Rony Abecidan
email: rony.abecidan@univ-lille.fr

Vincent Itier
email: vincent.itier@imt-nord-europe.fr

Jérémie Boulanger
email: jeremie.boulanger@univ-lille.fr

Patrick Bas
email: patrick.bas@cnrs.fr

Tomáš Pevný
email: pevnak@protonmail.ch

Leveraging Data Geometry to Mitigate CSM in Steganalysis

In operational scenarios, steganographers use sets of covers from various sensors and processing pipelines that differ significantly from those used by researchers to train steganalysis models. This leads to an inevitable performance gap when dealing with out-of-distribution covers, commonly referred to as Cover Source Mismatch (CSM). In this study, we consider the scenario where test images are processed using the same pipeline. However, knowledge regarding both the labels and the balance between cover and stego is missing. Our objective is to identify a training dataset that allows for maximum generalization to our target. By exploring a grid of processing pipelines fostering CSM, we discovered a geometrical metric based on the chordal distance between subspaces spanned by DCTr features, that exhibits high correlation with operational regret while being not affected by the cover-stego balance. Our contribution lies in the development of a strategy that enables the selection or derivation of customized training datasets, enhancing the overall generalization performance for a given target. Experimental validation highlights that our geometry-based optimization strategy outperforms traditional atomistic methods given reasonable assumptions.

I. INTRODUCTION

Cover-source mismatch, also known as CSM, is a widely recognized phenomenon in modern steganalysis [START_REF] Giboulot | Effects and Solutions of Cover-Source Mismatch in Image Steganalysis[END_REF] [2] [START_REF] Kodovský | Study of cover source mismatch in steganalysis and ways to mitigate its impact[END_REF]. Traditional steganalysis models are typically trained on controlled cover distributions obtained from standardized databases like BOSSBASE [START_REF] Bas | Break Our Steganographic System": The Ins and Outs of Organizing BOSS[END_REF] or ALASKABASE [START_REF] Cogranne | The ALASKA Steganalysis Challenge: A First Step Towards Steganalysis "Into The Wild[END_REF]. However, in practical steganalysis scenarios, pinpointing the exact distributions to which the target images belong is quite challenging. The cover distributions, often referred to as cover sources, exhibit significant diversity due to various factors inherent to the image acquisition process. These factors include the sensor quality, device settings, captured content characteristics, post-processing techniques applied, as well as the subsequent compression steps. These various stages of WIFS'2023, December, 4-7, 2023, Nuremberg, Germany. XXX-X-XXXX-XXXX-X/XX/$XX.00 ©2021 IEEE.

image development encompass a range of transformations, each influenced by specific parameters that affect the statistical properties of the resulting covers to any potential steganographic embedding.

A. Mitigating CSM: Prior Arts

It is shown in [START_REF] Giboulot | Effects and Solutions of Cover-Source Mismatch in Image Steganalysis[END_REF] that the processing pipeline is the cornerstone of the CSM, this pipeline encompasses a series of transformations commonly employed for aesthetic enhancement and compression purposes. However, in the domain of steganalysis, these transformations have a deep impact on the distribution of noise while maintaining the semantic integrity of the content. Despite the effectiveness of machine learning techniques in steganalysis, they often exhibit a high degree of sensitivity to the unique characteristics of the analyzed signals, thus giving rise to CSM, which can be seen in machine learning as a generalization problem.

To mitigate this issue, several approaches have been developed in the literature. In an ideal scenario, steganalysts would have access to cover distributions close to the ones of the images to scrutinize, enabling the creation of a specialized set of classifiers trained on these specific sources. For example when the CSM is only due to the JPEG quantization matrix or the camera model, Kodovský et al. [START_REF] Kodovský | Study of cover source mismatch in steganalysis and ways to mitigate its impact[END_REF] suggest choosing the classifier trained on the closest distribution w.r.t. the test images. They also suggest performing steganalysis on each evaluation image separately using the classifier trained on cover source that is most similar to that particular image. Various measures of source similarity are explored in this paper, and the most effective approach involved using a simple 2 norm to compare the centers of gravity of the sources. Another approach presented in the literature by Pasquet et al. [START_REF] Pasquet | Steganalysis with coversource mismatch and a small learning database[END_REF] involves the extraction of K clusters called islets from a mixture of different sources and the training of K specific ensemble classifiers. In a similar vein, Giboulot et al. [START_REF] Giboulot | Effects and Solutions of Cover-Source Mismatch in Image Steganalysis[END_REF] uses a multilinear classifier to assign the specific detector to be used for each evaluation image.

In our recent study [START_REF] Abecidan | Using set covering to generate databases for holistic steganalysis[END_REF], we report important conclusions regarding cover-source mismatch for various development parameters. Firstly, we highlighted the fact that denoising, downsampling, and post-resize sharpening play a significant role in the occurrence of CSM. Secondly, we observed that certain cover sources enable to build detectors that generalize more effectively than others. However, to the best of our knowledge, there is currently no existing work that comprehensively explores the relevance of specific sources in relation to particular targets.

B. Contributions

We propose an in-depth exploration of a grid of processing pipelines, focusing on our three parameters of interest, i.e. denoising, downsampling, and post-resize sharpening. Our aim motivation is to understand how we can derive relevant training sets for operational steganalysis. To ensure realism, we consider a scenario in which the distribution of the covers under scrutiny is unknown. We assume access to an unlabeled set of target images with an unknown proportion of cover or stego images. Then, our goal is two-fold:

• Learn how to identify the most relevant training database compared to some others in relation to a given target. • Develop a general strategy to build an appropriate training database for this target. Motivated by these considerations, this paper represents the first attempt to address the CSM issue by proposing a framework for automatically generating appropriate steganalysis databases. Our work proposes the following contributions:

• We demonstrate that the geometrical properties of the target distribution plays a crucial role in identifying irrelevant sources that do not generalize well on target distributions. • We present a simple yet efficient optimization algorithm for constructing relevant sources for specific targets. This algorithm leverages a geometry-based metric, the chordal distance, that evaluates the orthogonality between a source and a target. The structure of the paper is as follows: Section II presents the formalization of our objective and introduces the manifold hypothesis that is core of the subsequent analysis. In Section III, a series of experiments are conducted to gain a deeper understanding of the components that contribute to an appropriate generalization from the source to the target. In Section IV, a fresh perspective is presented to devise an optimization scheme that yields a target-specific relevant source leveraging a geometrical metric with interesting properties. The effectiveness of this novel approach is compared to conventional methods documented in prior literature. Lastly, Section V serves as the conclusion, summarizing the main findings and contributions of this research.

II. FORMALIZATION

A. Problem formulation

In accordance with [START_REF] Šepák | Formalizing cover-source mismatch as a robust optimization[END_REF], we define a processing pipeline as a vector ω ∈ Ω that encompasses all the parameters associated with the pipeline, such as the downsampling, the denoising coefficient, the JPEG quality factor, and more. In the context of steganalysis, we introduce an additional parameter γ to represent steganographer choices, including the embedding strategy and payload. For this particular task, machine learning models, acting as detectors are commonly used:

f (x | θ ω,γ ) : X → {cover, stego}.
x → y Here, θ ω,γ ∈ Θ represents the learned parameters using covers derived from the pipeline ω and potentially embedded following γ.

To effectively evaluate the CSM, two significant metrics have been introduced in [START_REF] Giboulot | Effects and Solutions of Cover-Source Mismatch in Image Steganalysis[END_REF] and [START_REF] Šepák | Formalizing cover-source mismatch as a robust optimization[END_REF]:

• The Intrinsic Difficulty of a source, quantified as the probability of error P E obtained after training on images from this source and evaluating on images from that same source:

E (x,y)∼P ((x,y)|ω,γ) (f (x | θ ω,γ ) = y). (1)
• The Regret between a source s and a target t, denoted as R s,t ≥ 0, or alternatively referred to as Source Inconsistency in [START_REF] Giboulot | Effects and Solutions of Cover-Source Mismatch in Image Steganalysis[END_REF], defined as the difference between the P E we obtain by training on s and evaluating on t and the Intrinsic Difficulty of t:

E (x,y)∼P ((x,y)|ωt,γ) (f (x | θ ωs,γ ) = y), -E (x,y)∼P ((x,y)|ωt,γ) (f (x | θ ωt,γ ) = y).
(

) 2
In this study, we assume that we have access to target samples coming from an unknown distribution. It is important to note that the cover-stego balance, i.e. the balance between the covers and the stegos is also unknown, i.e. that the CSM has to be solved in an unsupervised setting. Ideally, we want to find a source s that minimizes the regret with our target t. However, since computing the regret in this scenario is infeasible, the best we could aim is the use of a metric m correlated to the regret, computable without labels, and invariant to the cover-stego balance. Such a metric can be used as a benchmark for identifying and even creating the most effective source for our target dataset.

B. The manifold assumption

Traditionally in machine learning, specific features of interest are used to represent the images that are living in very high dimension. As an example for steganalysis, the famous feature extractor DCTr [START_REF] Holub | Low-complexity features for jpeg steganalysis using undecimated dct[END_REF] enables the extraction of 8000 relevant features for each image to steganalyze. However, dimension representing images coming from the same source belong to a manifold of significantly lower dimensionality than 8000 [START_REF] Bengio | Representation learning: A review and new perspectives[END_REF]. Intuitively, the manifold underlying the source should be invariant to the cover-stego balance given a reasonable payload that does not move too far the stegos from the covers. In what follows, we provide empirical support for the importance of estimating the manifold supporting the target. By using PCA, one can approximate it as a linear space. This estimation yields valuable geometrical information that elucidates the observed mismatch with particular sources.

III. UNDERSTANDING SOURCE RELEVANCE A. Experimental protocol

In [START_REF] Abecidan | Using set covering to generate databases for holistic steganalysis[END_REF], three operations promoting noise and content diversity were identified as important factors leading to CSM: denoising, downsampling and post-resize sharpening. In this study, we propose to investigate the factors that make a source more relevant than another for a specific target by creating a universe of sources obtained by developing RAW Images, leveraging these three parameters of interest.

For the experiments presented here, we randomly extract 2000 RAW Images of various sizes from the ALASKA dataset [START_REF] Cogranne | The ALASKA Steganalysis Challenge: A First Step Towards Steganalysis "Into The Wild[END_REF]. Among these, 1000 RAW Images are dedicated to the source and the remaining are for the target. Out of the target images, 500 RAWs will be used to create operational sets, representing real-life scenarios where there are no pairs of covers and stegos, no labels, and no knowledge of the cover-stego balance. We will consider three balancing for this set: only covers, only stegos or an equal proportion of cover and stegos. The remaining 500 RAWs from the target will be used to generate samples dedicated to evaluation and to the computation of the regret, i.e. with equal numbers of cover and stego images.

The impact of JPEG compression on steganalysis is already well-documented in the literature [START_REF] Giboulot | Effects and Solutions of Cover-Source Mismatch in Image Steganalysis[END_REF]. In our experiments, we propose to apply a JPEG compression with a quality factor of 85 at the end of our processing pipelines. This choice facilitates the estimation of the manifolds underlying the sources, considering our limited sample size. We perform this final JPEG compression using Imagemagick 1 for full control over the compression process. 1

imagemagick.org

In total, we study 10 3 combinations of parameters to explore a wide range of possibilities. It is important to note that we do not use a random cropping strategy as it often leads to low-textured covers in practice. Instead, we prefer the "smart" cropping technique released in the ALASKA2 Challenge [START_REF] Cogranne | The ALASKA Steganalysis Challenge: A First Step Towards Steganalysis "Into The Wild[END_REF], which aims to select crops with highly textured areas. Details about the cover generation process are presented in Fig. 1.

Starting with the 1000 source RAWs, we create 1000 pairs of cover-stegos for training. The evaluation is performed using the 500 cover-stego pairs derived from the RAWs dedicated to evaluation. The embedding is done using UERD [START_REF] Guo | Using statistical image model for jpeg steganography: Uniform embedding revisited[END_REF] with a payload of 0.5 bpnzac. To simplify the process and save computational resources, we then train linear classifiers using DCTR features [START_REF] Holub | Low-complexity features for jpeg steganalysis using undecimated dct[END_REF] from our sets of covers and stegos. This payload allows us to obtain cover sources with a reasonable Intrinsic Difficulty, ranging from 11% to 30%.

Once the cover distributions are generated, and the detectors are trained on each of them, we study CSM using a regret matrix R, where R[s, t] = R s,t and s, t ∈ [|1, 10 3 |] 2 indice all possible 10 3 generated bases whereas there are seen as source or target. We then analyze the correlation between the regrets observed and some potential metrics we picked. Quantile plots help us visualize how the regret distribution evolves within a sliding window around different values of our metrics. We scale the metrics by dividing them by their maximum value to make them comparable. For each metric, we use points from 0 to 1 with a step of 0.01 and a window size of 0.3, which balances the tradeoff between localization and estimation accuracy.

We list below the three different metrics we used in this paper. The two first come from the litterature and the last one is new.

B. 2 between Centers of Gravity

To evaluate if the source and the target are mismatching, [START_REF] Kodovský | Study of cover source mismatch in steganalysis and ways to mitigate its impact[END_REF] recommends computing the 2 norms between their centers of gravity, 2 CG . This is a very appealing strategy, cheap to execute and easily explainable. However we expect its success to be highly dependent of the cover-stego balancing. For three operational target scenarios: only covers, only stegos, or a balanced proportion of both, we compute the 2 CG between the sources and operational targets in our universe. The 2 CG is comparable for the scenarios with one class, but it is changing significantly when we consider the two classes scenario. This makes sense as the center of gravity should not change much when we switch from using only covers to using only stegos as the operational target. However, a mix of cover and stego leads to a different gravity center than this common one. Fig. 2. Quantile plots representing the evolution of the regret according to the 2 CG between sources and operational targets (dependent of the classbalancing). Q1 is the first quartile, Q3 is the third quartile and Q(90%) is the 90th percentile.

We present in Fig. 2 a quantile plot illustrating the evolution of the regrets in our universe according to the 2 CG between source and operational gravity centers. There is a clear correlation between the 2 CG and the regret. High 2 CG leads to high regrets while low 2 CG leads to low regrets. However, the regrets variance is non-negligeable and a low 2 CG does not ensure a low regret.

C. Maximum Mean Discrepancy

As a second proxy to the regret, we propose considering a distance between distributions. One well-known metric in the literature is the maximum mean discrepancy (MMD). This metric is essentially an L 2 distance in a Hilbert space implicitly defined with a kernel function k(x, y) : R d ×R d → R with real features of dimension d. The MMD is highly relevant in estimating the discrepancy between two distributions, but its effectiveness relies on its association with a characteristic kernel that complies with specific properties. When these properties are met, the metric is minimized if and only if the two distributions are identical. One compelling aspect of this metric is its simplicity and efficiency in estimation, requiring only a few samples from the distributions. For practitioners seeking a reliable and robust baseline, Feydy et al. [START_REF] Feydy | Geometric data analysis, beyond convolutions[END_REF] recommend using the Energy Distance kernel:

k(x, y) = -x -y .
This well-known kernel in statistics produces appealing monotonic flows without the need for any parameter tuning. We can easily exploit it using the geomloss library [START_REF] Feydy | Interpolating between optimal transport and mmd using sinkhorn divergences[END_REF]. We measure the MMD between each source-target pair in our universe, using again our three scenarios for the operational balancing. After the measurement, we find no significant difference of the MMD between each scenario. In Fig. 3, we discover that the MMD is also well correlated to the regrets. However, the regret variance near the lowest values of the MMD is higher than the ones seen near the lowest values of the 2 CG . More clearly here, a low MMD does not imply a low regret.

D. Assessing orthogonality between sources

As the detector relies on the manifold supported by the source, any significant difference between the target and source manifolds can lead to a noticeable regret. This is the case when the two manifolds are not aligned.

Using the minimal angles between two orthogonal bases, namely principal angles, one can derive several metrics assessing misalignment between the two subspaces they span [START_REF] Knyazev | Principal angles between subspaces in an a-based scalar product: Algorithms and perturbation estimates[END_REF]. Considering two subspaces of different dimension N and K, and the principal min(N, K) angles θ i between those planes, we can then define the normalized squared chordal distance NSCD [START_REF] Ye | Schubert varieties and distances between subspaces of different dimensions[END_REF]:

NSCD = min(N,K) i=1 sin 2 (θ i ) min(N, K)
.

When NSCD = 0 the two subspaces are equal while, when NSCD = 1, the two subspaces are orthogonal.

For our experiments, we estimate the manifolds as the linear subspaces spanned by the orthogonal eigenvectors enabling to preserve 99.9% of the variance computed through PCA (thus the dimension of subspace is not fixed). It is worth noting that this decision involves a careful tradeoff between dimensionality reduction and capturing sufficient variance to explain operational regrets. Afterwards, we compute the NSCD between every combination of source and target within our universe, taking again into account our three scenarios for the cover-stego balance. As one could expect, there is no significant difference of the NSCD w.r.t. the balance since the manifolds are not strongly modified after embedding. We observe in Fig. 4 that there is a strong correlation between the NSCD and the operational regret in our universe. This time, the regret variance around the lowest values of the NSCD is pretty low. It appears to be the best proxy for the regret and clarifies well why a source is more suitable than other for a given target.

IV. MITIGATING CSM WITH THE CHORDAL DISTANCE

A. Comparison with classical atomistic strategies

We propose here to compare the operational regrets obtained for each target of our universe given different strategies :

• Using a relevant source for each target image with the help of a multi-classifier trained to recognize the most representatives sources of our universe. • Applying a majority vote to choose one relevant source for the target among the most representatives ones. • Selecting the source that minimizes the 2 CG distance w.r.t. the operational set.

• Selecting the source that minimizes the MMD w.r.t. the operational set. • Selecting the source that minimizes the NSCD w.r.t. the operational set. Instead of using 10 3 sources for the majority vote and the multi-classifier, which would severely degrade the performances due to a high number of candidates, we use our methodology from [START_REF] Abecidan | Using set covering to generate databases for holistic steganalysis[END_REF] to extract a small subset of representatives sources that can achieve less than 5% regret for all targets. In practice, this enables to work on only 8 sources in terms of generalization. Focusing on only these sources, the efficiency of these strategies is preserved while minimizing space and computation demands. Moreover, because there exist sources that are very close to each other, we want to evaluate our metric-based methods only on pairs of source/target which are enough different from each other. To address the bias induced by evalution on too close pairs we remove candidates if their MMD is below the 1st decile Q(10%) of the MMD distribution that is invariant to operational balancing. This is done for the 3 last strategies to make a fair comparison. The two first strategies use representatives to select sources and are immune to this bias. Moreover, in our evaluations the sources will always have an equal proportion of cover and stego meanwhile the operational set will present different balancing.

We present, in Table I, the statistical information relative to the distribution of regrets obtained following the different strategies. Concerning the two first strategies, the majority vote is less satisfying compared to the others meanwhile the multi-classifier is among the best in terms of efficiency and invariance to the operational balancing. However, this particular strategy cruelly lacks of interpretability.

On the other side, due to the invariance to cover stego balancing from the MMD and the NSCD, it is not surprising to see very similar regret distributions in the 3 cases. The strategy using the 2 -norm is simple and already reasonable in many of the cases. However, its effectiveness depends on the cover stego balance. In the case where the operational target is made up of an equal proportion of covers and stegos, there is about 20% of regrets observed higher than 5% using this strategy whereas this lowers to 9% with the MMD and 2% with the NSCD. It is worth mentioning that theoretically, there are situations where the NSCD is very low and the regret is high. One such example is when the target stems from a significant shift in the source manifold. Curiously, such cases are not present in our experiments.

B. Geometry-based optimization

Since the NSCD exhibits a high correlation with the regret, we suggest leveraging it as a valuable tool for data-adaptation. The methodology involves starting with a set of RAW images, performing image development operations, computing the NSCD in relation to the target, and repeating the development to minimize the NSCD as much as possible. To optimize the selection of development parameters, we propose employing well-established heuristics such as simulated annealing. By testing this straightforward concept in our universe, specifically focusing on the most challenging scenarios where regrets are higher than 20%, we observe satisfying results presented in Table II. Out of the 30,000 cases studied, 88% of the regrets obtained at the end of the optimization are below 5%, with a maximum iteration count of 100. These experiments clearly indicate the superiority of this strategy over the previous method, which required the creation of 10 3 sources.

C. Impact of the target size

With a very limited amount of target samples, the NSCD is not well estimated and leads to wrong source selections as shown in Table III. For instance, we observe that NSCD is not anymore invariant to operational balancing and much less useful when the amount of target samples is equal to 10. Speaking more generally, we observed through several experiments that when the noise level in the target rises, approximating the manifold becomes more challenging and a larger number of samples is required to achieve accurate estimation of the NSCD. Here, we observe still an acceptable performance with 100 samples (with only 4.6% regrets higher than 5%).

V. CONCLUSIONS AND PERSPECTIVES

In this paper, we explore a universe of sources derived from processing pipelines, focusing on denoising, downsampling, and post-resize sharpening parameters, with the primary aim of understanding what makes some sources more relevant than others in operational steganalysis. In our scenario, the cover distribution of target images is unknown and the steganalyst is unaware of the proportion of covers and stegos. The main goal is to develop a general strategy for designing training databases tailored to specific targets which may have different distributions but allow us to minimize the regret. We show that the geometrical properties of the target play a key role in identifying relevant and irrelevant sources that respectively do or do not help to generalize well on target distributions. To this end, we present the NSCD, a metric assessing the orthogonality between subspace spanned by source and target DCTr features. Our optimization algorithm, which uses the NSCD proved to be efficient in guiding source selection.

Looking ahead, we want to explore whether the NSCD can be used to generalize on images from entirely unknown distributions, such as those obtained from platforms like Flickr. Moreover, combining the metrics exhibited here to create a promising new composite metric could yield even more powerful results. At last, our ongoing research investigates whether NSCD can help to identify optimal sources with state-of-theart deep neural networks for steganalysis. Encouraging results support further investigation. In conclusion, this paper serves as an initial step toward database adaptation for steganalysis, i.e. generating automatically tailored steganalysis sources for operational targets.

Fig. 1 .

 1 Fig. 1. Generation of 10 3 pipelines. Note that the different scaling factors are only due to crops of different sizes.

Fig. 3 .

 3 Fig.3. Quantile plots representing the evolution of the regret according to the MMD between sources and operational targets (dependent of the classbalancing). Q1 is the first quartile, Q3 is the third quartile and Q(90%) is the 90th percentile.

Fig. 4 .

 4 Fig.[START_REF] Bas | Break Our Steganographic System": The Ins and Outs of Organizing BOSS[END_REF]. Quantile plots representing the evolution of the regret according to NSCD (invariant by balancing). Q1 is the first quartile, Q3 is the third quartile and Q(90%) is the 90th percentile.

TABLE I INFORMATION

 I ABOUT REGRET DISTRIBUTIONS OBTAINED AFTER APPLYING DIFFERENT ATOMISTIC STRATEGIES IN OUR UNIVERSE OF 10 3 PIPELINES. %(R > 5) IS THE RATIO OF REGRETS HIGHER THAN 5% COMPUTED FOR ALL TARGETS FOR EACH STRATEGY (ALL RESULTS ARE IN %)

TABLE III INFORMATION

 III ABOUT THE REGRET DISTRIBUTIONS OBTAINED SELECTING THE SOURCE MINIMIZING THE NSCD ACCORDING TO THE NUMBER OF OPERATIONAL SAMPLES AVAILABLE. THE COLUMN MAX IS FOR THE MAXIMUM REGRET OBSERVED ACCORDING TO EACH CASE.

		Only Covers	Only Stegos		Mix
	N samples	Max	%(R>5)	Max	%(R>5)	Max	%(R>5)
	10	27	45%	27	44%	24	23.8%
	100	16	2.7%	16	2.5%	16	4.6%
	500	16	1.6%	16	1.5%	16	2%

ACKNOWLEDGMENTS

Our experiments were possible thanks to computing means of IDRIS through the resource allocation 2022-AD011013285R1 assigned by GENCI. This work received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 101021687 (project "UNCOVER") and the French Defense & Innovation Agency. The work of Tomas Pevny was supported by Czech Ministry of Education 19-29680L.


M Duncianu

Véronique Riffault

Alexandre Tomas

Validation of a new

come

Validation of a new flow-reactor for the study of secondary organic aerosol (SOA) formation

M. Duncianu*(1,2), V. Riffault (1,2), A. Tomas (1,2), P. Coddeville (1,2)

(1) Université Lille Nord de France, F-59000, Lille, France (2) Ecole des Mines de Douai, Département Chimie et Environnement, 941 rue Charles Bourseul, BP 10838, 59508 Douai cedex, France duncianu@ensm-douai.fr

Aromatic and biogenic compounds known to be relatively abundant in the atmosphere are usually easily oxidized by common tropospheric species (OH, O3, NO3), which contributes significantly to the formation of low vapor pressure products, considered as the main precursors of SOA. In order to improve the understanding of SOA formation mechanisms, a new flow reactor has been developed in our laboratory to study the early stages of particle formation.

The controlled flows of ozone and volatile organic compound enable stable concentrations in the reactor and provide a steady state of the reaction in the reactor and the conditions for pseudo-first order kinetics. By changing either the flow or the distance between the injector head and the sampling point, the concentrations at different reaction times can be measured, thus allowing deducing mechanistic and kinetic parameters.

The exhaust lines are used for collecting gaseous (on adsorbent cartridges subsequently analyzed by TD-GC/FID/MS) and particulate samples (number and size distribution of particles formed using a SMPS, average composition of the particles with an AMS). Using these various instrumental techniques combined with gas chromatographic analyses will permit the determination of the kinetics and the influence of various physical parameters on the chemical mechanisms of SOA formation. The ozonolysis of a series of unsaturated alkenes (methylated pentenes) was chosen for kinetic validation, while the α-pinene, already well documented in the literature was chosen to validate the system and the analytical chain for both kinetic and particulate phase measurements. Results are presented and compared with those of the literature.

Experimental setup

The cylindrical reactor developed in the laboratory has been designed to work with total flows of about 1 to 3 L min -1 , corresponding to reactions times between 10 s and several minutes. A mobile injector is used to introduce the reagents separately and ensure their rapid mixing into the Pyrex tube with a 1-m length and a 10-cm i.d. section, in a laminar flow regime at atmospheric pressure and room temperature.

The injection head has been designed to allow good mixing of the reactive gases at transit times of seconds and to support the formation of a laminar flow into the reactor. To this end, the volume of the gas mixing chamber of the injection head was minimized by filling it with glass beads (diameter 2 mm).

The laminar flow in the reactor ensures a stationary mode. The volume of the flow reactor may vary depending on the position of the sliding injection head, in order to watch the evolution of the reagents and products at various reaction times, and to estimate kinetic and mechanistic parameters. Considering a fixed distance between the movable injection head and the sampling point, different reaction times may be achieved by changing the flow rate of the reactants in the reactor.

A canister containing tens of ppm of volatile organic compound (VOC) is used for the generation of a continuous gas flow with the help of a mass flow controller (MFC). The zero air is used as a carrier gas towards the injection head and also ensures the dilution of VOC at the requested level of concentration (Figure 1). A controlled flow of carbon monoxide is also added into the mixture of gasses as a scavenger of the OH radicals potentially formed in the ozonolysis processes. An ozone generator provides a controlled flow of oxidant (7.4 × 10 12 to 4.4 × 10 13 molecule cm -3 , ensuring pseudo-first order kinetic conditions) which reaches the injection head on a separate line. The outlet analytical chain of the reactor includes an AMS (Aerosol Mass Spectrometer), on the same sampling line with a SMPS (Scanning Mobility Particle Sizer) to analysze the particulate phase, and cartridges filled with three different adsorbents for the subsequent analysis of the gas phase. The AMS measures in real time the average chemical composition of aerosols as a function of their size. The SMPS is used to obtain complementary information concerning the size distribution of particles by coupling a differential mobility analyzer (DMA) and a condensation particle counter (CPC). The sampling strategy for the gas phase involves the exposure of a single cartridge at a time and the procedure is repeated in identical experimental conditions at least three times in order to estimate the concentration of compounds, but also the reproducibility and accuracy of sampling. Ozone traps (scrubbers) consisting of a dry coating of KI on the walls of a copper tube are used upstream of the cartridge sampling in order to prevent additional degradation processes of the VOCs by ozone during sampling and thermal desorption. An O3 analyzer monitors O3 levels in the reactor as well as the efficiency of the scrubber. Sampled cartridges are thermodesorbed and analyzed by gas chromatography coupled with mass spectrometry. Thermodesorption techniques were preferred over techniques requiring sample pretreatment. To optimize the analytical method in terms of detection sensitivity and result reproducibility, the glass insert of the chromatograph, where the thermodesorbed compounds are trapped prior to injection into the column, was tested in two different configurations: empty, in cryogenic conditions (-100 °C) and filled with a few mg of Carbopack B at a temperature of 0°C. By comparing the results of the ozonolysis of alphapinene (3.1 × 10 12 molecule cm -3 ) in both configurations, there is an increase of detection sensitivity, reproducibility and linearity in the case of the filled insert. Moreover, the rate coefficient obtained for the ozonolysis reaction, k = 1.1 × 10 -16 cm 3 molecule -1 s -1 , is closer to the recommended value than in the case of the cryogenic configuration, k = 1.7 × 10 -16 cm 3 molecule -1 s -1 with the empty insert.

Kinetic study of VOC ozonolysis

Considering VOC ozonolysis in pseudo first order reaction conditions, where [O3] >> [VOC], the integrated rate law can be written as:

0 t [VOC] ln k't [VOC]        (1)
According to this relation, the graph of the logarithm of the ratio between the initial concentration in VOC, [VOC]0, and at time t [VOC]t, as a function of the reaction time t, gives a slope k '= k [O3] (Figure 2). The obtained slope gives the value of the rate coefficient knowing the concentration of ozone in the reactor.

Ozonolysis of methylated pentenes

In order to validate the analytical chain and the kinetic measurements performed in the reactor, the ozonolysis of a series of unsaturated alkenes (methylated pentenes) was chosen.

The ozonolysis reactions of 2,4,4-trimethyl-1-pentene (tM1P) and 2,4,4-trimethyl-2-pentene (tM2P) have been studied in excess of O3.

The experimental results give the value of the rate coefficients considering an average concentration of ozone in the reactor of 1.8 × 10 13 molecule cm -3 as obtained from a large number of measurements using a calibrated ozone analyzer. Given the experimental conditions a value of k = 1.35 × 10 -16 cm 3 molecule -1 s -1 was calculated for the reaction of tM1P with ozone, while the similar reaction of tM2P present a higher reactivity with a determined value of k = 2.11 × 10 -16 cm 3 molecule -1 s -1 (Figure 2). These results need to be completed with the same kinetic approach at different initial concentrations in reagents. These preliminary results are in good agreement with the literature in the case of tM2P (k = 1.39 × 10 -16 cm 3 molecule -1 s -1 , [START_REF] Grosjean | Rate constants for the gas-phase reaction of ozone with 1,1disubstituted alkenes[END_REF], while for tM1P a significant difference can be observed, compared with the literature (k = 9.73 × 10 -18 cm 3 molecule -1 s -1 , Leather, 2010).

Ozonolysis of alpha-pinene

The ozonolysis of alpha-pinene is an important source of oxidized species, which contribute significantly to the atmospheric formation of SOA and its reaction rate coefficient has been estimated by many previous studies. The ozonolysis of alpha-pinene was carried out in the reactor at ambient temperature in dry air (RH ~ 0%). With the same experimental setup and for [O3] = 3.4 × 10 13 molecule cm -3 , a value of k = 1.1 × 10 -16 cm 3 molecule -1 s -1 for the rate coefficient of the reaction, in good agreement with those in the literature (e.g. k = 9.0 × 10 -17 cm 3 molecule -1 s -1 , Tillmann 2009) was determined (Figure 3).

Number / size standard distribution of aerosols

The distribution of aerosols generated in the ozonolysis of alpha-pinene was monitored as a function of reaction time using the SMPS.

The aerosol sampling was conducted using the central sampling tube of the flow reactor. The observed distribution of the particles formed after the nucleation processes is unimodal, fairly broad, and centered around 90 nm. It seems little influenced by the different reaction times ranging from 1.5 to 6 minutes. This suggests that during this period there is only one mode of particle formation and the processes of nucleation / coagulation are dominant. Further experiments are needed to confirm these results. It is planned to study the influence of some physicochemical parameters such as humidity on the particle formation, or the influence of preexisting aerosols into the reactor.

Finally, analyses using the AMS will allow to study the chemical composition of the formed aerosols. Connected to the same sampling line as the SMPS, it will provide complementary information on particle characterization (size distribution and chemical composition).

2.0x10

Figure 1 .

 1 Figure 1. Schematic of the experimental setup

Figure 2 .

 2 Figure 2. Kinetics of tM1P and tM2P ozonolysis -[tM1P]0 = 7.6 × 10 11 molecule cm -3 , [tM2P]0 = 7.6 × 10 11 molecule cm -3

Figure 3 .

 3 Figure 3. Kinetics of ozonolysis of alpha-pinene -[VOC]0 = 3.1 × 10 12 molecule cm -3

Figure 4

 4 Figure 4. dN/dln(dp) (cm -3 ) as a function of particle diameter for different reaction times in the ozonolysis of alpha-pinene

Acknowledgements

Our laboratory participates in the Research Institute of Industrial Environment (IRENI) which is financed by the Communauté Urbaine de Dunkerque, the Nord-Pas de Calais Regional Council, the French Ministry of Education and Research, and European funds (FEDER).


Sylvain BELLUC Université de Nîmes (EMMA), France

The Sense of a Meaning: A Portrait of the Artist as a Young Man and the Rise of Semantics As a Künstlerroman, A Portrait of the Artist as a Young Man charts Stephen's gradual discovery of his artistic calling, a discovery which eventually crystallises in his wish to become "a priest of the eternal imagination, transmuting the daily bread of experience into the radiant body of everliving life." Stephen's slow realisation of his vocation, however, goes hand in hand with his evolving approach to the medium used for that transmutation, namely language. Interestingly, the latter decades of the nineteenth century, which is the period in which the action of Joyce's semi-autobiographical novel is set, saw huge advances made and new directions taken in the field of language study. It is not surprising, therefore, that just as Stephen fashions his political ideas as a response to the competing discourses which echo around him on some of the burning issues of the time, his attitude toward language, far from evolving in a historical vacuum, bears the unmistakable imprint of the linguistic concerns of his age.

Indeed, a case can be made that Stephen's constantly changing ideas on the relationship between words and reality in A Portrait mirrors the evolution of Western linguistic thought in those crucial few decades of its history which coincide with Joyce's early life. That period witnessed the discipline known as "comparative philology" supersede an approach to language which still very much relied on guesswork. While scholars, until then, had been positing often fanciful links to account for resemblances between given words, their time and energy were now devoted to sifting out textual evidence in order to trace out subtle shifts in meaning over time. That new direction in language study also led to the elaboration of evermore precise phonetic laws, thus contributing to the emergence of linguistics as a science in its own right. Those twin ground-breaking approaches led to the publication of dictionaries of a new type, such as Walter Skeat's Etymological Dictionary, which came out in 1882, the very year of Joyce's birth, and which Stephen is said to "read by the hour" in Stephen Hero, or the OED, which soon came to be regarded as the most accomplished exemplar of the new method. The period also saw the publication of books by Richard Trench aimed at popularising etymology, which, as I have shown elsewhere, was a great source of fascination and inspiration for Joyce. It fell, however, to Michel Bréal, in France, to give the field of semantics its true scientific credentials and thus place it on a firm institutional footing.

That radical departure entailed, of course, an entirely new conception of language, which accorded with contemporary discoveries in science, especially in biology, geology, and palaeontology. The age-old belief, based on a literal reading of the Bible, in a potentially retrievable Ur-language which functioned as a fountainhead of purity suddenly left room for an interest in developmental processes, whether they be phonetic, morphological and semantic. And yet, the shift from one approach to the other didn't go without tensions or contradictions, as the new publications contained clues implying that scholars who were contemporary to Joyce still clung, in some respects, to the former model. Richard Trench thus refers to Jacob Boehme's concept of the signature of things (signatura rerum), according to which Adam, in the second chapter of the Book of Genesis, had managed, thanks to a particular capacity given him by God, to see through the very essence of every creature he named and give it a name that matched its nature, a theory which rests on a belief in a transparent and direct relationship between word and world. At the end of the preface to the first edition of his dictionary, Walter Skeat, for his part, compares the "physical laws" which preside over the evolution of the lexicon to "the working of divine power", adding "It is therefore possible to pursue the study of language in a spirit of reverence similar to that in which we study what are called the works of nature; and by aid of that spirit we may gladly perceive a new meaning in the sublime line of our poet Coleridge, that "Earth, with her thousand voices, praises God" (EDEL xii). Such remarks testify to a belief in an immanent conception of language, one not so dissimilar, ultimately, to Boehme's.

Such a context is crucial to understanding Stephen's intellectual trajectory in A Portrait. A core element of it is his gradual discovery that the supposedly direct and univocal link between words and single objects is illusory, and that each word, instead, has a semantic and phonetic history of its own. That realisation is a step-by-step process which the novel charts. It starts on the very first page of the book with the words "moocow" and "baby tuckoo", which are used in such a way that they undermine the conception of language as a nomenclature made up of discrete units whose shape is the product of a mimetic link with the thing they designate in real life. The passage as a whole demonstrates that no word stands outside history since language is inevitably received as a legacy from previous generations, and that our relationship to reality is always already textualized in some way or another. Another key stage in Stephen's growth is the slow, and in some ways painful, realisation that each word literally "makes sense" through its different types of relationship with other items in the lexicon. In an earlier paper, I attempted to show that that discovery starts in the famous episode in which Stephen hears Rody Kickham hurl an insult at Simon Moonan ("We all know why you speak. You are McGlade's suck"). It sets off a whole train of thought going in his mind about the unsettling aura that surrounds the word "suck," leading him to remember the image of dirty water going down the hole of a basin: Suck was a queer word. The fellow called Simon Moonan that name because Simon Moonan used to tie the prefect's false sleeves behind his back and the prefect used to let on to be angry. But the sound was ugly. Once he had washed his hands in the lavatory of the Wicklow Hotel and his father pulled the stopper up by the chain after and the dirty water went down through the hole in the basin. And when it had all gone down slowly the hole in the basin had made a sound like that: suck. Only louder.

As Derek Attridge has shown, the trouble that the word "suck" creates in Stephen is not so much due to the supposedly mimetic relationship it entertains with the action of water going down a basin as to its polysemy, since the word "echoes the primary taboo word "fuck," and it names a specific sexual activity that could have taken place between the two males in question". The troubling effect caused by the word "suck" is thus due to its phonetic and semantic relationship with another item in the lexicon. Ironically, however, Stephen still clings to his belief in a tight, univocal and somehow mimetic relationship between words and things. Unable to understand that the link between reality and the phonemes of which "suck" is made up is arbitrary and that the agitation he feels is the consequence of language's organization as a closeknit system of phonetically and semantically inter-dependent units, he has no other option than to turn to a meaning of the word "suck" different to the one used by Rody Kickham, and to conclude that the ugly sound the word has to his ears can only be put down to the dirtiness of that other action it supposedly designates, namely the aspiration of dirty water down a hole.

At that point of the narrative, therefore, Stephen still equates language with a nomenclature, that is to say, with a system for naming things. As the etymology of the word "nomenclature," which derives from the Latin "nomen," meaning "name", shows, each word is thus reduced to a label and functions as a proper name. His mind privileges things over ideas, making the very notion of meaning redundant. His understanding of the nature and use of language is still rudimentary, or, one might say, in its infancy. It will take another episode, again with Rody Kickham, for it to develop further. It is on that precise episode which I would like to focus today. It witnesses Stephen's conception of language being attacked on its own ground, as it were, namely (pun intended) that of proper names. While thus far, he has regarded ordinary words as proper names, he suddenly realizes that it is precisely proper names which, because they have an indirect motivation, function, conversely, like ordinary words. The scene presents itself to the reader in the shape of a memory which emerges in Stephen's mind while he is on the rugby pitch with his classmates. Keeping as far away from them as he can not to take part in the match, Stephen compares his frail constitution to Rody Kickham's sturdier one. His mind then moves away from Kickham to Nasty Roche, another classmate of his who distinguishes himself by his coarse hands and colloquial language, and he remembers a series of questions that Nasty Roche once put to him:

-What is your name? Stephen had answered: -Stephen Dedalus.

-What kind of a name is that? And when Stephen had not been able to answer Nasty had asked: -What is your father? Stephen had answered: -A gentleman. Then Nasty Roche had asked: -Is he a magistrate? (P 6)

The question "What kind of a name is that?", where the demonstrative pronoun "that" is used to refer to language and not to reality, is bound to unnerve Stephen. In his eyes, there are no "kinds" or "sorts" of names, only names, each of which refers to a specific individual, hence his silence and confusion. Nasty Roche is thus forced to reformulate his question so that it expresses his true intention. He changes its form and shows that each proper name, for him, works as an index to its bearer's social status: "What is your father?" Such an attitude to names and to words in general, equating them with vessels in which stores of information are locked up, accords with the method adopted in historical linguistics in the 19 th century. Richard Trench's On the Study of Words contains numerous illustrations of it. For instance, he mentions the story according to which the German Emperor Maximillian 1 st learned by chance the meaning of the name of his House, the Habsburgs, when he heard a Swiss peasant pronounce it in its unabbreviated form: Leibnitz tells us, and one can quite understand, the delight with which a great German Emperor, Maximilian I, discovered that "Habsburg," or "Hapsburg," the ancestral name of his house, really had a meaning, one moreover full of vigor and poetry. This he did, when he heard it by accident on the lips of a Swiss peasant, no longer cut short and thus disguised, but in its original fullness, "Habichtsburg," or "Hawk's tower," being no doubt the name of the castle which was the cradle of his race (SW 326).

Maximilian's feeling of surprise is comparable to Stephen's, as both result from a sudden awareness that even proper names can have a meaning. Although Nasty Roche doesn't resort to the so-called "historical method", his question testifies to the very same attitude to language as the one on which that method rests, since it consists in seeing Stephen's family name not simply as a label, but as a record of his family history, and therefore as a guide to his social standing. Stephen's foreign-sounding name, however, gives it an opacity which defeats Roche's attempts at deciphering it. His remark, nevertheless, is enough to open Stephen's eyes to the historical information contained within words, including his own family name.

Shortly later in the novel, another episode will serve to bring that lesson more fully home to Stephen. Lying on a bed in the school infirmary next to a classmate called Athy, he starts chatting with him, and the conversation soon turns to their respective family names: « You have a queer name, Dedalus, and I have a queer name too, Athy. My name is the name of a town. Your name is like Latin » (P 20). Athy here shows particular insight in noting the Latin ring of the name "Dedalus". His remark further muddles the line between common and proper names, for he has managed to identify the Latin origin of "Dedalus" only by isolating its "us" suffix. The analysis he has carried out proves to be accurate, as the Latin noun "daedalus" comes the Greek "daídalos," which is made up of the verbal basis "daídalé," meaning "to adorn," "to embellish," and of the suffix "os".

Athy's remark thus proves that proper nouns, just like any other words, are affected by the organisation of language as a system, not so much because each of them was originally formed out of one or several nouns, but because speakers submit them to mental processes which are exactly the same as those to which ordinary words are submitted. By mentally separating the last two letters from the rest of Stephen's name, Athy treats it in precisely the same fashion as he does the Latin words taught to him daily at school, such as the noun "mare" which Father Arnall asks him to declinate a few pages later. Such a process may accord with the results of so-called "scientific etymology" in the case of "Dedalus", but it can just as well result in analyses which pertain to folk etymology.

The "Nestor" episode of Ulysses provides a fitting illustration of it when a pupil of Stephen's draws a fanciful link between the word "pier" and the name of King Pyrrhus from Ancient Greece:

-You, Armstrong, Stephen said. What was the end of Pyrrhus? -End of Pyrrhus, sir? -I know, sir. Ask me, sir, Comyn said. -Wait. You, Armstrong. Do you know anything about Pyrrhus?

A bag of figrolls lay snugly in Armstrong's satchel. He curled them between his palms at whiles and swallowed them softly. Crumbs adhered to the tissue of his lips. A sweetened boy's breath. Welloff people, proud that their eldest son was in the navy. Vico Road, Dalkey.

-Pyrrhus, sir? Pyrrhus, a pier (U 2.18-26).

Although borne out by scientific etymology, Athy's remark in A Portrait rests on precisely the same method as that of the hapless Armstrong in "Nestor". Not only does it illustrate a cognitive process which is a staple of language use, but it further shows that proper nouns are affected by it too.

The rest of the dialogue between the two schoolchildren provides a further illustration of it:

Then he asked: -Are you good at riddles? Stephen answered: -Not very good. Then he said:

-Can you answer me this one? Why is the county Kildare like the leg of a fellow's breeches?

Stephen thought what could be the answer and then said: -I give it up.

-Because there is a thigh in it, he said. Do you see the joke? Athy is the town in the county Kildare and a thigh is the other thigh.

-Oh, I see, Stephen said.

-That's an old riddle, he said (P 20).

While Armstrong found a pier in Pyrrhus, Athy finds a thigh in his own name. His gesture, which suggests that any proper name, with a tiny bit of ingenuity, can be inserted into the system of differences that is language (a point elaborated upon by Jacques Derrida in his seminal work Of Grammatology), has far-reaching theoretical and methodological consequences. Not only does it put the final nail in the coffin of the conception of language as a nomenclature, it hints at the myriad segmentations and mental associations on which our daily use of language rests, a field of research which pioneers of the fledgling discipline of semantics had precisely been turning their attention to in the decades before the publication of A Portrait. Joyce's works, therefore, do more than simply record the recent impact of comparative philology on language study, they herald a concern for phenomena which had been dismissed for centuries as quaint or marginal, but which had suddenly found themselves rehabilitated by contemporary scholars such Michel Bréal and Ferdinand de Saussure, for whom they were proper terrain for the linguist to investigate. It is precisely a similar rehabilitation that one finds throughout Joyce's works, from the so-called "malapropisms" of "The Sisters" to Molly's confusion of the words "carrot" (the vegetable) and "carat" (the unit for measuring the weight of jewels) in "Penelope". Joyce's promotion of those phenomena from the status of aberrations to that of staple elements of language use is very much of its time, and even looks forward, in some ways, to the works of post-structuralist thinkers, who made much of the role played by folk etymology in our everyday use of language. Joyce's concern for both the diachronic and synchronic approaches to language thus mark out his works as truly transitional. They are on the cusp between the historicist model characteristic of the nineteenth-century, which aimed at replacing an approach to language based on myth by a scientific method and which perceived the past meanings of a word as integral to its identity, and a structuralist model whose main focus in on the numerous links posited by speakers between different items in the lexicon and which by necessity takes on board all sorts of unexpected, abnormal and funny phenomena.