductor). [START_REF] Klamt | From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design[END_REF][START_REF] Klamt | COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient[END_REF] In general, a molecule is represented by a few distinct COSMO surfaces, each one corresponding to a relevant geometrical configuration. Note that for some small or rigid molecules (such as benzene), a single COSMO surface is enough. To obtain the COSMO surfaces (represented by COSMO files in a computer), a combination of molecular modeling and conformational search steps is required. [START_REF]COSMO Conf 4.2[END_REF] For molecules of small to average size, such as fragrances, obtaining the relevant COSMO files represents a moderate computational cost (from minutes to hours as a background task on a personal computer). The COSMO-RS model then provides chemical potentials of molecules by evaluating the interactions between the charged molecular surfaces obtained through COSMO calculations. More details about the procedure required to obtain COSMO files for a given molecule are given in the Supporting Information.

COSMO-RS theory

Combining quantum chemistry results with a simple statistical thermodynamic approach, COSMO-RS can predict the pseudo-chemical potentials of molecules in liquid phases.

COSMOtherm, a software tool that applies COSMO-RS theory, also includes a semiempirical model that predicts the pseudo-chemical potential in gas phase, and a QSPR model that predicts the Gibbs free energy of melting (i.e. transfer from pure solid to pure liquid phase). [START_REF] Cosmotherm | [END_REF] Based on these pseudo-chemical potentials, the properties of interest in this paper, which are based on such chemical potentials, can then be estimated (Figure 2). Specifically, COSMO-RS takes as a reference a universal standard state (the "ideal conductor", here denoted by a star superscript "*") to calculate pseudo-chemical potentials.

By definition, the pseudo-chemical potential [START_REF] Ben-Naim | Molecular Theory of Solutions[END_REF] and the chemical potential are related by eq. 1:

(1) in this equation,

is the pseudo-chemical potential of component i in phase S, is its actual chemical potential, and is the mole fraction of component i in phase S. Finally, R is the ideal gas constant and T is temperature. The pseudo-chemical potential of compound i in phase S can be straightforwardly interpreted as a measure of the affinity of the compound i for the phase S.

Combining eq. 1 with the thermodynamic requirement of equal chemical potentials in all phases gives:

(

In this equation, and are the chemical potentials of the molecule i in phases S1 and S2, respectively, whereas and are the pseudo-chemical potentials of the molecule i in phases S1 and S2, respectively. and are the mole fractions of the molecule i in phases 1 and 2, respectively. Thanks to eq. 2, the COSMO-RS pseudo-chemical potentials can be used to predict the equilibrium distribution of species in relevant phases.

In this article, a brief description of the procedure to predict these standard-state chemical potentials in the liquid phase (the core applicability domain of COSMO-RS) is provided. The interested reader is referred into the descriptions already available in literature for more details, as well as for the empirical models used for the gas and solid phases. [START_REF] Klamt | COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids[END_REF][START_REF] Eckert | Fast solvent screening via quantum chemistry: COSMO-RS approach[END_REF] First, the molecule of interest is placed in a realistically shaped cavity (or molecular surface), itself in a virtual conductor environment thanks to the continuum solvation model COSMO.

This conductor induces a screening charge density σ on each point of the molecular surface.

By taking account of the 3D distribution of the screening charge density on the surface of the molecule, a surface composition function is defined, called the σ-profile. Then, the COSMOtherm software uses statistical thermodynamics to calculate the chemical potential of a surface segment from the local properties of the segments in the mixture (i.e. polarization charge density, but also underlying atom type). [START_REF]COSMOtherm Reference Manual[END_REF] The pseudo-chemical potential of a molecule in the liquid phase is then obtained by summing the chemical potentials of the segments, weighted by their σ-profile. The link between the pseudo-chemical potentials and the properties of interest in this paper is presented below. These properties are always estimated based on an adapted variation of eq. 2.

The solubility of a solute i in a solvent S (in mole fraction) reflects the affinity balance between the solvent and the pure ( ) compound phases. It is calculated according to equation 3: [START_REF]COSMOtherm Reference Manual[END_REF] (3)

where n i S is the number of moles of the compound i in the solvent S, μ i *,P represents the pseudo-chemical potential of the pure compound i, μ S *,i corresponds to the pseudo-chemical potential at infinite dilution in the solvent S, and ΔG fus = μ *,solid i -μ *,liquid i is the Gibbs free energy of melting of the pure solute (which can be approximated from a QSPR model as stated previously, but also obtained from reference experimental solubilities, or from melting point and heat of fusion [START_REF] Klamt | Prediction of aqueous solubility of drugs and pesticides with COSMO-RS[END_REF] ). This solubility is already a good estimate in the diluted regime.

Nevertheless, the solubility of the solute can be refined iteratively until convergence by reusing eq. 2 including finite concentrations of solute in the solvent to predict the pseudochemical potential in the solvent until the predicted solubility converges or full miscibility ( =1) is reached. [START_REF]COSMOtherm Reference Manual[END_REF] It is worth noting that the equation assumes that the mole fraction of the solute in the solid phase is 1 (i.e. it neglects the formation of solid solvates). Combining a simple estimate for the molar volume of the solvent (based on the volume of the COSMO cavity as the main contributor), as well as the molar weight of the solute, with the predicted mole fraction solubilities, COSMOtherm also provides the solubility in molar concentration (WS), as well as in mass concentration. The partition coefficient log P i ow between octanol and water is calculated from equation 3, which combines eq. 4 with the definition of molar concentration: 36

where c i octanol and c i water are the concentrations of the solute i in octanol and in water, respectively, x i octanol and x i water are the corresponding mole fractions of the solute i, V water and V octanol are the molar volumes of the two solvent phases, and μ *,i water and μ *,i octanol are the pseudo-chemical potentials of the solute i in water and in octanol, respectively. Because water is soluble in octanol, the octanol phase was not defined as a pure octanol phase but as a "wet octanol" one with a molar ratio of 0.726 in octanol. The vapor pressure of a pure compound, based on the affinity balance of the solute for itself and the gas phase, is predicted using the equation below. [START_REF]COSMOtherm Reference Manual[END_REF] (5) in this equation, is the pseudo-chemical potential of the solute i in the ideal gas phase.

This equation is obtained by combining eq. 2 with the ideal gas relation pV = nRT. In addition, the temperature at which pseudo-chemical potentials are evaluated can be iterated until the computed VP becomes equal to the atmospheric pressure, yielding a BP prediction.

Finally, the activity coefficient at infinite dilution of the solute i in solvent S (for example water), , by definition, is related to the pseudo-chemical potentials as follows:

The HLC reflects the affinity balance between the solvent and gas phases. Since the HLC is defined as the product of the activity coefficient at infinite dilution with VP, it can be predicted by COSMO-RS 36 by combining eqs. 5 and 6:

(7)

Computational method

WS, log P, VP, BP, and HLC were predicted using the software package COSMOtherm (COSMOlogic GmbH & CO KG, Leverkusen, Germany). The COSMOthermX Version 19.0.1 software and the BP_TZVPD_FINE parameterization were used. The COSMO input files were taken from the COSMOtherm database or calculated using the COSMOconf software. The TZVPD-FINE quantum chemistry parametrization was used to predict the properties.

Results and discussion

Experimental versus predicted properties for a reference data set

The experimental data extracted from the Yaws' database were compared with the predicted ones calculated with the COSMO-RS theory for the five target properties. A set of 166 raw materials (RMs) was selected from the handbook. Not all five experimental data are available for the RMs. Indeed, though BPs are available for all of them, only 195 VP, 140 WS, 138

HLC and 123 log P are listed for the 166 RMs. The whole data are given in Table S2. Figure 3 represents the predicted values as a function of the calculated ones for the 5 properties.

As shown in Figure 3a, there is a very good correlation between calculated and experimental BP values for the whole set of molecules. The accuracy of the prediction is excellent with a R 2 of 0.99. The root-mean square error (RMSE) is 5.7 K which is better than the 15-18 K reported by Klamt [START_REF] Klamt | Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena[END_REF] and Wang [START_REF] Wang | Application of the COSMO-SAC-BP Solvation Model to Predictions of Normal Boiling Temperatures for Environmentally Significant Substances[END_REF] for their prediction of a test set compounds of 61 common molecules with various chemical functions and 369 chemicals including pollutants, herbicides, insecticides and drugs. The improvements made on the predictive model since the publication of Klamt, especially with a more thermodynamically consistent COSMOspace and the use of the FINE cavity which describes better the chemical potential for many compounds, can explain the better accuracy presented here. The model in COSMO-SAC software used by Wang also does not consider the FINE cavity which could explain lower accuracy. The maximum deviation is found for acetamide and diacetone alcohol with 25.6 K and 24.2 K standard deviation respectively.

The prediction of the octanol-water partition coefficient (log P) for 118 molecules is also well correlated to the experimental data (Figure 3b). The accuracy of the prediction is high with R 2 of 0.97. The RMSE (0.15 log units) is better than the one obtained in the COSMO-RS parameterization article [START_REF] Klamt | Refinement and Parametrization of COSMO-RS[END_REF] for a set of 168 organic molecules with a RMSE of 0.3 log units and by Buggert et al. [START_REF] Buggert | COSMO-RS Calculations of Partition Coefficients: Different Tools for Conformation Search[END_REF] with a RMSE of 0.4 log units for a set of 31 organic molecules with various chemical functions. It corresponds to the standard found by Klamt and Eckert [START_REF] Klamt | COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids[END_REF] and by Wille et al. [START_REF] Wille | Effect of Electrolytes on Octanol-Water Partition Coefficients: Calculations with COSMO-RS[END_REF] of 0.25 log units. Here, amine derivatives (triethylamine and diethylamine) and long linear alkanes (dodecane and decane) are predicted with the highest log P difference of over 1 log unit difference.

Prediction of VP values is also very satisfactory with a R 2 of 0.96 and a RMSE of 0.13 log units (Figure 3c). It matches the results of Klamt et al. [START_REF] Klamt | Refinement and Parametrization of COSMO-RS[END_REF] with a RMSE of 0.14. The average accuracy is also consistent with the literature with a 0.25 log unit difference. However, for our data set, the factor of the linear correlation is 0.93 which implies a noticeable deviation from the axis bisection. This can be explained by higher predicted VP values than experimental ones for molecules with very low volatility (< 0.001 bar). Indeed, measurement for such molecules is not straightforward and can lead to a significant error. The highest error was found for nonyl acetate (1.82 log unit difference). The problem comes from the experimental vapor pressure given in the Yaws handbook. Indeed, Krasnykh et al. [START_REF] Krasnykh | Vapour pressures and enthalpies of vaporization of a series of the linear n-alkyl acetates[END_REF] have measured the vapor pressure of nonyl acetate at 6.42•10 -5 bar at 25 °C whereas Yaws gives a vapor pressure equal to 5.79 10 -7 bar. The modification of the experimental value gives a 0.25 log units difference with the predicted data from COSMO-RS which is more acceptable.

COSMO-RS theory also shows good results for the prediction of the WS of the 135 molecules (Figure 3d). The correlation is very accurate as indicated by the R 2 of 0.92. The RMSE is 0.18 which is better than other results from the literature. Klamt et al. [START_REF] Klamt | Prediction of aqueous solubility of drugs and pesticides with COSMO-RS[END_REF] have reported a 0.5 log unit on a set of 107 pesticide-like and 150 drug-like molecules. Oleszek-Kudlak et al. [START_REF] Oleszek-Kudlak | Application of the COnductor-Like Screening Model for Real Solvents for prediciton of the aqueous solubility of chlorobenzenes depending on temperature and salinity[END_REF] have studied the water-solubility of 12 chlorobenzene derivatives and observed a RMSE of 0.14 whereas Kholod and al. 43 obtained a RMSE of 0.9 for the water-solubility of 27 nitro compounds. However, the solubility of solid compounds is overestimated, in particular phenolic derivatives which are usually solid. It may be due to the empirical account for crystal packing, as ΔG fus is approximated by a QSPR model. Moreover, the water-solubility of fragrance is not accurate for very soluble compounds (> 0.25 g/g H 2 O ). In this case, experimental inaccuracies could explain the discrepancies, as it is harder to measure the solubility of highly soluble compounds. Finally, the 133 HLC predictions are quite accurate with a R 2 of 0.97 and a RMSE of 0.19 (Figure 3e). The average log unit difference is 0.25 which is better than the one reported by Eckert et Klamt [START_REF] Eckert | Fast solvent screening via quantum chemistry: COSMO-RS approach[END_REF] for the validation set of 150

Henry's law constants of 0.38.

Prediction of the properties of fragrance molecules

The reference data set provides good correlations between experimental and COSMO-RS predicted data. This approach was then applied to a set of 16 common fragrance molecules which were not included in the training set of 166 molecules. Table 1 summarizes the experimental and COSMO-RS predicted values.

All the correlations obtained for the set of fragrance molecules are shown in Figure 4.

Whatever the properties, they are generally well predicted. The prediction of the BP (Figure 4a) is very good with a RMSE of 6.4 K which is far below the calculation error of the COSMO-RS theory. A deviation between experimental and calculated values is obtained for vanillin with a BP overpredicted by 36.7 K. This discrepancy can be accounted for by its high boiling point which is near the limitation of accuracy of the COSMO-RS theory. The octanolwater partition coefficient (log P) gives with a RMSE of 0.14 and the average log P difference is almost equal to the 0.25 expected by the COSMO-RS theory [START_REF] Klamt | COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids[END_REF] (Figure 4b). The highest deviation is obtained for D-limonene with a 0.86 log P difference. The VP prediction gives a RMSE of 0.18 log units and an average difference of 0.26 log units (Figure 4c). Anethole and pelargol exhibit the highest deviation with respectively 0.85 and 1.09 log difference. This can be explained by the difficulty of precisely measuring the vapor pressure of low volatile compounds (1.73x10 -5 bar and 2.75x10 -4 bar respectively). The water-solubility prediction is consistent with the expectation with a RMSE of 0.21 log units and an average difference of 0.29 log units (Figure 4d). Only the prediction of furfuryl alcohol is not very accurate (log difference of 0.90), probably due to its very high solubility in water. Finally, regarding the HLC, with a RMSE of 0.24 log units and an average log difference of 0.34 log units, the highest errors are obtained with pelargol (1.04 log units) and 2-phenylethanol (0.69 log units) (Figure 4e). However, the Henry's law constant depends on water-solubility and vapor pressure and for pelargol and 2-phenylethanol, it turns out that the deviation of their vapor pressure is high. Therefore, this could explain the high deviation for their Henry's law constant.

Predicting the perfume's notes from molecular structures

A perfume is a mixture of 20 to 100 molecules with specific properties. As an example, Table 2 reports the composition of a real perfume with oriental notes. Fragrance molecules are classified into three categories: top, middle and base notes. While a top note is smelled immediately after the application of a perfume, a base note can be smelled long after the application, and a middle note is in-between these two extremes. Thus, it reflects the perfume character and its specificity over time. However, it is very common than one molecule can belong to two note classes due to different odors which can appear at different time scale.

Table 2 reports the main note as well as the potential secondary note of the 33 fragrance molecules constituting the oriental perfume. The classification has been made according to odor analysis by experts and analytic data from gas chromatography.

The knowledge of the physicochemical properties of each molecule can provide information on the affiliation of one compound to a group of scents. However, the experimental data are sometimes not available for some compounds. For the oriental perfume, the prediction of the BP, VP, log P and HLC with the data reported in the literature is rather good. The RMSE for the boiling point is 11.2 K which is higher than the RMSE for our reference data set. The RMSE of the vapor pressure is 0.23 which is in the acceptability range of the method. The deviation comes mainly from molecules with a very low volatility for which the experimental measurement of BP is not straightforward. The RMSE is equal to 0.32 for the log P and HLC which is a standard error. The correlation graphs between experimental and predicted values are given in Supporting Information (Figure S3). The vapor pressure, the Henry's law constant and the octanol-water partition coefficient are good descriptors to evaluate the group of scents. By plotting the logarithm of the vapor pressure versus the logarithm of the Henry's law constant and the logarithm of the octanol-water partition coefficient for each molecule, it turns out that this approach allows to clearly identify the group scents of molecules as shown in Figure 5.

As expected, the top notes correspond to molecules with high log HLC over the fragrance log Such an approach can be useful in understanding when new molecules perform during perfume application but also with which molecules it is possible to play in order to meet perfectly the technical specifications. Moreover, this approach can also be used to replace some problematic molecules (for safety and/or toxicity reasons) while the hedonic accords has to be kept. For instance, the substitution of Lilial has been one of the most investigated issue for the perfumery industry over the last past years. Armanino et al. [START_REF] Armanino | What's Hot, What's Not: The Trends of the Past 20 Years in the Chemistry of Odorants[END_REF] have proposed 17

P
molecules likely to substitute Lilial in the current perfume compositions (Table 3). All the substitutes have been selected thanks to their lily-of-the-valley smell. Some alternatives are direct derivatives of cyclamen aldehyde, and the difference is coming from the substitutions in ortho, meta or para of the aromatic group (2-8, 16, 17). Others were developed to be nonaromatic ingredients (9-11, 13,14). The propanal side chain is an important odor vector and the distance of the aldehyde osmophore to the bridgehead atom C 3 is kept. Finally, the aldehyde function has been replaced by alcohol (12, 15). Using the COSMO-RS method, we have determined their log P, VP and HLC (Table 3).

Even if all these molecules belong to the class of lily-of-the-valley odorants, some of them may not perform at the same time as Lilial does. Plotting the predicted properties (log HLC, log VP and log P) of Lilial substitutes clearly shows that only Hivernal 3, Josenol 15, Nympheal 16 and Mimosal 17 do not belong to the middle class as Lilial (Figure 6).

The positioning of the molecules from their physicochemical properties predicts a base note performance and may lead to change in the hedonic character of the perfume because Lilial is predicted as a middle note. Therefore, when using one of these molecules, it may be necessary to associate them with another compound to reach the same release as Lilial. For example, a composition containing both Hivernal and Lilyflore has been proposed to match the Lilial release. 46 According to the prediction, the other molecules should well perform to substitute the Lilial.

Conclusion

Five essential physicochemical properties for fragrance molecules, namely the boiling point BP, the octanol-water partition coefficient log P, the vapor pressure VP, the water-solubility WS and the Henry's law constant HLC, have been predicted using the COSMO-RS theory for a large data set of 161 molecules. Accurate predictions were obtained for most molecules for all these properties, with RMSE of 0.1-0.2 log units. Predictions were less accurate for molecules with low vapor pressure (< 0.001 bar) and high water-solubility (> 0.25 g/g H 2 O ).

Overall, it is clearly shown that the COSMO-RS approach is particularly well suited to fragrance molecules.

In addition, the determination of the note class of the compounds is well mapped either by plotting the vapor pressure versus the boiling point, or the Henry's law constant versus the octanol-water partition coefficient as it is illustrated with an oriental perfume. Thus, identifying the performance time for new captives can be essential to solve the current problematics in the perfumery industry. In particular, the replacement of compounds due to safety issues like Lilial without damaging the hedonic accords all along the lifetime of the fragrance is still under investigation despite the current proposal of alternatives. All the experiments are performed at 298.15 K. For the octanol-water partition prediction due to the partially miscibility of water in octanol, the octanol phase is a mixture of octanol/water at a molar fraction 0.726/0.274

  range and high VP (over 0.20 mbar), visually represented in blue. Base notes correspond to molecules with low log HLC and low VP (under 0.01 mbar), in brown. Middle notes are the group in-between the two other classes, identifiable by the orange color. Some molecules (2, 15, 20, 25, 29, 31) seem to not be perfectly mapped from their predicted properties due to their secondary class. Indeed, linalool oxide is a top note which can impact in a longer time scale which makes it also middle class. Conversely, phenyl acetaldehyde is a middle note impacting also the top note group by a strong rose smell at the beginning. Coumarin, caryophyllene and eugenol are three base note molecules with secondary impact in the middle class due to their high vapor pressure.

Table 1 .

 1 Experimental and predicted properties for 16 common fragrance molecules.[START_REF] Yaws | Yaws' Handbook of Thermodynamic and Physical Properties of Chemical Compounds[END_REF]

			Log HLC (bar)	Log Pow	Log VP (mbar)	BP (K)		Log WS (ppmv)
	Name	Chemical structure	Exp. 29	Pred.	Exp. 29	Pred.	Exp. 29	Pred.	Exp. 29	Pred.	Exp. 29	Pred.
	furfuryl alcohol		-1.65	-1.59	0.28	0.65	-0.06	-0.17	443.15	455.19	6.00	5.1
	benzyl alcohol		-1.84	-1.45	1.10	1.37	-0.95	-0.68	477.85	479.27	4.63	4.54
	2-phenylethanol		-0.80	-1.45	1.36	1.69	-0.94	-1.03	492.05	500.46	3.69	4.25
	pelargol		1.22	0.17	3.99	3.8	-0.56	-1.53	485.15	493.43	2.17	2.25
	furfural		-0.73	-1.24	0.41	0.19	0.46	0.2	434.85	464.79	4.90	5.05
	hexanal		1.29	1.12	1.78	1.87	1.18	1.14	401.45	404.73	3.75	3.76
	benzaldehyde		0.15	-0.18	1.48	1.41	0.24	0.14	451.90	466.09	3.82	4.09
	4-methyl-2-pentanone		0.88	0.6	1.31	1.25	1.38	1.39	389.65	391.86	4.28	4.52
	2-heptanone		0.87	0.56	1.98	1.93	0.73	0.65	424.05	427.57	3.63	3.88
	hexyl acetate		1.44	1.19	2.83	2.99	0.31	0.12	444.65	445.75	2.71	2.83
	ethyl butyrate		1.30	1.09	1.85	1.89	1.35	1.2	394.65	396.64	/	3.36
	ethyl benzoate		0.61	0.57	2.64	2.82	-0.43	-0.5	486.55	483.72	2.86	2.85
	vanillin		-3.37	-3.5	1.21	1.12	-3.48	-2.75	558.00	600.67	4.04	4.66
	indole		-1.47	-0.98	2.14	2.36	-1.76	-0.85	526.15	519.41	3.27	3.94
	anethole		0.74	1.17	3.39	3.63	-1.12	-0.84	508.45	501.56	2.05	1.9
	D-limonene		3.16	2.88	4.83	4.09	0.49	0.43	449.65	437.85	1.14	1.43
	RMSE		0.24		0.14		0.18		6.42		0.21
	Δ exp/calc		0.34		0.20		0.26		9.07		0.29

Table 3 .

 3 Calculated log P, log VP and log HLC of the fragrance molecules likely to substitute Lilial in perfume compositions.

	N°	molecule	log P	log VP (mbar) log HLC (bar)
	1	lilial	4.12	-2.52	-0.01
	2	bourgeonal	3.78	-2.50	-0.31
	3	hivernal	3.91	-2.88	-0.59
	4	cyclemax	3.44	-1.97	-0.15
	5	silvial	4.38	-2.49	0.28
	6	florhydral	3.78	-2.12	0.05
	7	mefloral	4.19	-2.36	0.24
	8	cyclamenaldehyde	3.96	-1.96	0.39
	9	tillenal	3.22	-1.27	0.21
	10	aquaflora	3.31	-1.53	0.03
	11	starfleur	4.57	-2.26	0.61
	12	lilyflore	3.16	-2.39	-1.37
	13	lilybelle	3.79	-1.99	0.09
	14	mugoxal	3.94	-2.32	-0.08
	15	josenol	2.88	-2.66	-1.91
	16	nympheal	4.26	-2.84	-0.17
	17	mimosal	3.59	-3.02	-0.95

Acknowledgments

The authors thank the company IFF for financial support by means of doctoral fellowship and Shyam Vias (IFF (R&D), Union Beach, NJ, USA) for the very useful discussions and comments on fragrances and COSMO-RS.

The authors have no conflict of interest in relation to this work.

Table 2. Experimental and COSMO-RS predicted boiling point (BP), vapor pressure (VP), octanol-water partition coefficient (log P) and Henry's law constant (HLC) of the 33 fragrance molecules constituting an oriental perfume. Experimental BP values were extracted from the Scifinder® database while experimental VP and logP were obtained from the Good Scents Company website, and HLC were found in the compilation of Sander.


Mauricio Díaz
email: mauricio.diaz@inrialpes.fr

Peter Sturm
email: peter.sturm@inrialpes.fr

Finding Images with Similar Lighting Conditions in Large Photo Collections

When we look at images taken from outdoor scenes, much of the information perceived is due to the ligthing conditions. In these scenes, the solar beams interact with the atmosphere and create a global illumination that determines the way we perceive objets in the world. Lately, exploration of the sky like the main illuminance component has began to be explored in Computer Vision. Some of these studies could be classified like color-based algorithms while some others fall in the physicsbased category. However most of them assume that the photometric and geometric camera parameters are constant, or at least, that they could be determined. This work presents a simple and effective method in order to find images with similar lighting conditions. This method is based on a Gaussian mixture model of sky pixels represented by a 3D histogram in the La * b * color space.

Introduction

Nowadays, the Internet has become an interactive system that allows anyone with a compact camera to share their visual experiences. This fact has been the starting point for large online image databases such as Flickr or Picasaweb. Computer vision scientists have not taken too much time to make use of these tools, and the development of new algorithms that exploit them is an activity in progress. Among these works, an excellent example is the PhotoTourism project [START_REF] Snavely | Modeling the world from internet photo collections[END_REF]. The main goal is to make a sparse 3D reconstruction of a popular monument from thousands of images using structure-from-motion type algorithms. Applications like that allow the user to explore unstructured photo collections.

The work presented in this article is also motivated by another kind of application that could exploit the richness of the photometric information available. For example in photomontage applications human intervention is often necessary to create realistic images. If one wants to insert an object from a photo into an environment determined in a second photo, both images should show up as if they had been taken under the same conditions. In that case, a human expert could retouch the images and force them to match illumination conditions and ⋆ Supported by the Programme Alβan, the European Union Programme of High Level Scholarships for Latin America, scholarship No. E07D402742CO.

shadows [START_REF] Agarwala | Interactive digital photomontage[END_REF][START_REF] Burt | Enhanced image capture through fusion[END_REF]. Our work is developed on the basis that we can exploit the above freely accessible collections and try to find a group of images that depict similar illumination conditions. In a general context, one of the most successful approximations to extract information about the illumination is to use a spherical object in such a way that it can reflect and capture the light distribution when the photo is taken [START_REF] Stumpfel | Direct hdr capture of the sun and sky[END_REF]. The main disadvantage of this method is that it requires access to the scene at the moment of the click. In his thesis [START_REF] Charles | Surface reflection model estimation from naturally illuminated image sequences[END_REF], Love did some observations that let us think that the sky is a very important illumination source and, as consequence, one of the essential factors involved in the color perception of outdoor scenes. Some other researchers have proposed to find the behavior of the sky illumination using only images for example, using physically-based models [START_REF] Lalonde | What does the sky tell us about the camera?[END_REF], or other ones using advanced techniques for color correlation [START_REF] Lalonde | SIGGRAPH 2007 26[END_REF][START_REF] Jacobs | Consistent temporal variations in many outdoor scenes[END_REF]. If one does not limit analysis to photos including sky portions, there are several works in the image completion context (hole filling or inpainting) [START_REF] Hays | Scene completion using millions of photographs[END_REF][START_REF] Wilczkowiak | Hole filling through photomontage[END_REF] and in the context of color classification using raw pixels [START_REF] Manduchi | Learning outdoor color classification[END_REF][START_REF] Sunkavalli | What do color changes reveal about an outdoor scene?[END_REF]. Some of the researchs that explore the sky as information source show restricted constraints, for example the use of a single camera or an a priori knowledge about the calibration (in the photometric and geometric sense). These constraints try to reduce the number of variables involved in the color perception process (surface reflectance, light sources, sensor response). For instance, the work of Lalonde et al. [START_REF] Lalonde | What does the sky tell us about the camera?[END_REF] proposes an algorithm to find similar sky images given the intrinsic camera parameters and a physicallybased sky model. The main idea consists in finding a sky model for each given image and to compare the features that define these models. This process can only be applied to images taken with a static camera, for example time lapse sequences. In [START_REF] Lalonde | SIGGRAPH 2007 26[END_REF], an automatic photomontage system that uses a presegmented object library is described. The method used by the authors to determine the global illumination matching consists of calculating the χ 2 distance between 3D-histograms that represent the sky. Short distances are recognized as possible matches. In our experiments, this metric presents a low performance due to the high dependance to the color workspace.

The present work aims to find the matches between sky zones of multiple images in a large image collection using minimum information about the camera parameters. For this, we propose the union and improvement of three stages previously developed in other contexts. The first one, a preamble stage that allows the sky pixels segmentation. A second stage where the pixels are represented by a sum of Gaussians in the La * b * space (section 2.1). Finally a third stage that compares the estimated models (section 2.2). The final part of this article (section 3) presents some results and discusses the algorithm proposed. In the literature, it is common to find physically-based models that express the sky luminance as a function of diverse variables, among them, sun position and atmospheric turbulence [START_REF] Igawa | Models of sky radiance distribution and sky luminance distribution[END_REF][START_REF] Perez | All-weather model for sky luminance distribution -preliminary configuration and validation[END_REF]. These models have been used in Computer Vision under some constraints, like a fixed point of view. In the present work the images are extracted from a large database and came from different cameras. This fact increases dramatically the problem complexity because we do not have any information about the geometry of the scene. Moreover, we do not know how the data captured by the sensors was modified during the acquisition process (most cameras apply post-processing algorithms to enhance the "perceptual quality" of the images). Our methodology is based on the camera's final output, a jpeg file, assuming that most of the time this image does not represent faithfully the real world illumination at the acquisition time. To accomplish the goal of this work, the first stage consists in extracting the sky pixels for each image. The application described in [START_REF] Hoiem | Geometric context from a single image[END_REF] allows us to make an automatic segmentation of the image sky.

Representation and Comparison of Sky Regions

To determine a model from sky pixels is a decisive step in the formulation of our problem. For that reason, the choice of the color space plays an important role. The CIE (Commission Internationale de l' Éclairage) [START_REF] Committee | Spatial distribution of daylight -luminance distributions of various reference skies[END_REF] have created several standards and nowadays, the last model published (CIECAM02) has reached an excellent performance as well as a high degree of complexity [START_REF]Colour appearance model for colour management applications[END_REF]. This color appereance model allows a trustworthy representation of the real world. However the parameters required are, in some cases, impossible to acquire. The La * b * space and the xyY space used by [START_REF] Lalonde | SIGGRAPH 2007 26[END_REF] and [START_REF] Lalonde | What does the sky tell us about the camera?[END_REF] are simpler models derived from the CIE's works. Although these color spaces are used in a vast number of works, it is important to take precautions when they are applied. For example, the spaces above mentioned are always attached to a predetermined "reference white", usually unknown. In this work we use the La * b * color space because of its good results in distinguishing color differences, but under the assumption that all the images were taken using a natural global illumination. That means that the "reference white" used in the transformation is the same for all images (Illuminant D65). Following the work done by Lalonde et al. [START_REF] Lalonde | SIGGRAPH 2007 26[END_REF], we build color histograms for the sky region in each image. These histograms are probability distributions of the colors in terms of the variables L, a * and b * . Figure 1 shows some of those histograms in their 3D space. Color and point size represent the bin magnitude 3 . One can note that the pixels are spread mainly on the negative part of the b * axis which corresponds to variations between yellow and blue. On the other hand, the histograms of images, where the sky is white and/or partially cloudy, are distributed throughout the space and they are not easily distinguishable using this representation. We believe that these histograms have different modes, and that they could be modeled using a mixture of Gaussians.

According to our observations, the sky in each image is modeled following the next equation:

M (x) = K k=1 π k N (x|µ k , Σ k ) , (1)
for an undetermined K (in our implementation we limit this value to 4). One well-known method to find the parameters in equation ( 1) is the Expectation- Maximization algorithm (EM) [START_REF] Bishop | Pattern recognition and machine learning (information science and statistics[END_REF]. The output of this method corresponds to the variables π k , µ k , Σ k that describe the model in such a way that the probability of the solution is maximized. Our model is formulated in terms of a joint probability distribution of the sky pixels X, the latent variables Z and the goal is to find the set of values θ that maximize the likelihood function (θ represents the variables π k , µ k and Σ k ). The values La * b * of the sky pixels x n are organized in the matrix X in which the n th row is given by x T n . In order to briefly summarize this algorithm, an iterative 2 step process runs until it reaches a convergence parameter. The E step calculates the joint probability distribution P (Z|X, θ last ):

P (Z|X, θ last ) = π k N (x n |µ k , Σ k ) K j=1 π j N (x n |µ j , Σ j )
, and the M step updates the values of π k , µ k , Σ k . The model dimension is a crucial factor. In our case, the number of Gaussians used in the mixture is determined based on the Akaike information criterion (AIC) [START_REF] Bishop | Pattern recognition and machine learning (information science and statistics[END_REF]. Different values of K in the equation ( 1) are evaluated and, the model that maximizes the likelihood is chosen. In figure 1, the ellipsoids that form the Gaussian Mixture model are shown for a constant variance.

Comparison between histograms of the sky

Once the sky model for each image is estimated, we proceed to compare different models. In the present case, it is necessary to measure the difference between two or more probability distributions. In our context, the well-known Kullback-Leibler divergence (KL) should be a good option, although it does not possess the property of symmetry. Given two probability distributions p(x) and q(x) the KL divergence is defined by:

KL(p||q) = -p(x)ln q(x) p(x) dx . ( 2
)
It is widely proven that when the distributions are Gaussian, equation ( 2) can be expressed in closed-form. However, in the case of a Gaussian mixture, it is difficult to find an analytically tractable expression or even more, a computer algorithm to solve this problem efficiently. According to the work of Hershey and Olsen [START_REF] Hershey | Approximating the kullback leibler divergence between gaussian mixture models[END_REF], the only method for estimating KL(p||q) with arbitrary accuracy when p(x) and q(x) are mixtures of Gaussians, is the Monte Carlo simulation. Nevertheless, other approximations may be valid, depending on the context. For example, a commonly used approximation is the simplification of the Gaussian mixtures p(x) and q(x) by simple Gaussians p(x) and q(x). In this case, the mean and covariance estimated are:

µ p = a π a µ a Σ p = a π a Σ a + (µ a -µ p)(µ a -µ p) T . (3)
The KL divergence (KL sim ) is calculated using the estimated mean (µ p) and variance (Σ p). Hershey and Olsen use variational methods to find a better approximation of the KL divergence. One of their contributions is a measure that satisfies the symmetry property but not the property of positivity. In this case, the approximated divergence KL app (p||q) is given by:

KL app (p||q) = a π a log a ′ π a ′ e -KL(p||p ′ ) b ω b e -KL(p||q) . (4)
This value could be seen as a measure of dissimilarity between two distributions. Hershey and Olsen's contribution allows us to compare two sky models keeping the variables for each Gaussian that composes the mixture.

Results

This section shows some results of the experiments developed using the models estimated and the comparison measure described in the last section. To test our method, we re-create a database with 4250 images of Sacre Coeur's Cathedral (Paris) downloaded from the Flickr website4 . Images that do not correspond to the desired scenes or are taken during the night or using artificial lighting had been removed. Our goal is to compare two or more outdoor images using the above methods applied on sky regions. To test our approach, we classified 500 images from the database by hand according to: sunny (si ), partially cloudy (pci ) and completely cloudy (cci ). It is important to emphasize the subjective nature of this "ground truth". The main idea consists in comparing the distances between one selected image and the other ones that belong to the same class (intra-class distance) and those belonging to other classes (inter-class distance). Figure 2 shows the intra-class and inter-class mean distances computed for 70 images from the class si using the KL sim divergence and the KL app divergence. For these two measures, we find that the class cci differs clearly from the other two by medium values of greater amplitude. However, among the class si and the class pci the difference is not sufficient when using the measure KL sim . As we may expect, the approximated KL app divergence shows a better performance and discrimination is easier. Table 1 presents the average of the inter and intra-class divergences for all images in the class si according to the two measures described. The difference between images belonging to classes si and cci is clearer when we use the KL app divergence. Once again, it can be explained by a better approximation of the KL divergence.

Another experiment was developed in order to find the success rate of the algorithm when running on 500 images using the KL app divergence. The objective this time is to find the closest images and whether or not they belong to the same class that the query image, according to the ground truth (see table 2). Figure 3 shows the four most similar images found for three query images.

Conclusions

In this paper, we proposed a 3-steps pipeline (segmentation, modelisation and comparison) for grouping outdoor images with similar lighting conditions, based on techniques previously developed. The model choosen for the sky pixles has been a mixture of Gaussian, based on the observations of histograms with multiple modes. This distribution allows us to accurately model the pixels, especially for images where the sky is not of uniform color. On the other hand, the computation of the KL divergence has proven to be an adequate tool to group similar skies, despite the approximations made in the operation. These approximations must be carefully chosen in order to keep the benefits of using a multimodal distribution as model. For a finer grouping, other factors may be considered such as the position of the sun, clouds, shadows or information about the camera parameters that could be extracted from the metadata. Also, to obtain credible photomontages, information about the geometry of the scene could be valuable. The inclusion of these variables might produce natural and realistic compositions.

2. 1

 1 Sky Model in the La * b * color space

Fig. 1 .

 1 Fig. 1. Sky 3D-histograms and ellipsoids for the corresponding MoG models. (a) Image with sunny sky, (b) completely cloudy sky, (c) partially cloudy sky. (d) Model with four Gaussians. (e) Model with two Gaussians. (f) Model with four Gaussians.

Fig. 2 .

 2 Fig. 2. Mean values for the intra-class and inter-class divergence, (a) using the KL simple divergence and (b) using the KLapp divergence.

Fig. 3 .

 3 Fig. 3. Subset of typical results. In the first column we observe the query image. The following columns from left to right, show the images closest to the query image.

Table 1 .

 1 Average of the inter and intra-class divergences for all images in the class si.

		Average KL simple Average KLapp
	si class	45.60	4.27
	pci class	351.63	97.87
	cci class	50.95	13.73

Table 2 .

 2 Success rate on 500 images.

	Images	1 st Image 2 nd Image 3 rd Image 4 th Image
	All	78.7%	75.4%	72.0%	71.2%
	Class cci	77.3%	74.6%	70.8%	68.7%
	Class si	64.0%	68.8%	64.8%	59.1%
	Class pci	93.2%	82.0%	79.9%	84.8%

For figures, the reader is kindly invited so see the electronic version.

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