Florian Estrade

Céline Lescure

Léa Muzellec

Maud Pedrono

Xavier Palard

Marc Pracht

Samuel Le Sourd

Yan Rolland

Thomas Uguen

Etienne Garin

Radiation Treatment for HCC: A Retrospective Cohort Study

Keywords: Radioembolization, Yttrium-90, immune checkpoint inhibitors, anti-PD-1, lymphopenia, liver malignancies

come

Introduction

Selective Internal Radiation Therapy (SIRT), also known as Yttrium-90 radioembolization, is an emerging treatment modality of hepatic malignancies, including Hepatocellular Carcinoma (HCC), with potential role in the intermediate and advanced stages [START_REF] Salem | Y90 Radioembolization Significantly Prolongs Time to Progression Compared With Chemoembolization in Patients With Hepatocellular Carcinoma[END_REF][START_REF] Edeline | Selective internal radiation therapy compared with sorafenib for hepatocellular carcinoma with portal vein thrombosis[END_REF]. Another emerging treatment of HCC is immunotherapy. Phase 2 data of anti-PD-1 agent showed promising results [START_REF] El-Khoueiry | Nivolumab in patients with advanced hepatocellular carcinoma (CheckMate 040): an open-label, noncomparative, phase 1/2 dose escalation and expansion trial[END_REF][START_REF] Zhu | Pembrolizumab in patients with advanced hepatocellular carcinoma previously treated with sorafenib (KEYNOTE-224): a non-randomised, open-label phase 2 trial[END_REF]. Recently, the IMBRAVE150 phase 3 study results were presented, showing significant benefit of the combination of atezolizumab-bevacizumab in comparison with sorafenib [START_REF] Cheng | LBA3 -IMbrave150: Efficacy and safety results from a ph III study evaluating atezolizumab (atezo) + bevacizumab (bev) vs sorafenib (Sor) as first treatment (tx) for patients (pts) with unresectable hepatocellular carcinoma (HCC)[END_REF].

Baseline lymphopenia and high Neutrophils-to-Lymphocytes Ratio (NLR) have been showed in multiple cancers to have prognostic values, independently of treatment modality [START_REF] Templeton | Prognostic Role of Neutrophil-to-Lymphocyte Ratio in Solid Tumors: A Systematic Review and Meta-Analysis[END_REF].

Apart from this value at baseline, variations during treatment might also have an impact on survival. Radiation has a potential for direct toxicity toward blood white cells, especially lymphocytes [START_REF] Nakamura | Radiosensitivity of CD4 or CD8 positive human Tlymphocytes by an in vitro colony formation assay[END_REF]. Moreover, variations of lymphocytes and Neutrophils-to-Lymphocytes Ratio (NLR) have been shown to be prognostic in many contexts after external beam radiotherapy, including HCC [START_REF] Zhao | Minimum absolute lymphocyte counts during radiation are associated with a worse prognosis in patients with unresectable hepatocellular carcinoma[END_REF]. Few data exist as regards to the toxicity of SIRT for lymphocytes, mostly from small series, with no sufficient power to allow for prognostic evaluation [START_REF] Domouchtsidou | Impaired lymphocyte function in patients with hepatic malignancies after selective internal radiotherapy[END_REF][START_REF] Chew | Immune activation underlies a sustained clinical response to Yttrium-90 radioembolisation in hepatocellular carcinoma[END_REF].

There is a growing interest for the combination of immunotherapy with locoregional approaches [START_REF] Greten | Combined locoregionalimmunotherapy for liver cancer[END_REF]. SIRT has been described as a potentially interesting locoregional treatment to combine with immunotherapy, due to the theoretical immunosensitizing effect of radiation, albeit mostly studied with external beam radiotherapy [START_REF] Formenti | Combining Radiotherapy and Cancer Immunotherapy: A Paradigm Shift[END_REF]. SIRT might induce local inflammation [START_REF] Chew | Immune activation underlies a sustained clinical response to Yttrium-90 radioembolisation in hepatocellular carcinoma[END_REF]. However, this potential synergy might be mitigated if the direct toxicity toward lymphocytes reduces the availability of effectors of immunotherapy.

A c c e p t e d M a n u s c r i p t

The main objective of the study was to study variations in blood cells counts after SIRT and to evaluate their prognostic values in terms of overall survival (OS).

A c c e p t e d M a n u s c r i p t

Methods:

Study design

This retrospective and non-interventional cohort study enrolled HCC patients undergoing SIRT at the Centre Eugene Marquis in Rennes (Brittany, France) from January 2008 to January 2017. They could have been previously treated or not. They all met the following inclusion criteria: age ≥ 18 years old, PS ≤ 2, SIRT therapy recommended by specialized multidisciplinary team. This study was approved by the Ethic Committee of the CHU of Rennes. This report complies with the STROBE guidelines on cohort studies.

Treatment procedure

The SIRT procedure was performed as previously described [START_REF] Salem | Research reporting standards for radioembolization of hepatic malignancies[END_REF]. The aim of the diagnostic angiography was to define the best catheter position for right, left, or segmental treatment in order to target the lesion. Percentage of pulmonary shunting and absence of digestive uptake were assessed after 99m Tc macroaggregated albumin was injected selectively in the hepatic artery (185MBq). Planar and SPECT/CT acquisitions were performed. SPECT/CT acquisitions were conducted using the following parameters: window 140 ± 7.5KeV; 32 projections; 180°; 128 * 128; 30s/projection (Symbia T2 gantry, Siemens). The data was reconstructed using an iterative method (OSEM, 5 iterations, 8 subsets) with CT based attenuation correction and scatter corrections.

SIRT was performed 8 to 15 days later at a second angiography. SIRT was performed either with glass-microspheres (TheraSphere®, BTG, London, UK) or resin-microspheres (SIR-Spheres®, Sirtex Medical, Sydney, Australia). For patients treated with glass-microspheres, activity administrated was calculated with the aim of administering a dose between 80 and 150 Gy to the targeted liver volume without exceeding a cumulative dose of 30 Gy to the lungs; however, in case of segmental or bisegmental injection, dose to the segment could be A c c e p t e d M a n u s c r i p t higher than 150 Gy as previously described [START_REF] Garin | Boosted selective internal radiation therapy with 90Y-loaded glass microspheres (B-SIRT) for hepatocellular carcinoma patients: a new personalized promising concept[END_REF]. Segmentation (targeted liver and tumor) was performed on SPECT/CT data and not on the angiographic and CT data usually used, as previously described [START_REF] Garin | Personalized dosimetry with intensification using 90Y-loaded glass microsphere radioembolization induces prolonged overall survival in hepatocellular carcinoma patients with portal vein thrombosis[END_REF].

Follow-up

The patients had blood test performed during the two weeks before SIRT treatment, then at 3 months, at the same time as radiological evaluation. Primary objective was OS. OS was defined as the time between first SIRT treatment and death or last follow-up visit. Response was studied according to mRECIST. Toxicity was graded according to NCI-CTCAE v4.03.

Statistical analysis

Correlation between values and dose delivered to the whole liver, the tumor and the nontumoral liver were assessed with a Spearman's Rho test. To determine the most discriminating thresholds for continuous variables, a Receiver over Curve (ROC) analysis was performed, to select for the availability to predict a survival lower than the median (patients alive with shorter follow-up were censored). Survival was analyzed by the Kaplan-Meier method and by a univariate and multivariate Cox model. The multivariate model included variables associated with OS (p<0.05) in univariate analysis. Statistical analyses were done using SPSS software v18.0.

A c c e p t e d M a n u s c r i p t

Results:

Between January 2008 and January 2017, 232 patients were treated with SIRT for HCC, and 164 patients had blood test values available at both baseline and 3 months. Baseline characteristics are reported on Table 1. Median activity injected was 2.5Gbq (range: 0.23-350), median dose delivered to the treated liver was 120Gy (range: 26-248), median dose delivered to the tumor was 277Gy (range: 96-880), median dose delivered to the nontumoral liver was 85Gy (range: 0-194). Median OS of the cohort was 17.7 months (95% Confidence Interval (CI): 14,2-21,1). Response rate by mRECIST was 71% with 58% partial response and 13% complete response. 53 patients (23%) experienced grade 3 or more toxicities, the most frequent being development of ascites in 25 (10.8%).

There was frequent decrease of lymphocytes count following SIRT. Median lymphocyte count was 1.32Giga/Liter (G/L) (Standard deviation (SD: 0.64) at baseline vs 0.68G/L (SD:0.41) at 3 months. The mean variation of lymphocytes count between baseline and 3months was -44% (SD: 0.24), and 45% of patients had decrease higher than -50%. At baseline, 49 of the 164 patients (29.9%) had lymphocytes count <1G/L, while at 3 months, 132 of the 164 patients (80.5%) had lymphocytes count <1G/L. At 3 months, 52 (31.7%) patients had lymphocytes count between 0.5G/L and 0.75G/L, and 38 (23.2%) had lymphocytes counts lower than 0.5G/L, while corresponding figures at baseline were only 13 (7.9%) and 6 (3.7%) (Figure 1). There was a weak negative correlation between lymphocyte count at 3 months and dose delivered to the non-tumoral liver (spearman's rho =-0.29, p=0.001). There was no correlation between lymphocyte count at 3 months and dose delivered to the tumor or dose delivered to the injected liver.

At baseline, a lymphopenia <1G/L was not associated with worse OS (p=0.28), but at 3months, there was a trend towards lower OS (median OS 17.3 months vs 19.9 months, A c c e p t e d M a n u s c r i p t p=0.058). However, lower lymphocytes count at 3 months as a continuous variable was not significantly associated with worse OS (Cox univariate model, Hazard Ratio (HR) of 0.89 (95%CI: 0.61-1.32, p=0.58).

As the NLR was shown in different contexts to have better prognostic abilities than lymphocytes or neutrophils counts, NLR variations were then studied. Median NLR was 3.47 (SD:1.86) at baseline vs 5.74 (SD:6.12) at 3 months. Mean NLR variation at 3 months was +82% (standard deviation: 1.94). Higher NLR at 3 months as a continuous variable was associated with worse OS, with a HR=1.06 (95%CI: 1.03-1.09) p<0.001. The best thresholds were defined by ROC analysis associated with the prediction of OS, which were 7.2 for NLR and 0.67G/L for lymphocytes, both at 3 months. AUC of ROC curves were 0.64 (95%CI: 0.55-0.73, p=0.003) for NLR and 0.58 (95%CI: 0.49-0.67, p=0.10) for lymphocytes, showing better prognostic abilities for NLR than for lymphocytes. Using these thresholds, OS was significantly worse in patients with NLR at 3 months higher than 7.2, with median OS of 9.9 (95%CI: 6.2-13.5) vs 19.9 months (95%CI: 16.3-23.3) (p=0.003) (Figure 2A). It was also significantly worse in patients with lymphocytes at 3 months lower than 0.67G/L, with median OS of 14.3 (95%CI: 16.6-30.1) vs 23.4 months (95%CI: 10.0-18.7) (p=0.004) (Figure 2B).

Results were then studied in a multivariate Cox model (Table 2). In univariate analysis, baseline parameters associated with OS were HCV infection, PVT, albumin (as continuous variable), alpha-feto protein (as continuous variable). When NLR and lymphocytes count at 3 months were studied in a multivariate model in conjunction with baseline parameters, only PVT and NLR at 3 months were independently with OS. Respective Hazard Ratio for PVT and NLR at 3 months were HR=1.69, 95%CI: 1.18-2.43, p=0.005 and HR=1.07, 95%CI: 1.04-1.10, p<0.001 when NLR was studied as continuous variable and HR=1.56, 95%CI: 1.09-2.23, A c c e p t e d M a n u s c r i p t p=0.016 HR=1.67, 95%CI: 1.19-2.34, p=0.003 when studied with the 7.2 threshold. Results were identical when mRECIST response and grade ≥3 toxicities were also entered into the model.

A c c e p t e d M a n u s c r i p t

Discussion

The main results of this study are the following: (1) lymphocytes frequently decrease following SIRT, and lymphocytes counts are frequently very low (about a quarter of patients with lymphocytes <0.5G/L at 3 months); (2) the decrease of lymphocytes were correlated to the dose delivered to the non-tumoral liver; (3) a NLR at 3 months higher than 7.2, or a lymphocytes count lower than 0.67G/L are associated with statistically and clinically significant worse OS (about 2-fold decrease of the median); and (4) NLR at 3 months is an independent prognostic factors when studied concomitantly with baseline characteristics and response evaluation. Taken together, these results suggest that SIRT, as other radiation modalities, has a significant toxicity towards lymphocytes, and that the decrease of lymphocytes, as well as increase of NLR, after SIRT, have important consequences in terms of survival for the patients. This work was the first to evaluate lymphocytes and NLR variations in a large series of HCC treated with SIRT. Previous studies focused on other aspects of lymphocytes activity after SIRT. Domouchtsidou et al studied 25 patients and analyzed lymphocytes functions following SIRT [START_REF] Greten | Combined locoregionalimmunotherapy for liver cancer[END_REF]. They showed immediate decrease of lymphocyte proliferation as well as impairment of immune response. These results might suggest that lymphocytes might be less effective against HCC following SIRT. Combined with our results of decrease lymphocytes counts, this could suggest that SIRT might negatively impact the anti-tumoral immune response. This could also explain why the increase of NLR strongly and independently correlated with worse survival. In contrast, Chew et al evaluated 31 patients with in-depths characterization of circulating immune cells [START_REF] Formenti | Combining Radiotherapy and Cancer Immunotherapy: A Paradigm Shift[END_REF]. They showed that resected tumors following SIRT were more inflamed than tumors resected without neoadjuvant treatment. They also showed that the types of circulating lymphocytes were different A c c e p t e d M a n u s c r i p t between responding and non-responding tumors following SIRT. While important as they gave insight in functional parameters, Domouchtsidou's and Chew's studies were limited in numbers and could not demonstrate prognostic value of the variations of lymphocytes in terms of OS. The present study used easily available parameters that could be directly used clinically to offer prognostication.

In this context of frequent decrease of lymphocytes, the correlation of this decrease with the dose delivered to the non-tumoral liver emphasizes the need for appropriate dosimetry studying separately tumoral dose (to improve efficacy), but also non-tumoral liver doses (to ensure safety), not only to avoid liver deterioration but also to avoid lymphotoxicity [START_REF] Garin | Personalized dosimetry with intensification using 90Y-loaded glass microsphere radioembolization induces prolonged overall survival in hepatocellular carcinoma patients with portal vein thrombosis[END_REF][START_REF] Chiesa | A dosimetric treatment planning strategy in radioembolization of hepatocarcinoma with 90Y glass microspheres[END_REF]. Importantly, many previous works in different contexts have suggested that baseline higher NLR was an important negative prognostic factor in patients treated with immune checkpoint inhibitors [START_REF] Bigot | Prospective validation of a prognostic score for patients in immunotherapy phase I trials: The Gustave Roussy Immune Score (GRIm-Score)[END_REF][START_REF] Capone | Baseline neutrophil-to-lymphocyte ratio (NLR) and derived NLR could predict overall survival in patients with advanced melanoma treated with nivolumab[END_REF]. However, it is not clear whether this could be considered only a prognostic factor, or also a predictive factor of response. The present study raises questions about the frequent decrease of lymphocytes and increase of NLR following SIRT, that has the potential to negatively affect the outcomes for patients subsequently treated with immune checkpoint inhibitors. While this could be only a working hypothesis, one might still question the rationale to study the combination of SIRT with immune checkpoint inhibitors, while this appears to have mainly suggested with hypo-fractionated regimen of radiation [START_REF] Duffy | Tremelimumab in combination with ablation in patients with advanced hepatocellular carcinoma[END_REF]. One suggestion might be that studies combining SIRT with immunotherapy should better start the immunotherapy before administrating SIRT, to ensure that a sufficient number of active lymphocytes are still present.

This study has limitations. The retrospective nature of the work was associated with a significant number of missing data at 3 months (164 patients available from a cohort of 232 patients). Moreover, we were able to study only one time-point. The study of multiple time-A c c e p t e d M a n u s c r i p t points would have allowed to more precisely describe the course of lymphotoxicity of SIRT, as well as to better understand how long this toxicity might persist. However, as Yttrium-90 half-life is about 64 hours, the decrease described in this work at 3 months could represent long-term toxicity of the treatment. There was no validation cohort. However, this is the larger study focusing on variations of lymphocytes following SIRT. Finally, the possible consequences of these variations of lymphocytes as regards to immune checkpoint inhibitors efficacy are speculative and should be studied separately in cohorts of patients treated with these agents.

In conclusion, lymphopenia is a frequent toxicity of SIRT in HCC, and increase NLR at 3 months is independently associated with worse OS. These results should be taken into account when designing potential clinical trials of combination of immune checkpoint inhibitors with SIRT in HCC.

A c c e p t e d M a n u s c r i p t

Figure 1 :

 1 Figure 1: Percentage of patients with different levels of lymphocytes counts, at baseline and

Figure 2 :

 2 Figure 2: Overall survival according to (A) NLR at 3 months; (B) lymphocytes count at 3

Table 1 :

 1 Baseline characteristics of the 164 patients

	Median age	Median	68 (range: 37-83)
	Sex	Male	146 (89.0%)
	Performance Status	0	110 (67.1%)
	Cirrhosis Alcohol consumption Dysmetabolic syndrom HBV infection HCV infection Previous treatment for HCC before SIRT	141 (86.0%) 112 (68.3%) 71 (43.3%) 4 (2.4%) 19 (11.6%) 87 (53.0%) 26 (15.9%) 16 (9.8%) a n u s c r i p t Radiofrequency Any Surgery M
	ablation Sorafenib Transarterial Chemoembolisation Left liver Right liver Bilateral A c c e p t e d Extent of the disease	32 (19.5%) 45 (27.4%) 49 (29.9%) 108 (65.9%) 7 (4.3%)
	Maximal size of the lesion	Median	6.7cm (range: 1.2-
			17.0)


domain: info info.info-bt phys

text:
E D U S C H

T Dorval

N V I N C E N T †

M Wac H S M U T H

A G E N Ov E S I O

E Dusch

Three-dimensional point spread function model for line-scanning confocal microscope with high-aperture objective

Keywords: Confocal microscopy, Debye integral, line-scanning confocal microscope, point spread function

Point Spread Function (PSF) modelling is an important task in image formation analysis. In confocal microscopy, the exact PSF is rarely known, thus one has to rely on its approximation. An initial estimation is usually performed experimentally by measuring fluorescent beads or analytically by studying properties of the optical system. Yet, fluorescent line-scanning confocal microscopes are not widespread; therefore, very few adapted models are available in the literature. In this paper, we propose an analytical PSF model for line-scanning confocal microscopes. Validation is performed by measuring the error between our model and an experimental PSF measured with fluorescent beads, assumed to represent the real PSF. Comparison with existing models is also presented.

Introduction

Accurate point spread function (PSF) models are necessary for various tasks, such as deconvolution (see [START_REF] Sarder | Deconvolution methods for 3-D fluorescence microscopy images[END_REF] for a review), image resolution improvement [START_REF] Santos | Model-based resolution: applying the theory in quantitative microscopy[END_REF][START_REF] Thomann | Automatic fluorescent tag detection in 3D with super-resolution: application to the analysis of chromosome movement[END_REF] and data simulation to validate image-processing algorithms. As the exact PSF is rarely known, one has to rely on its approximation, which can be estimated using an experimental or an analytical approach.

In an experimental approach, the PSF is estimated by extracting image structures assumed to represent it. In confocal microscopy, this is usually achieved by measuring small fluorescent beads. Although this approach has the advantage of well reflecting the imaging conditions, the obtained PSF has a low signal-to-noise ratio (SNR) due to the small size of the imaged beads [START_REF] Mcnally | Three dimensional imaging by deconvolution microscopy[END_REF]. Moreover, knowledge of both the analytical and the simulated PSF allows a more precise characterization of the system.

An analytical approach consists in expressing the PSF using diffraction theory and knowledge of the optical microscope components. Although analytical PSF models have been well established for point-scanning confocal microscopes, they are not adapted to line-scanning confocal microscopes (characterized by a line illumination in the object space and a slit-shaped line detector). In [START_REF] Sheppard | Confocal microscopes with slit apertures[END_REF], the authors proposed a two-dimensional PSF model applicable only in the focal plane. More recently, [START_REF] Wolleschensky | High-speed scanning confocal microscope for the life sciences[END_REF] proposed a three-dimensional (3D) model for the LSM 5 live line-scanning confocal microscope (Zeiss, Germany). They make a paraxial assumption, valid only for an objective lens with low numerical aperture (NA), and compute the model with non-paraxial optical units, which can be considered as a first approximation for higher NAs [START_REF] Amos | Optical units. Handbook of Biological Confocal Microscopy[END_REF].

In this paper, we propose a 3D non-paraxial PSF model for a fluorescent line-scanning confocal microscope with a high-aperture objective lens, and show that the model tends asymptotically to the paraxial model of Wolleschensky et al., when the NA becomes small. During the validation process, we use as reference a measured PSF calculated by averaging fluorescent beads imaged on the LSM 5 live microscope, and compare the relative absolute error (RAE) of three models: nonparaxial point-scanning [START_REF] Gu | Advanced Optical Imaging Theory[END_REF], paraxial line-scanning [START_REF] Wolleschensky | High-speed scanning confocal microscope for the life sciences[END_REF] and the proposed non-paraxial line-scanning model.

Theoretical line-scanning PSF model

In this section, we first express the theoretical excitation and emission amplitudes of a point near the focus using the scalar Debye diffraction integral. Then, we present a 3D non-paraxial PSF model for fluorescent line-scanning confocal microscopes and its paraxial approximation.

When the NA becomes large, effects such as depolarization, apodization and aberration are more pronounced [START_REF] Gu | Advanced Optical Imaging Theory[END_REF]. Considering the vectorial property of electromagnetic waves, the vectorial Debye theory was proposed to take into account light depolarization in the focus of the lens. Nevertheless, a close approximation of the intensity distribution near the focus can be obtained by the scalar theory as shown by [START_REF] Born | Principles of Optics[END_REF]. In the following, we assume that the optical system is linear shift-invariant and aberration-free.

Let us consider a line illumination created and focussed by a cylindrical lens on the back-focal plane of the objective lens. A line is thus generated along the x direction by the objective lens onto the sample plane [START_REF] Wolleschensky | High-speed scanning confocal microscope for the life sciences[END_REF].

Figure 1 describes the light path along the y direction (left) and x direction (right). The emitted fluorescence is focussed by the confocal lens onto a slit, rejecting out-of-focus fluorescent points.

In confocal microscopy, the Point Spread Function is defined by the product of the excitation intensity distribution (characterized by the line illumination) and the emission intensity distribution (generated by the fluorescence) convolved with the area of the detector projected into the object space:

PSF(x, y, z) = |h ex (x, y, z)| 2 |h em (x, y, z)| 2 * D (x, y) , (1)
where * denotes the convolution, D is the detector, and h ex and h em are the excitation and emission amplitude distributions, respectively. In line-scanning microscopes, the detector is characterized by the slit in the y direction and by the line CCD detector elements in the x direction. In the widefield case, it has been shown that the CCD elements are usually small enough to be neglected in the image formation process [START_REF] Van Kempen | Image restoration in fluorescence microscopy[END_REF]. In a similar way and as shown in Fig. 2, the PSF for line-scanning microscopes can be approximated by

PSF(x, y, z) = |h ex (x, y, z)| 2 |h em (x, y, z)| 2 * S (y) . (2)
The slit S situated in front of the line detector is considered as a finite-size incoherent pinhole, that is, it detects the light intensity [START_REF] Wilson | The role of the pinhole in confocal imaging system[END_REF].

Since an illumination line covers the total sample plane in the x direction, diffraction effects are not important owing to the wide illuminated area. Therefore, we assume the excitation amplitude along the line to be constant. The waves in the field between the objective lens and the focal plane are defined as a superposition of plane waves. Using the scalar Debye theory [START_REF] Born | Principles of Optics[END_REF], the excitation amplitude near the focal point can be written as the integration of these plane waves according to the angle of convergence. Thus, we express the excitation amplitude according to the y and z direction as (see Appendix A for details):

h ex (y, z) = α -α P (θ) exp (-i k ex y sin θ ) exp (-i k ex z cos θ) k ex cos θ d θ, ( 3
)
where α is the aperture half angle of the objective and k ex = n 2π λex is the excitation wave number. Under the sine condition, fulfilled by an aplanatic lens as generally used on commercial microscopes, the apodization term P(θ) is equal to √ cos θ. Similarly to a point-scanning confocal microscope, the emission amplitude distribution in front of the slit can be expressed by the scalar Debye diffraction integral for a circular lens:

h em (x, y, z)

= α 0 P (θ)J 0 (k em sin θ x 2 + y 2 ) × exp (-i k em z cos θ) k em sin θd θ, ( 4
)
where the emission wave number k em is equal to n 2π λem , and J 0 is the zero-order Bessel function.

Hence, the non-paraxial line-scanning PSF can be written as

PSF NP (x, y, z) = α -α √ cos θ exp(-i k ex y sin θ ) × exp(-i k ex z cos θ)k ex cos θd θ 2 s -s α 0 √ cos θ J 0 k em sin θ x 2 + (y -y s ) 2 × exp (-i k em z cos θ ) k em sin θd θ 2 dy s , ( 5
)
with s representing the half slit width in airy units.

Figure 3 shows the normalized intensity PSF along each direction.

Approximation to low NAs

Equation ( 5) can be simplified for small NAs (inferior to 0.7). Under the assumptions (sin θ ≈ θ ) and (cos θ ≈ θ ), if we rewrite θ = αt, we find that Eq. ( 5) tends asymptotically to the following paraxial model:

PSF P (x, y, z) = 1 -1 exp (-i k ex yαt) × exp i 2 k ex zα 2 t 2 k ex d t 2 × s -s 1 0 J 0 k em αt x + (y -y s ) 2 × exp i 2 k em zα 2 t 2 k em td t 2 dy s , (6)
which is equivalent to the paraxial model given by [START_REF] Wolleschensky | High-speed scanning confocal microscope for the life sciences[END_REF].

Validation

In this section, we compare our model with two other analytical models: non-paraxial point scanning [START_REF] Gu | Advanced Optical Imaging Theory[END_REF] and paraxial line scanning [START_REF] Wolleschensky | High-speed scanning confocal microscope for the life sciences[END_REF]. We calculate an experimental PSF by measuring multiple PSF-like fluorescent beads, averaged to increase the SNR. The experimental PSF measurement is first presented, and then we compare the RAE between each model and the measured PSF.

Experimental PSF measurement

Material. Molecular Probes' PS-Speck beads used in our experiments are fluorescent spheres with a diameter of 0.175 μm(±0.005 μm). These fluorescent micro-spheres have an excitation and emission wavelength of 505 and 515 nm, respectively. The beads were imaged on the LSM 5 live microscope with a resolution of 0.05 × 0.05 × 0.1 μm per voxel. We used a 488 nm/100 mW laser, a 505-nm emission long-pass filter and a 63× oil-immersion objective lens (NA = 1.4).

PSF-like structures extraction.

We have developed a semiautomated method to extract the PSF-like fluorescent beads. Since the beads are randomly distributed over the sample, some may overlap and appear as clusters on the images. These clusters must be excluded from the measurement process; otherwise it yields an inaccurate PSF estimation. Therefore, we define a criterion to discriminate background noise, isolated beads and bead clusters.

In the detection algorithm proposed by [START_REF] Thomann | Automatic fluorescent tag detection in 3D with super-resolution: application to the analysis of chromosome movement[END_REF], the images are filtered with a Gaussian kernel of variance σ 2 that approximates the microscope's PSF, and a score is calculated for each local maximum as the product of the local average intensity and the Gaussian curvature κ (determinant of the Hessian matrix of the filtered image). This criterion is efficient to detect bright isotropic spots, but not adapted to our problem where the brightest structures are in fact bead clusters.

In our case, the Gaussian filtering is used to discriminate the size of the spots. The variance σ 2 affects the value of κ: a small σ 2 gives a high κ for small spots and low κ for large spots, and conversely, a large σ 2 gives a low κ for small spots and a high κ for large spots. For the background noise, intensity changes in all direction are randomly distributed, yielding a low κ. Thus, the Gaussian curvature is sufficient to discriminate each class. To extract the beads, the variance σ 2 is chosen to fit their size, and we apply a manual thresholding on the Gaussian curvature. κ Finally, isolated beads are cropped and averaged to get the measured PSF.

Beads averaging. To average the beads, we perform a sub-pixel accurate registration using the Polak-Ribiere method [START_REF] Polak | Computational Methods in Optimization[END_REF] to maximize the joint histogram mutual information [START_REF] Viola | Alignment by maximization of mutual information[END_REF]. This criterion is widely used in the IRM field and is well suited for comparing images with different intensity ranges.

Bead image deconvolution. The experimental PSF measured using this protocol is larger than the analytical PSF model due to the beads' size. [START_REF] Van Der Voort | Restoration of confocal images for quantitative image analysis[END_REF] proposed to correct the blurring effect caused by the beads in estimating the experimental PSF by a deconvolution approach. Based on this work, we assume that the PSF was degraded by convolution with a virtual bead of diameter 0.175 μm under Poisson statistics, and we use the well-known iterative Richardson-Lucy algorithm to restore the experimental PSF. Original image and restored experimental PSF are presented in Fig. 4.

Results and discussion

To compare the analytical PSF models, we calculate the RAE with the experimental PSF:

RAE = n i =1 |PSFM i -PSFA i | n i =1 PSFM i ,
where PSFM and PSFA are, respectively, the measured and the analytical PSF, and n the number of pixels taken into consideration. Figure 5 shows the measured and simulated maximum centred PSFs along the xy, xz and yz view. Our model approximates the measured PSF with a RAE of 0.67 compared to 0.84 for the paraxial model and 0.95 for the point-scanning confocal model. Figure 6 shows the RAE along the axial direction, that is, computed plane by plane, between the measured and simulated PSFs. The RAE for the paraxial line-scanning model and the point-scanning model are always larger, showing that our model remains a better approximation everywhere along the z axis.

Despite the SNR increase by averaging fluorescent beads, the measured PSF is still corrupted by different sources of noises. Thus, the error could be reduced by including a noise model within the simulation process. Moreover, in the measured PSF, a divergent cone can be seen in the xz section (Fig. 5a). This phenomenon due to spherical aberrations is common in fluorescence microscopy. An additional aberration called coma can be seen in the xy section due to misalignment of the optical axis. We have assumed that the system is aberrationfree, but taking these aberrations into account would -0.9 0 0.9 0.75 1 z-axis Relative Absolute Error

Conclusion

We have presented an accurate PSF model for line-scanning confocal microscopes. A point-scanning confocal microscope PSF, a paraxial line-scanning confocal microscope PSF and our model were compared against an experimental PSF measured by averaging small fluorescent bead images. Our results show that our model substantially surpasses existing models. Still, it could be further improved by taking into account factors of disturbance such as depolarization and aberration [START_REF] Török | Electromagnetic diffraction of light focused through a stratified medium[END_REF] and [START_REF] Haeberlé | The point spread function of optical microscopes imaging through stratified media[END_REF]. In our future work, we will use this model in a deconvolution process to improve structure detection in several biological applications.

Fig. 1 .

 1 Fig. 1. Scheme of a fluorescent line-scanning confocal microscope.

CFig. 2 .

 2 Fig. 2. Normalized intensity of the non-paraxial PSF model with (dashed line) and without (solid line) considering the detector along the line for different slit sizes: s → ∞ (a), s = 1 (b) and s → 0(c) (Units are in μm).

CFig. 3 .

 3 Fig. 3. Normalized intensity of the non-paraxial PSF model (Eq. 5, solid line) and of the paraxial PSF model (Eq. 6, dashed line) along the x (line) axis (a), the y(slit) axis (b) and the z(optical) axis (c) (units are in μm).

C

  Fig. 4. xy, xz and yz views of the measured PSF before (a) and after (b) deconvolution. The measured PSF represents an average of more than 150 beads.

CFig. 5 .

 5 Fig. 5. xy, xz and yz views of the measured PSF (a), our non-paraxial model -RAE = 0.65 (b), paraxial line-scanning model -RAE = 0.84 (c) and point-scanning model -RAE = 0.95 (d).

Fig. 6 .

 6 Fig. 6. RAE along the z-axis (in μm) between the measured PSF and the point-scanning model (point line), the paraxial line-scanning model (dashed line) and our non-paraxial model (solid line).

Acknowledgements

We thank Regis Grailhe and the Dynamic Imaging Platform of Institut Pasteur Korea for acquiring the beads images on the line-scanning confocal microscope. We also thank the reviewers for their constructive and detailed reviews of this manuscript.

Appendix: Excitation Amplitude

The scalar (or vectorial) Debye theory states that the amplitude (or electro-magnetic field) of a point near the focus can be expressed as a superposition of plane waves integrated on the lens aperture field A, leading to

where P (k y , k z ) is the pupil function (or the vectorial electromagnetic field distribution). This equation can also be seen as the Fourier transform of the pupil function. Using Fourier analysis, the PSF can be determined by the Fourier transform of the wavefront at the exit pupil plane. The wave vectors k y and k z can be described by the convergence angle θ of the pupil:

Under these transformations, the integration field dA and the pupil function are given by

Finally, the integration is performed in the limit of the maximal angle of convergence α. The excitation amplitude becomes h (y, z) =


Svetlana Radtchenko-Draillard

The effects of cultural and personal differences of the protagonists on the international negotiation

Keywords: Negotiation, Conflict, Interdependence, Cultural and Personal Differences, Decision-Making Strategy, Agreement

International negotiation is a process by which two or more opposing parties interact in order to reach an acceptable position with regard to their differences. Reducing these differences is a choice between two or more equally possible, but sometimes contradictory, solutions, which is often determined by international negotiations. The aim of this research is to highlight the psychological effects of cultural and personal differences on the choices of decision-making strategy by adversaries in major international negotiations during the Second World War. I have established that negotiators who wish to find an acceptable solution or break a cognitive impasse have often found themselves under the influence of a mechanism of an "optimum of creativity" that actually promotes their development of the cognitive process. The conclusion of a final agreement and its results have a significant influence on interpersonal relationships.

Introduction

The very essence of human existence is constructed from impulses, which are of a similar order in all human beings and which aim for their satisfaction in latent or manifest permanent conflicts. Civilization is the necessary path from family to humanity: it is inextricably linked to the innate conflict of eternal struggle between life's impulses and death drives. In accordance with the idea of Freud (1932Freud ( -1933)"It is a general principle, then, that conflicts of interest between men are settled by the use of violence. This is true of the whole animal kingdom, from which men have no business to exclude themselves. In the case of men, no doubt, conflicts of opinion occur as well which may reach the highest pitch abstraction and which seem to demand some other technique for their settlement" (p.204). Then Freud specifies in the next page "The community must be maintained permanently, must be organized, must draw up regulations to anticipate the risk of rebellion and must institute authorities to see that those regulations-the laws-are respected and to superintend the execution of legal acts of violence". (p.205) [1].

The various research results show that the identification process is the result of a series of repeated test situations encountered by individuals in their group. Cultural differences, often difficult to observe and measure, are obviously very important. In my view, in diplomacy and international relations, the interaction of interpersonal values and interests in international negotiations is a possible definition of the term "negotiation of cultural identifications." This term also includes various negotiations that take part in the ongoing process of building cultural identification. In this sense, it makes sense to include the activity of diplomacy (as a process of sublimation that relies on the arts of communication and negotiation, the request for recognition of the other/by the other). We believe that any identification is in fact relational and interpersonal. Negotiators coordinate their actions in accordance with the international mutual recognition standard. Lacan writes (1964) -"Undoubtedly, being negotiated is not, for the human subject, an exceptional situation contrary to the verbiage that concerns human dignity, or human rights. Everyone negotiates at all times and at all levels, because any light understanding of the social structure can be defined as an exchange" (p.10). [2] In the age of interactions in international relations, the increasing number of conflicts is growing due to cultural, ethnic or interpersonal differences. These conflicting trends often seek to be resolved through the international negotiation mechanism.

Cultural Identifications and International Negotiation

International negotiation is a complex and specific process by which two or more adversary of different nationalities interact with the aim of reaching an acceptable position given their conflicts and their differences. Just as the process of negotiating over divergent interests is influences by the parties' identities, the identities are shaped by the way the process is conducted. However, culture profoundly influences negotiation process, communication, cognition, and subjective behaviour of protagonists. More specifically, international negotiation of all types (political and diplomatic conferences, treaties, summits, economic and commercial contracts, scientific exchanges and congress, etc.) is always affected by cultural phenomena which can make relations difficult and non-transparent. Successful international negotiations require an understanding of the negotiation style of those on the other side of the table, and the acceptance and respect of their cultural beliefs and norm. On the other way, ignoring and negligent culture differences can create barriers that hinder agreements or complicate the unfurling of the negotiation process. Knowledge of the culture and values of the protagonists could have a positive effect on the perception of the country and on the communication of negotiators. By setting behavioural norms, boundaries between good and evil, culture influences how negotiating actors will seek to understand, integrate the culture of the other (including, on how to reason, analyze the situation and seek solutions). In this sense, culture promotes certain acts of communication and prohibits others. If we take into account the fact that each individual belongs to several groups (sometimes family, sometimes friends, sometimes the nation), which do not perfectly intersect the groups of others, any encounter between two individuals (adversaries) implies a greater or lesser degree of interculturality. In this regard, Moscovici (1984) wrote "The negotiation is a dialogue, a joint product of two negotiators, each acting in a way defined by their role and gradually transforming into a kind of soliloquy with several voices and using conformity. He adds "It is more accurate to think of compliance as a form of negotiation between the individual and the group, which engages about a conflict over how to define reality." (p. 42). [3] The preparation of the negotiation plays a crucial role and depends very much on the goals and motivation of opponents in conflict or who must resolve international conflicts together. From Pruitt's point of (2015)

"Except when there is substantial third-party pressure for settlement, participants in intractable conflict will only enter negotiation if they are motivated to end the conflict and optimistic about negotiation's chances of success. Also there were two main channels of communication, each channel providing credibility to the other and serving as a back-up if the other failed. In two of the cases the communication was face-to-face and friendly, but in the third it was distant and mediated by a chain of two intermediaries. A possible reason for this difference is that the parties were positively interdependent in the first two cases but not in the third" (p.59) [4]. Moreover, in the crucial situations of this communication, the way negotiators express themselves is a creation. Each time, it takes original forms and even if the protagonists use a common or similar language code and have to formulate the same message, we can assure that they will never express themselves in the same way. In international negotiation, these communication variables are included in the category of variables, related to the encounter between actors (internal and external communication with the opposing party, detailed sequencing of messages, language styles, psycholinguistic aspects, accuracy of translation and interpretation, intercultural ethics, etc.) and depend mainly on the political and ideological orientations of the protagonists and the characteristics of their personality (attitudes to risk , self-control, self-esteem, resistance to stress, confidence, etc.). The communication variables are also interdependent with other variables in international negotiation: dynamic variables (movement) during their course (strategic choice, terms of negotiation), behavioral and cognitive variables. [START_REF] Dupont | La négociation : conduite, théorie, applications[END_REF]Kremenyuk 2002). In addition, knowledge of the adversary's culture and values could have a positive effect on the perception of the country and on the mutual perception of negotiators. That's why culture represents a major risk factor in international negotiation. I think that some cultural variables influence the strategy and the cognition of negotiators, including 1)theirs values and beliefs, 2) their mode of communication, 3) national stereotypes and prejudices, 4) previous conflicts, nationalism and chauvinism, 5) social and economic practices, 6)modes of political authority, 7) future perspectives in international interactions, etc. They will have to be harmonized in order to establish the appropriate strategies and tactics required to reach an easy solution. The methods of negotiation vary with culture.

The actions of protagonists are often affected by cultural variables and group stereotypes (considered as 'pictures in our heads' by Lippmann, 1922) or rigid or over-simplified judgements, which lead people to judge others in terms of their ethnic identity rather than specific information [START_REF] Kruglanski | The psychology of being 'right': The problem of accuracy in social perception and cognition[END_REF]). Bion's observations about the role of group process in group dynamics are set out in Experiences in Groups where he refers to recurrent emotional states of groups as basic assumptions. According to certain researchers [START_REF] Druckman | Negotiations, social psychological perspectives[END_REF]Walton and McKersie, 1965;[START_REF] Zartman | International Multilateral Negotiation[END_REF], cultural variables are an obstacle in international negotiation. They often cause mistrust, hostility and jalousie with regard to the other. In addition, negative cultural variables propagate conflicts and perversion in the moral psychopathology and degrade the interpersonal and international relations. On the other hand, other researchers consider that cultural national variables can be positive and capable of acting as a facilitation factor to minimise conflicts and increase empathy between negotiators [START_REF] Kremenyuk | International Negotiation: Analysis, Approaches, Issues[END_REF]Pruitt, 1992, Radtchenko-Draillard, 2011). Finally, the influence of cultural variable's on the behaviour of protagonists and their proposals during negotiation (either as an obstacle, or facilitator) can also pursue different needs associated with different motivations, such as the need for closure, fear of invalidity or need for structure or specific conclusions. The specificity of the decision making process during an international negotiation therefore lies in the comprehension by negotiators, whose capacity of logical reasoning is closely linked to the realization of their own needs and interests. Their goals are sometimes dependent on unforeseeable circumstances or the unpredictable. Walton and McKersie (1965) consider that "The negotiators are subjected of three tendencies which determine their behaviour, namely: first tendencies urge negotiators to sign agreements favourable at the opposite party (which can be an out-group or different country); second tendencies urge negotiators to sign agreements favourable on their own group (which can be an in-group or their own country ); third tendencies urge negotiators to sign agreements favourable an all parties (which can be two and more groups or country) or a compromise". [5]. For Druckman (1993), flexibility in negotiation is indicated by a variety of behaviors of protagonists which may be correlated. This choice reflects a willingness to accept a smaller payoff than is possible to obtain while trusting that the other will also cooperate. If he does not cooperate, you lose and he wins. There are risks involved in both cooperative and competitive choices: a cooperative choice may be exploited; a competitive choice may lead to mutual losses. He add "The conception of competitive and cooperative moves made corresponds to changing or not changing positions on issues during a negotiation. Cooperation consists of moving in the direction of the other's positions or away from one's own initial position, demonstrating flexibility. Competition consists of sticking to your own position in the hope that others will move toward that position, resulting in one's own position prevailing as the outcome of the negotiation. (...) Flexibility can be shown to occur in other ways and may be influenced by aspects of the situation other than (or in addition to) the opponent's moves or concessions. It can be reflected in the verbal exchanges between negotiators or in their perceptions of the situation and opponent. " (p.236-237) [6] In my opinion, first tendencies determine an interdependence oriented towards all desires of adversaries, where the convergent intentions are interconnected with recourse to cooperation and peace or alliance (positive effects of interaction); second tendencies reinforce an antagonistic interdependence where the divergent intentions are oriented towards a narcissistic desire and egoism with recourse to competition or perversion in the perception of the other (negative effects of interaction), third tendencies favourite a ambivalence toward interdependent objectives, where the divergent intentions of adversaries are oriented towards the partial satisfaction of desires and compromise (mixed effects). So, the decision making process could develop a different strategic pattern: 1) integrative (satisfactory agreement for everyone), 2) distributive (decision is beneficial to one protagonist gain and detrimental to the other), 3) compromise and consensual (intermediate or partial agreement for everyone, consensus), In applying his "mathematical theorem of negotiation" Nash considers (1950) "It is also possible to envisage a mixed strategy with an optimal solution and a point of resistance/anchor, which corresponds to the result below which the opposing party is likely to refuse to sign the agreement. It is termed the BATNAthe Best Alternative to the Negotiated Agreement, which can be flexible, modulated and variable during the international negotiation". (p.155-162). [7]. The uncertainties about the initiatives and the reactions of the opposite party are important and the negotiator is likely to act with much flexibility in difficult and unforeseeable circumstances. I would suggest that the choice of the strategic form of the decision making process mostly depends on the objectives of the negotiation, the intergroupal and interpersonal relations, the current and future international situation and the subjective particularities of the negotiator's personality (for example, confidence or defiance, empathy or jalousie with regard to other).

Subjective particularities in personal cognition and the behaviour of the negotiators

The personality of the negotiator and the priorities of his actions in international negotiations determine his outcome. [START_REF] Rubin | The social psychology of bargaining and negotiation[END_REF] argue that individuals have personal predispositions that encourage them to act in a specific direction when faced with an anticipated or unforeseen element. In negotiation, these predispositions shape their perception of the people with whom they must interact and influence their negotiating strategies, the selection of information they will pass on to their opponents, their behaviours and expectations to the negotiating results. Finally, in interpreting the negotiation, they develop the concept of interpersonal orientation, which they define as "a relatively stable predisposition to act, favourably or not, to the behaviour and expectations of the adversary.

The negotiator is obliged to react to the competing demands of two fields: his own and that of the adversary; this dual reactivity is a role conflict resulting from its position at the border; this conflict can be represented in terms of psychological complexity -as a juxtaposition of images that the negotiator has with regard to representatives of the opposing party and the various factions of his own group, his political and ideological orientation and his own position When communicating with his adversary during international negotiations, the protagonist (political leader, chief) could use various sources of power: the power of coercion (threat, persuasion, bluff, overbid, etc.), the power of cooperation (competence, trust, rewards, etc.), the power of persuasion and accommodation, etc. The threat is a form of pressure very often used in competitive international negotiations: threatens to break the ceasefire, trigger war, economic blockade and embargo, breakdown of diplomatic relations or breakdown of negotiations.

It should also be remembered that, more often than not, international negotiations are beginning to take place between several representatives of each group; the original position than delegates. [START_REF] Iklé | How Nations Negotiate[END_REF] formulates three qualities essential to the good negotiator: he must be realistic, he must be flexible, and he must be patient. This model, proposed by [START_REF] Iklé | How Nations Negotiate[END_REF], was shown to be quite useful for distinguishing among different types of international cases in terms of their processes and influences. Negotiating solutions to such problems is difficult for several reasons. Key among the challenges is the needs to negotiate the information base, which can itself be a source of contention that can stall the decision processor, bring it to court. The negotiator also seeks different solutions in his intrapersonal thinking when solving problems in the search for individual, interpersonal and intergroupal/international interest. The point is to be able to think with a common concept the negotiator's different reasons to defend a particular solution. When the negotiation begins to develop the news solutions can appear and negotiator must the engage in a discussion with their own party to try to modulate their anticipation and their wishes. If some negotiators can be flexible, they can be faced to intransigence on the part theirs counterparts. who have a high level of self-esteem (negative factor" (p.37-38) [12]. At present, this anxiety analysis grid is suitable for the study of negotiations. Empirical analysis of national stereotypes in international negotiations through the use of simulations also highlights the fact that there is a link between the content of national stereotypes about its group and its opponent (other) negotiators and their choice of decision-making strategy. In my view, during the negotiation, developing confidence or ambivalence of wishes or distrust of others is a set of options for power techniques, which affect the nature of cooperation (alliances) or competition (conflicts) in interpersonal and international relations. I think that the negotiator (diplomat, political leader, head of state) can use the various sources of power of influence and attitudes in an international negotiation: coercive power and unfavourable attitudes (threat, challenge, indifference, jealousy, etc.) or cooperative power and favourable attitudes (competence, rewards, promises, trust, etc.). International negotiation is therefore an important and difficult activity. It must not only minimize conflicts or objections of interest, but above all create the value of "mutual understanding." Through international negotiation, the divergent wills of the negotiators seek from the outset to create this new reality through a process of transformation of the interests of each group or delegation and the main values of identity committed. Such a transformation is based on a tension between the distributional, mixed and integrative forces, whose relative and specific weight will give the activity its strategic orientation. Finding a good balance between these tensions sums up the art of "good negotiator" who must put his personal strength, experience, reflexive thinking and training at the service of understanding with opponents. I believe that the achievement of solving problem solving depends on the logical analysis of problem solving, the construction of motivation and the perception of rationality during a negotiation that is likely to influence mutual agreement.

Empirical analysis of the impact of personal and cultural factors on the course of negotiation

The main purpose of our empirical study is to analyze the three essential stages of negotiation:

the identification of the conflict and the means to resolve it; finding goals and selecting them in decision-making and their consequences. Knowing that it is also affected by cultural phenomena (differences in objectives, moral, political, economic or social differences, conflicts of the past, etc.), negotiators must absolutely combine them to reach the desired arrangement and then adapt strategies and tactics in order to reach mutual agreement.

According to my main hypothesis, the specificity of decision-making in the negotiation is in its understanding by adversaries, whose logical reasoning skills are closely linked to the achievement of their priority interests and objectives for their country, precisely (a)

negotiators, who are very convinced that their proposal is the best for them and the good of their country -choose the risk strategy; (b) negotiators, convinced that the integrative solution, combining their proposals and the proposals of their opponents, is the best way to reach a mutually beneficial agreement -choose the realistic or optimal strategy; (c) negotiators, who believe that they must gradually advance their proposals and, at the same time, analyse their opponents' proposals in a thorough and careful manner -choose the strategy of prudence. In addition, in seeking mutual agreement with adversaries, it is important that the negotiator properly assesses the probability of his success and failure, measures his personal expectations, wishes and adapts one of the trends of the Atkinson's theory of achievement motivation (1964) a) tendency to achieve success, b) tendency to avoid failure. It is a question of being able to think with a common concept the different reasons of the negotiator to defend a particular solution. According to this idea, the resolution of these trends implies a choice between two solutions or more equally possible but sometimes contradictory for adversaries (war or peace, authority or democracy, threat or diplomacy, hostility or mutual agreement, etc.) which is often determined by international negotiations, and can be understood by psychological vectors such as identity issues, the impact of political discourse Etc. It can also be added that cultural variables (values, prejudices, stereotypes, past experiences with another country), reinforced by the taking of the particular decision-making strategy and personal feelings towards their opponents influence the behaviour and cognitive process of opponents, especially at the beginning of the negotiation. I also applied in my presented a detailed and argued proposal with ease of implementing divergent ideas from other partners, they often used cooperation with exchanges of ideas and promises to have common strategy with others in their military actions, etc.). Then, Russian negotiators (USSR delegation) very often used the realistic strategy with some elements of the risk strategy and the strategy of prudence (e.g., they frequently used the exchange of concessions with the rapid evaluation of a proposal from their opponents and the presentation of a new flexible solution and incorporating elements of their first proposal and the proposals of others etc.). British negotiators (UK delegation) have very often used the realistic strategy, however, they were much more cautious during the outcome of an agreement (e.g., they often developed complementary proposals with elements of their opponents' proposal, but they expressed some scepticism and doubts about their opponents' proposals and frequently argued about the benefit of their main proposal, etc.).(See Figure n°1) . Through these processes, all negotiators had the tools to arrive at clear judgments and creative and acceptable solutions, influencing an integrative mutual treaty and a prospect of their future collaboration to fight their common enemy (Nazi Germany and allies). In conclusion, the Treaty of Tehran provided for the establishment of the second front in Normandy and Provence (France) and the definition of the final strategy for allied nations during the Second World War.

During the Yalta Conference (Crimea, USSR), American, British and Russian negotiators (as allied nations during the Second World War) essentially used a realistic or optimal strategy with an integrative proposal and globalizing the wishes of all participants. Their cooperative tactics (e.g., reciprocity, promises, rule-making and logrolling) have been very effective in this conference. Empirical analysis highlights the fact that realistic or achievement strategy was predominant in the actions of all negotiators. Specifically, American negotiators (USA delegation) have very often used realistic strategy with some elements of the risk strategy (e.g., they actively participated in the development of a reciprocal agreement with the exchange of ideas and logrolling and globalized solutions beneficial to all; they had empathetic attitudes and evaluated qualitatively and quickly proposals of opponents, etc.).

Then, Russian negotiators (USSR delegation) often used realistic strategy with some elements of the strategy risk and prudence strategy (e.g., they sought convergent solutions with the definition of benefits for each stakeholder and they had emphatic attitudes with promises and confidences; they also used persuasion to convince the other protagonists during the discussion, etc.). British negotiators (UK delegation) often used realistic strategy with some elements of prudence strategy and risk strategy (e.g., they often used an exchange of concessions with opponents with the verification and evaluation of opponents' proposals; they had empathetic attitudes with flexibility in preparing the agreement, etc.). Despite these few discrepancies in the behaviour and cognition of negotiators, these findings attested to the significant preponderance of integrative interventions, linked to the use of realistic strategy or achievement. (This largely confirms our first hypothesis) Just as action between adversaries would only make sense in the light of a shared intention, building itself during the negotiation.

In our view, the evolution in the negotiating dimension was consistent with its homogeneity.

(See Figure n° 2). The mutual agreement (Treaty of the Three Great Powers) provided for the capitulation of Germany unconditionally, the division of Germany into the fourth parts (United States, United Kingdom, USSR and France), military intervention in Japan, and it also proclaimed a declaration on "free Europe" with the division into two blocs (Western and Eastern) and the accession to the United Nations project. With regard to the personal satisfaction of the negotiators (after the Yalta Conference and the official press statement), all the negotiators (Americans, Russians and British) seemed to be very satisfied with the outcome of the conference and expressed a desire to continue their negotiations.

At the Potsdam Conference (Germany), American negotiators (USA delegation), Russian negotiators (USSR delegation) and British negotiators (UK delegation) most often use mixed strategies. During this conference, all negotiators regularly used the argument and definition of preferences for each party, and often used the segmentation technique (for example, breaking down an object into several parts and treating them separately). The American negotiators (USA delegation) exchanged ideas with the protagonists in order to find "common ground" and often used the elements of the risk strategy (e.g. they quickly presented the proposals at the beginning of the negotiation and assessed all the proposals of the other opponents, putting forward differing points of view in order to reach an agreement, etc.). The Russian negotiators (USSR delegation) put forward proposals converging with those of the opposing parties (realistic or optimal strategy), but they also used the risk strategy elements (e.g., they quickly evaluated all proposals with their detailed summary; they often used persuasion to convince others, but at the same time they also looked for convergent solutions to reach an agreement, etc.). The British negotiators (UK delegation) argued for the plausibility of their own solutions (e.g. they conducted an in-depth analysis of the opponents' proposals with the request for additional information and defined preferences for each party, security to the Security Council, which may meet whenever peace is threatened. According to the Charter, the United Nations has four purposes: 1) to maintain international peace and security; 2) to develop friendly relations among nations; 3) to cooperate in solving international problems and in promoting respect for human rights; 4) and to be a centre for harmonizing the actions of nations. The Security Council is composed of fifteen Members:

five permanent members with the right of veto: China, France, Russian Federation, the United Kingdom, and the United States, and ten non-permanent members elected for two-year terms by the General Assembly All members of the United Nations agree to accept and carry out the decisions of the Security Council. While other organs of the United Nations make recommendations to member states, only the Security Council has the power to make decisions that member states are then obligated to implement under the Charter.

In conclusion of this analysis it should be added that the negotiation process depends mainly on political, diplomatic and international objectives, as well as the cultural and interpersonal characteristics of the protagonists, in accordance with our first hypothesis. (See Figure n°4)

Moreover, there was also an effect under homogeneous conditions: the positive interpersonal actions of the State have a significant impact on interpersonal relations during the negotiations, however, the very important and effective agreements reached (treated) at the end of the Potsdam Conference did not fully satisfy the interests and personal objectives of the main actors (second hypothesis was therefore partially confirmed). It should be added that the change of the Head of Delegation of the United States and the United Kingdom (President Truman and Prime Minister Attlee in the last part of the negotiation certainly influenced the relations between the negotiators and in particular with the head of the delegation of the USSR Stalin; because the atmosphere during this conference was tense. After this conference, there was a breakdown in relations between the Allies, which contributed to the bipolarity of the World and the beginning of the Cold War.

CONCLUSION

In an era of ongoing interactions in international relations, many important political, security, economic and environmental interdependencies are closely linked to the growing number of conflicts caused by cultural differences and interpersonal conflicts. In reducing these conflicts, international negotiations can be defined as the science and art of reaching mutually acceptable agreements. My empirical study is based on an analysis of the main cultural and personal variables and in particular on the behaviour and cognition of negotiators. In this sense, I have interpreted their impact on the three main decision-making strategies of the negotiators (risk strategy, realistic or optimal strategy and prudence strategy). Given the complexity and specificity of the international negotiations analysed, as well as the many analytical approaches used in my analysis, I was able to analyze the link between a realistic decision-making strategy, integrative tactics, positive cultural variables (cultural similarities, alliances in the past, favourable intentions and positive stereotypes) and positive feelings and favourable attitudes towards opponents. I also found that there is another link between risk strategy, distributive tactics, negative cultural variables (significant cultural differences, past conflicts, negative prejudices and stereotypes, etc.) and negative feelings and attitudes towards other adversaries. In addition, I have found that there is an intermediate link between the prudent strategy, mixed tactics, mixed cultural variables and the ambiguous feelings of adversaries (influenced by difficult negotiating conditions, including information imperfection, competing interests, risks, ambiguous attitudes, etc.); in the case of the implementation of this prudent strategy the negotiation process is often unclear, uncertain, chaotic, and does not exclude surprising and unexpected changes in the outcome phase of an agreement. I also found that the integrative choices of negotiators correspond to changes in positions where flexibility is defined as a cooperative process to advance realistic strategy and distributional choices correspond to non-changes in position where rigidity is presented as a persistence in maintaining a position over the risk strategy. (This largely confirms my first main hypothesis). However, beyond this distinction, I found that in the negotiations discussed

  several individuals have to define a position together in relation to another group. In this regard, it is important to distinguish the different roles of protagonists in international negotiations: (a) the protagonists, who act as representatives of their group or country; b) experts who are present to advise negotiators, provide information and arguments, and prepare proposals and counter-proposals; (c) the president in multilateral international negotiations, who has a role to introduce debate, distribute speech, enforce procedural forms and fixed schedules, etc.; (d) groups of negotiators (delegations): in the case of international negotiations where two parties are involved, each delegation is facing the other and when there are more than two delegations, the phenomena become more complicated because of the multiple roles and goals of different delegations. From the point of view[START_REF] Hermann | Effects of negotiators 'personalities on negotiating behavior[END_REF] the leaders are more flexible during negotiations and show more independence from

[ 10 ]

 10 Ryan and Deci's theory of self-determination(1985) also provides some very important elements. According to this theory, motivation is based on two essential needs: a) the need for competence, b) the need for self-determination.Ryan and Deci (2000) distinguish the self-determination continuum showing three types of motivation with their regulatory styles, their rules of causality, and corresponding processes "1) intrinsic motivation based on the theory argues, that social-contextual events (e.g., feedback, communications, rewards) that conduce toward feelings of competence during action can enhance intrinsic motivation for that action; accordingly, optimal challenges, effectanceprorooting feedback, and freedom from demeaning evaluations were all found to facilitate intrinsic motivation , 2)extrinsic motivation based on-the extrinsically motivated behaviors that are externally regulated; such behaviors are performed to satisfy an external demand or reward contingency; 3) amotivation results from not valuing an activity when amotivated, people either do not act at all or act without intent--they just go through the motions". (p. 70-73)[11]. In addition, according to the empirical studies of Radtchenko-Draillard (2011), anxiety (high level) may play a different role in the problem-solving process during negotiation: a) it can stimulate anticipation, the development of the most creative, unusual solutions and the development of intrinsic motivation among negotiators, who have a high level of self-esteem (positive factor); b) it can promote developed argumentation, persuasion, preferences for global solutions in agreement with the adversary among negotiators, who have an average level of self-esteem (positive factor); (c)it may increase the justification of its initial position, the disapproval of certain solutions of the adversary with the analysis of their "disadvantages" among negotiators, who have a low level of self-esteem (negative factor). On the other hand, anxiety (low level) can lead to excessive confidence in one's own solutions and a lack of thorough verification in the problem-solving process among some negotiators,

  empirical study the concept of Rubinstein's externalization (1957) according to which "... all the psychic phenomena of personality find their explanation in the very unified node of internal conditions by which external influences are transformed and external causes act, in turn, by internal conditions that also develop as a result of external actions(1957, p.257) outcome of an integrative and mutually beneficial agreement for all can influence the level of satisfaction of the protagonists and strengthen the positive personal variables and the interdependence of their relations. In order to test my hypotheses as part of my empirical study, I have developed the qualitative analysis grids for the choice of the decision-making strategies during an international negotiation which measures: 1) the valuation of distributivism (rigid), of interactivity (flexible) and of mixed behaviours; 2) the measurement of choice decision-making strategy (divergence-convergence; fluidity of rational inferences/impulsiveness of wishes/scepticism; game of options of attitudes; 3) the result of the agreement). It includes the following types of personal interventions: a) interventions related to risk decision making strategy and based on the quick evaluation of proposals, divergent and fluid ideas, b)interventions related to realistic or optimal decision making strategy and based on the reasoned analysis of proposals, convergent solutions; c)interventions related to the decision making strategy of prudence, based on hesitation, exhaustive verification of proposals and difficult for these acceptation. (See Annexe). This grid was tested and validated during our preliminary study of 64 subjects of different nationalities who participated in the simulation of international negotiation in the laboratory (formal negotiation) During my experimental study, I examined three international conferences: 1. The Tehran Conference in Iran (1943, November 28th -December 2th) with Roosevelt as chief negotiator for the USA, Churchill as chief negotiator for the United Kingdom, Stalin as chief negotiator for the USSR; 2. The Yalta Conference in USSR (Crimea, Russia) (1945, February, 4-11th) with Roosevelt as chief negotiator for the USA, Churchill as chief negotiator for the United Kingdom, Stalin as chief negotiator for the USSR; 3) The Potsdam Conference in Germany (1945, Juliet 17th-August 2th) with Truman as chief negotiator for the USA, Churchill and Attlee as chiefs negotiators for the United Kingdom, Stalin as chief negotiator for the USSR. I first studied the cultural factors (antecedents, conflicts in the past, aims, and cultural stereotypes) and subjective attitudes of the protagonists towards their adversary on their choices of decision-making strategy, of attitudes and of behaviour in the initial phase. I also analysed also the effects of the international negotiations process (principal phase or discussion phase). I finally analysed the result (mutual agreement) and the perspective of this agreement within international relations. Using the official documents of the conferences (documents from the archives of the meetings and official treaties signed at the end of the negotiations) I carried out the empirical and statistical analysis of the interventions of three delegations (USA, USSR, UK) during these conferences. This analysis assesses the level of frequencies or repetitions (very rare, rare, from time to time, often, very often) of interventions corresponding to one of the three strategies of decision-making. The stake of the research is to analyze the role and the consequence of the principal negotiations in the resolution of international conflicts (during the Second Word War and The Great Patriotic War for USSR (of 1941-1945 Precisely, during the Tehran (Iran) Conference, American negotiators (USA delegation) often used realistic strategy or achievement with some elements of risk strategy (e.g., they

  proposed compromises and sometimes expressed an ambivalent attitude with scepticism towards certain proposals or pointed out the disadvantages, etc. for example, they justified them -risk strategy, etc.). (See Figuren°3) This mutual agreement (treaty) provided for the pacification, disarmament, denazification of Germany, the trial of war criminals, and the mutual initiative for the creation of the United Nations with the Security Council at the san Francisco conference, USA (1945, 26 June). Just as the process of negotiating on competing political interests is influenced by the identity and subjective specificities of the parties, these factors are shaped by the way the process is conducted. The decisions of the Potsdam Conference after their publication were supported by other countries around the world. In order to maintain world peace and reduce the various inter-ethnic and international conflicts the United Nations Charter established six main organs of the United Nations, including the Security Council. It gives primary responsibility for maintaining international peace and

Figure n°1 :Figure n°3 :

 n°1n°3 Figure n°1: Histogram of the frequency of interventions by negotiators from three countries (USA, USSR, UK) using decision-making strategies (risk strategy, realistic strategy, and prudence strategy) during the Tehran conference

Tehran (USSR) Tehran (UK) Yalta (USA) Yalta (USSR) Yalta (UK) Potsdam (USA) Potsdam (USSR) Potsdam (UK)

Annexe:

Psychoanalytic grids for the thinking and decision-making strategy of negotiators during the negotiation

A. Risk strategy:

A (1) The negotiator quickly and easily presents all the proposals the initial phase.

A (2)

The negotiator quickly evaluates all proposals and summarizes the opponent's proposals initial phase. A (3) The negotiator easily puts forward divergent points of view and proposes his solutions to reach an agreement in the discussion phase. A (4) The negotiator uses coercive attitudes, distributive attitudes (threat, bluff, higher offer, cunning, ultimatum, contempt, etc.) and self-determination to promote its solutions; it's uncompromising approach to his opponent's solutions in the discussion phase. A (5) Negotiator presents unusual and crucial solutions without hesitation (in a trading area) in the final phase. A (6) The negotiator is overconfident about their proposals and critically analyses the opponent's proposals in the final phase.

B. Realistic strategy or achievement B (1)

The negotiator presents a detailed and thoughtful proposal in the initial phase. B (2) The negotiator gives an in-depth analysis of the opponent's proposals and asks it defines preferences for each part in the initial phase.

B (3)

The negotiator proposes an additional or comprehensive proposal with elements and builds an " BATNA or a cognitive agreement zone" in the discussion phase. B (4) The negotiator uses cooperative attitudes, empathetic attitudes (exchange of ideas, logrolling, promises, trust, reciprocity, etc.) in the discussion phase. B (5) The negotiator looks for convergent proposals in a flexible manner with the opponent in the final phase.

B(6)

The negotiator is involved in the development of a reciprocity agreement and solutions of both parties in the final phase.

C. Prudence strategy C(1)

The negotiator asks the adversary for information and information and has ambivalent opinion of the opponent's proposals in the initial phase.

C(2)

The negotiator hesitates, is equivocal and slow in the presentation of his proposal or presents sequences proposal in the initial phase. C(3) The negotiator performs deductive analyses and controls (with doubt and anchoring) of the opponent's solutions during the discussion phase C(4) The negotiator uses ambivalent attitudes, sceptical attitudes (distrust, hesitation, possibility of circumstances, etc.), and he disagrees with the solutions and points out their disadvantage of the discussion phase.