Fanchao Meng

Coraline Lapre

Cyril Billet

Goëry Genty

AND John M Dudley
email: john.dudley@univ-fcomte.fr

Instabilities in a dissipative soliton-similariton laser using a scalar iterative map

Numerical simulations of a dissipative solitonsimilariton laser are shown to reproduce a range of instabilities seen in recent experiments. The model uses a scalar nonlinear Schrödinger equation map, and regions of stability and instability are readily identified as a function of gain and saturable absorber parameters. Studying evolution over multiple roundtrips reveals spectral instabilities linked with soliton molecule internal motion, soliton explosions, chaos, and intermittence. For the case of soliton molecules, the relative phase variation in the spectrum is shown to be due to differences in nonlinear phase evolution between the molecule components over multiple roundtrips.

There is currently much interest in the real-time characterization of mode-locked dissipative soliton fiber laser dynamics. Dispersive Fourier Transform measurements of spectral variations are a particular focus, revealing soliton build up dynamics [1][2][3][4][5], soliton molecules with internal motion [6,7], and soliton explosions and pulsations [8][9][10][11][12][13][14]. Work has also reported complex intermittence where a laser randomly alternates between sequences of metastable molecules, explosions, and chaos [15].

Although measuring such instabilities has been relatively straightforward, interpreting the underlying physics has proven more difficult. Certainly insight has been obtained from complex cubic quintic Ginzburg-Landau equation (CGLE) studies [16][17][18][19], as well as iterative map simulations based on nonlinear Schrödinger equation (NLSE) modelling for fiber segments, and suitable transfer functions for other elements [6,8,[20][21][22]. However, although these approaches have reproduced some results seen experimentally, simulations have generally considered specific descriptions for key components, such as saturable absorption based on nonlinear loop mirrors [22], vector polarization evolution [20], or rate-equation gain dynamics [6,8]. The question remains to what degree instabilities observed experimentally can be reproduced using more generic models.

In this Letter, we simulate a dissipative soliton laser using an iterative cavity map based on only scalar NLSE propagation and widely-used models for gain and saturable absorption.

= 1.1 × 10 -3 W -1 m -1
. Net cavity GVD is +0.22 ps 2 . (b) Evolution of temporal (blue, left axis) and spectral (red, right axis) widths for stable single pulses (q 0 = 0.9, P sat = 150 W, E sat = 0.4 nJ, g 0 = 0.78 m -1 ).

Although saturable absorbers in many lasers use nonlinear polarization evolution, our ability to reproduce instabilities seen in experiments with a scalar model highlights the role of basic NLSE dynamics. Moreover, we generate a detailed stability map of laser operation, and explicitly reproduce both internal motion dynamics of soliton molecules, and complex sequential instabilities.

We consider a soliton-similariton laser [23,24] as in Fig. 1, with normal group velocity dispersion (GVD) Erbium-doped fiber (EDF) , anomalous GVD single-mode fibre (SMF1 and SMF2), a saturable absorber (SA), and a spectral filter. The parameters (see caption) are adapted from Ref. [15]. Each fiber segment is modelled by a modified scalar NLSE [23]:

∂A ∂z = - iβ 2 2 ∂ 2 A ∂τ 2 + ĝ 2 A + iγ|A| 2 A. (1)
Here, A = A(z, τ) is the pulse envelope with z the propagation coordinate and τ co-moving time. β 2 and γ are the GVD and nonlinearity parameters for each segment. To study the ability of the simplest model to reproduce complex dynamics, higher-order terms are not included. The EDF gain is:

ĝ(ω) = g 0 /(1 + E/E sat ) × 1/(1 + Ω 2 /Ω 2 g
) where g 0 is the unsaturated (small signal) gain, and Ω g corresponds to a 40 nm gain bandwidth. E = |A| 2 dτ is the intracavity energy, and E sat is a gain saturation parameter [25]. Ω = ωω 0 is the (angular) frequency detuning, with ω 0 corresponding to a wavelength of 1550 nm. The saturable absorber is described by the function [23]: T(τ) = 1q 0 (1 + P(τ)/P sat ) -1 where q 0 is modulation depth, P(τ) = |A(z, τ)| 2 is instantaneous power, and P sat is saturation power. We use q 0 ≥ 0.7, consistent with previous modelling of similar lasers [26]. The spectral filter was a 10 nm intensity FWHM supergaussian with unity transmittance at line center. A lumped linear intracavity loss of 2.2 dB was applied after the filter to model output coupling and insertion losses. Simulations used 2 13 points, a 500 ps time span, and adaptive spatial steps. In this regime, this model has previously reproduced linearlychirped parabolic pulses as seen in experiment [15]. To study instabilities, we systematically varied the saturable absorber and gain parameters to identify regimes with qualitatively different behaviour. Figure 2 shows the different stability regions identified (see legend and caption) as a function of: (a) saturable absorber parameters (q 0 , P sat ) at a fixed gain setting and (b) gain parameters (g 0 , E sat ) for a fixed saturable absorber setting. The parameter range considered encompassed values used in similar studies [21,23,26].

The initial conditions used for Fig. 2 were single and double gaussian pulses (2 ps FWHM), injected at Point A in Fig. 1. The parameter spaces were finely gridded and the behaviour of the model was studied towards either convergence or instability. For some parameters, the seed rapidly decayed, corresponding to the below-threshold region. We sought convergence up to 10 5 roundtrips but in many cases, steady state was reached at only several 100's of roundtrips. We describe Fig. 2 as follows. The green region corresponds to convergence towards a stable single pulse. These single pulse states were found to be insensitive to a wide range of initial conditions: pulse durations of 1-30 ps and peak powers of 0.1 mW-10 W. Even when seeded from noise, the simulations still converged to a final state depending only on the laser parameters. Noise seeds used ranged from a one photon per mode background to 100% (uniformly distributed) random intensity modulation.

The orange region corresponded to either stable single pulses or molecules depending on the initial conditions. In particular, single pulse seeds yielded ∼10 ps stable single pulse solutions, but if the seed was a double pulse with separation 40-200 ps, the simulations converged to a stable molecule with identical separation. This behaviour is consistent with similar modelling of stretched-pulse lasers, where attraction to the stable state is attributed to cross-phase modulation and nonlinear gain [27]. We note, however, that for other regimes, separations different from the seed have also been reported [28]. We also remark that when noisy initial conditions were used in this regime, simulations converge to either single or double pulses in a random way depending on the particular noise on the seed.

The blue region corresponds to only stable molecules being observed irrespective of initial conditions (i.e. even for single pulse seeds). Note that the boundaries between the regions in Fig. 2 depend weakly on the separation used for the doublepulse initial conditions. For purposes of reproducibility, we plot results here for a separation of 150 ps.

The steady state pulse energy varied over the stability map as follows. For Fig. 2(a): green region (2.0-2.6 nJ ); orange region (2.2-2.9 nJ single pulses, 2.2-3.1 nJ double pulses); blue region (2.3-3.1 nJ). For Fig. 2(b): green region (12 pJ-0.73 nJ ); orange region (0.68-1.7 nJ single pulses, 0.70-1.8 nJ double pulses); blue region (1.5-2.9 nJ).

As discussed above, double pulse seeds of separation 40-200 ps resulted in stable molecules (orange and blue regions in Fig. 2). However, decreasing the separation below ∼40 ps was found to induce variation in the relative phase between the molecule components, arising from enhanced interactions between the pulse tails [28,29].

Such phase variations manifest experimentally through changes in the fringe structure of the molecule spectrum with roundtrips [30], previously seen in real time spectral measurements [2,6,7,15]. Specifically, for a molecule consisting of two pulses centred on ω 0 with temporal separation T and relative phase ϕ, the spectrum is:

S(ω) = | Ẽ(ω -ω 0 )| 2 (1 + cos[2π(ω - ω 0 )/Ω p + ϕ])
where Ẽ(ωω 0 ) is the spectral amplitude of each pulse, and Ω p = 2π/T gives the frequency separation between adjacent fringes in the spectrum. As ϕ varies with roundtrip, the fringe structure is then displaced.

Our model reproduces this behaviour, and Fig. 3 shows two examples. Fig. 3(a-d) corresponds to Point 1 in Fig. 2(a) with P sat = 170 W, q 0 = 0.87. Here Fig. 3(a) shows the time-domain profile of the molecule at the EDF output after a particular roundtrip, and by following the spectrum over 500 subsequent roundtrips (zooming into a 10 nm span near 1550 nm), Fig. 3(b) shows the spectral modulation oscillating with a ∼65 roundtrip period. The relative phase between the molecule components can be extracted from the spectrum [30] or in our case directly from the complex field, and is shown in Fig. 3(c).

This oscillatory phase has been described as analogous to molecular vibrations [6], attributed to roundtrip-to-roundtrip peak power oscillations experienced by the two components of the molecule [29]. These oscillations are seen in our simulations, and shown in Fig. 3(d) at the EDF output. They arise physically from pulse tail-mediated interaction and the effects of gain and loss, including gain saturation [31]. Our simulations confirm quantitatively that these oscillations induce the observed spectral phase variation. Specifically, consider two pulses in a molecule of peak power P 1 (z) and P 2 (z) as they circulate at any point in the cavity z. Accounting for the different nonlinearity of the cavity segments by a z-dependent γ(z), the difference in nonlinear phase between the component pulses δφ k+1 after roundtrip k + 1 is related to that after roundtrip k by δφ k+1 = δφ k + γ(z)[P 2 (z) -P 1 (z)]dz, where the integral is performed around the cavity (over the k-th roundtrip). From the simulations which yield peak power at every point in the cavity, it is straightforward to calculate this nonlinear phase and compare with the phase computed from the full field. For roundtrips above 250, Fig. 3(c) compares the phase variation calculated from the peak power integration (dashed black line) with that from the complex field (solid green line) and there is essentially exact agreement.

The results in Fig. 3(e-h) correspond to Point 2 in Fig. 2(a) with P sat = 250 W, q 0 = 0.87. At this higher saturation power, the relative phase between the molecule components shows linear displacement with roundtrip (sometimes referred as an infinite or diverging phase [6]) with periodic oscillation about this linear trend (see inset in Fig. 3(g)). Again computing the nonlinear phase variation from the peak power variation yields essentially exact agreement with that obtained directly from the simulation complex field.

These simulations yield insight into the conditions under which the different behaviour in Fig. 3 Outside regimes of stability or internal motion, the white regions in Fig. 2 correspond to simulations where no convergence was seen, and large temporal, spectral and energy fluctuations over multiple roundtrips. The evolution here depended sensitively on initial conditions, with different random noise yielding very different behaviour. Figure 4 shows typical results, using initial conditions of 6 ps pulses with uniformly-distributed 100% multiplicative noise. These conditions were found to reproduce transitions between qualitatively different behaviour over 100's of roundtrips as seen in experiments.

Figure 4(a) corresponds to Point 3 in Fig. 2(a) with P sat = 950 W, q 0 = 0.87. Figures . 4(b) and (c) correspond to Points 4 and 5 in Fig. 2(b) with E sat = 0.68 nJ, g 0 = 0.59 m -1 and E sat = 0.68 nJ, g 0 = 0.60 m -1 respectively. For all cases, we plot (top to bottom): energy fluctuations; spectral evolution; temporal intensity evolution; temporal autocorrelation function evolution. Although simulations yield the temporal intensity directly, we also plot the autocorrelation because it is this that is usually derived from experimental measurements [30]. These results are remarkable in yielding features of spectral evolution similar to those seen in recent experiments. Figure 4(a) for example shows intermittent molecule states (similar to experiments in Ref. [2]), Fig. 4(b) shows metastable molecule states interrupted by explosion dynamics (similar to experiments in Refs. [15,32]) and Fig. 4(c) shows the decay of a molecule state into essentially a broadband chaotic field with intermittent very short-lived single pulse states (similar to experiments in Ref. [15] ).

The conclusions are as follows. Firstly, a scalar model for a dissipative soliton laser has been shown to reproduce a range of instability behaviour seen in experiments. For soliton molecule evolution, the model reproduces oscillating and diverging phase, and in both cases allows the phase evolution to be associated with variations in peak power of the molecule components. To our knowledge, this is the first time that the link between peak power evolution and oscillatory or divergent phase has been shown quantitatively. Outside the stability regimes, a range of spectral and autocorrelation evolution dynamics were observed similar to recent experiments. It is particularly significant that although the results in Refs [2,15] were obtained using nonlinear polarization evolution as the saturable absorber mechanism, our simulations yield similar results assuming only scalar propagation and generic models for gain and saturable absorption. This suggests that the instabilities in recent experiments are not contingent on gain dynamics or nonlinear polarization evolution, but rather arise from basic NLSE interactions. Although quantitative comparison with experiment may require fully realistic models, the essential physical features can be reproduced using a simpler reduced approach. In the context of Fig. 4, our results confirm previous studies showing how complex instabilities appear to be intrinsic to the interaction between nonlinearity, dispersion and dissipation [16]. Of course, understanding how particular instabilities are triggered remains an open question, but we anticipate that the ability to study such problems using a scalar model will yield new general insights, also with regards to issues of multistability and higher-order molecule formation.

Funding. Agence Nationale de la Recherche (ANR-15-IDEX-0003, ANR-17-EURE-0002); Academy of Finland (298463, 318082 Flagship PREIN).

Disclosures. The authors declare no conflicts of interest.

Fig. 1 .

 1 Fig. 1. (a) Schematic: EDF, erbium doped fiber; SMF, single mode fiber; SA, saturable absorber. L AB = 11 m with β 2 = +40 × 10 -3 ps 2 m -1 , γ = 6 × 10 -3 W -1 m -1 . L SMF1 = 2.42 m and L SMF2 = 7.8 m with β 2 = -21.7 × 10 -3 ps 2 m -1 and γ= 1.1 × 10 -3 W -1 m -1. Net cavity GVD is +0.22 ps 2 . (b) Evolution of temporal (blue, left axis) and spectral (red, right axis) widths for stable single pulses (q 0 = 0.9, P sat = 150 W, E sat = 0.4 nJ, g 0 = 0.78 m -1 ).

Figure 1 (

 1 Figure 1(b) plots stable single pulse intracavity evolution.In this regime, this model has previously reproduced linearlychirped parabolic pulses as seen in experiment[15]. To study instabilities, we systematically varied the saturable absorber and gain parameters to identify regimes with qualitatively different behaviour. Figure2shows the different stability regions identified (see legend and caption) as a function of: (a) saturable absorber parameters (q 0 , P sat ) at a fixed gain setting and (b) gain parameters (g 0 , E sat ) for a fixed saturable absorber setting. The parameter range considered encompassed values used in similar studies[21,23,26].

Fig. 2 .

 2 Fig. 2. Stability regimes as a function of: (a) saturable absorber parameters (q 0 , P sat ) at fixed E sat = 0.4 nJ, g 0 = 0.78 m -1 , and (b) gain parameters (g 0 , E sat ) for fixed P sat = 150 W, q 0 = 0.70. The colored legend describes the different regimes (see text). In (a) the red points (1, 2) correspond to the soliton molecule results in Fig. 3. The red points (3, 4, 5) in (a) and (b) correspond to the results in Fig. 4.

  is seen. Specifically, if the peak powers of the constituent pulses vary about a common mean as in Fig 3(d), then the average position of the fringes remains constant with roundtrip but the fringes display periodic oscillation. In contrast, if the peak powers of the pulses vary about distinct means as in Fig 3(h) then the fringes show an overall linear displacement with roundtrip and also display oscillation about this linear trend.

Fig. 3 .

 3 Fig. 3. Molecule internal motion. Results in (a-d) correspond to point 1 in Fig. 2(a) and show oscillating phase. We plot: (a) temporal intensity showing trailing (blue) and leading (red) pulses at one particular roundtrip. Following 500 roundtrips we show: (b) spectral evolution over a 10 nm span showing oscillations; (c) corresponding phase evolution computed from the simulated field (green), and calculated only from the peak power (black dashed, shown from roundtrips 250-500); (d) peak power evolution for leading (red) and trailing (blue) pulses. Results in (e-h) correspond to point 2 in Fig. 2(a) for a diverging phase. The seed in both cases was a Gaussian double pulse with 14.5 ps separation.


domain: sdv shs

text:
Christel Renaud
email: c.renaud@groupe-esa.com

Marc Benoît

Frédérique Jourjon
email: f.jourjon@groupe-esa.com

Renaud Christel

Marc Benoit
email: marc.benoit@mirecourt.inra.fr

Jourjon Frédérique

An approach for

Keywords: viticulture, Life Cycle Assessment, grape characteristics, multi criteria rating, environment viticulture, Analyse du Cycle de Vie, caractéristiques du raisin, évaluation multicritères, environnement

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Social and economic pressure on the wine sector to adopt sustainability is growing. The key points of the French government's policy on ecological and sustainable development were formalized following an Environmental Round Table in 2007 (www.legrenelleenvironnement.fr ). The policy includes the new requirement for environmental information on mass consumption products from 2012 ("Act Grenelle 2", final version not published yet) and the target of a 50% reduction in the use of pesticides between 2008and 2018(ACT No. 2009-967). This is relevant to the wine sector.

French consumers embrace the tradition and natural aspects of wine and their affinity to it might be eroded by their evolving knowledge of production practices (Brugière, 2009). Protected Designation of Origin (PDO), wines embody the localized and traditional technical know-how (Lamine, 2005), but the PDO is only a guarantee of origin, but not environmental Comment citer ce document : Renaud, C., Benoit, M., Jourjon, F. ( 2010). An approach for evaluation of compatibility between grape quality and environmental objectives in Loire valley PDO wine production. In: Congrès Mondial de la Vigne et du Vin (p. 7 p.). Presented at 33. World Congress of Vine and Wine 8. General Assembly of the OIV, Tbilissi, GEO (2010-06-20 -2010-06-25).

Renaud C. et al., 33ème Congrès Mondial de la Vigne et du Vin, Tbilissi -Géorgie -20-27 juin 2010, in press quality (Hirczak, 2007). As the French are very concerned of the risk of agrochemical spraying on food crops (Credoc, 2009), the image of wine could be jeopardised by the use of 20% of pesticides (in mass) on 3.7% of French UAA in viticulture (Aubertot et etc., 2005). The French PDO wine producers are thus faced with this new societal and institutional demand. Similarly, if they wish to strengthen their position in the world market, they must take into account the environmental requirements of key international markets. It is then necessary to assist the wine industry in addressing this risk through the evolution of its practices towards being more environmentally friendly. The grape growers of the Loire Valley are seeking support for such development in environmental practices without damaging the quality of their wines.

This paper introduces the approach implemented in order to provide, to wines sector agents, inputs useful for choosing viticultural technical paths that meet the objectives of product quality and environmental quality in Loire Valley protected denominations of origin vineyards. This research is implemented in the frame of the scientific programme of UMT Vinitera * . The originality of this research is situated in product multi-criteria rating of quality and environment, which corresponds to a new research field emerging internationally, and in the adaptation of Life Cycle Assessment method to the wine grape production.

OBJECTIVES

This project aims to i) measure the levels of compatibility between indicators of grape quality (Qg) and of environmental quality (Qe) of the vineyard management technical paths † (TKPv) in these attributes ranging from antagonisitic to synergistic relationships, and ii) to identify, within the TKPv, the techniques responsible for these situations, in order to assist wine industry stakeholders in the choice of TKPv.

The research strategy intends to i) identify the diversity of existing vineyard management practices, ii) establish a typology of TKPv, iii) chose existing vineyard plots representing this diversity as an experimental device, iv) characterize the soil and climate of these plots as covariables, v) observe the TKPv on the plots for three years on the attributes of Qe and Qg, vi) confront Qe and Qp indicators of TKPv in a matrix structured in degrees of compatibility, vii) identify the parts of the process playing the main role on the TKPv position in the matrix, and viii) adapt the matrix into a tool for wine sector agents.

METHOD

This research focuses on grape production, which represents both a significant part of the environmental impact of wine (Gazulla et etc. 2010) and is a crucial aspect of the quality of the product. The two main cultivars of the central Loire Valley: cv. Chenin Blanc and cv. Cabernet Franc will be utilised. Measurements are planned for 3 consecutive vintages (2010-2012) and will be performed at the plot level (a single unit in the vineyard with homogeneous characteristics). The project will be conducted in conjunction with key stakeholders so it has strong application in the wine sector. LCA has been chosen for the evaluation of the environmental quality of the TKPv because it is the most complete tool in the field of global and multi-criteria assessment of environmental impacts (Boeglin et etc., 2005). It has recently been chosen, in a simplified form, to assess and display the environmental impact of consumer products in France, which directly concerns the wine industry. However, this method only deals with potential impacts (Jolliet and Crettaz, 2001). Appropriate models for impacts on biodiversity and soil quality are still under construction. Currently, estimation of the uncertainty of results remains difficult in agricultural LCA (Payraudeau et al, 2005).

The method is currently applied and adapted to agricultural systems (Audsley et etc., 2003, Brentrup et etc., 2004) and of particular interest to this research, perennial fruit production as well (Mouron et etc., 2006). Research utilising LCA in viticulture and oenology has been published (Aranda et etc. 2005;Petti et al, 2006;Pizzigallo et etc. 2006;Gazulla et etc. 2010), but have not addressed the method in detail for application in vineyard management.

This research is broken down into five stages:

Stage 1: Establishment of the experimental and observational network representing the diversity of TKPv of central Loire Valley PDO vineyards.

The diversity of TKPv existing in the region is identified by: -A survey of 100 grape growers with diverse socio-economic profiles, different production systems, from different PDO, in order to describe their TKPv on 300 plots. -A typology of TKPv from this survey and existing databases on 100 variables using the data mining platform CORON (Ducatel et etc. 2010), and Factorial Multiple Correspondence Analysis (FMCA).

The sample of plots used for the study will be selected by TKPv types in order to contrast potential Qe and Qg. Two networks will be designed: one comparing TKPv in the same environment (soil, climate) and the other observing TKPv in various environments.

Stage 2: Evaluation of Qg and Qe on the selected plots TKPv

The evaluation of Qg requires the following:

-The choice of grape quality criteria (biochemical, sensory, physical, microbiological, xenobiotics) through a survey with expert winemakers. -The measure of grape quality on the chosen criteria at harvest.

The evaluation of Qe requires the following:

-Adaptation of the LCA method for wine grape production (functional unit, impacts, completion of Eco-invent data base) following the iterative process of LCA. -Calculation of environmental impacts using LCA (Simapro software, Ecoinvent database).

An inventory of flux data will be made with grape growers once or twice a year depending on their practices traceability.

Stage 3: Evaluation of the compatibility of Qg and Qp for each TKPv

The environment (soil and vintage climate) will be characterised as co-variables through existing detailed cartography and annual weather data.

Comment citer ce document : Renaud, C., Benoit, M., Jourjon, F. ( 2010). An approach for evaluation of compatibility between grape quality and environmental objectives in Loire valley PDO wine production. In: Qe and Qg datasets will be crossed using Multiple Factorial Analysis (Escofier and Pagès 1998) and including environmental co-variables.

TKPv will be positioned in a matrix crossing Qg and Qe following the design of:

-A typology of Qg and Qe through a combination of criteria -A matrix of compatibilities between Qg and Qe using this typology Stage 4: identification, within TKPv, of vineyard management techniques responsible of TKPv position in QgXQe matrix

The key techniques influencing grape quality will be identified through literature review. The techniques causing the main environmental impacts will be identified both by LCA results on the experimental network and literature.

Stage 5: Development of a tool to assist the wine sector agents in their TKPv choices.

The tool will be developed from the matrix.

METHODOLOGICAL ISSUES

This approach identifies five main methodological issues. LCA adaptation to the grape production process and the treatment of complex data have been developed in previous articles (Renaud et etc., 2010 (a) and (b)). The relevance of considering 3 vintages for this study is the focus of this paper. The choice of grape quality indicators to be considered for Qg evaluation and construction of a tool to aid decision making will be developed in a subsequent paper.

In order to validate if a sample of 3 consecutive years will be sufficient to explore the potential variability of grape quality according to the climatic conditions, the CV of two grape quality indicators have been calculated on series of 2 to 30 consecutive vintages . This longitudinal data has been obtained from a sample of Loire Valley Cabernet Franc grapes from the same plot (Data sourced from INRA EU-1117 in the framework of UMT VINITERA).The indicators utilised are sugar (figure 1) and anthocyanins content (figure 2). The average CV for both criteria is stable and this increases with the number of years utilised.

Whilst affected by climatic variation, the sugar content's natural variation appears to be limited and most likely regulated by the grower's choice of harvest date. Even if the individual Sugar CV values vary 5 times more for a 3 year series than for an 8 years series, the average CV remains low (under 0.12).

Anthocyanins are subject to uncontrolled variations, with an average CV reaching 0.25, but with lower individual CV values variation than sugar. A consecutive sample of three vintages might not be sufficient to get results consistent with a longer period (i.e. 30 years). Concerning the proposed measurements for this research, the 3 vintages will need to be tested in comparison to present data and charts in order to determine if the sample is representative.

CONCLUSIONS

The expected results are i) the identification of TKPv diversity, ii) a built typology of Loire Valley TKPv for the studied cultivars, iii) an operational method to characterize TKPv by the relationship between Qe and Qg, iv) the positioning of each TKPv type within the QeXQg matrix, structured in increasing degrees of compatibility, v) a list of the vineyard management techniques responsible for this position in the matrix TKPv QeXQg, vi) an advisory tool developed with the actors from this matrix, vii) adapted LCA method for grape production processes in the Loire Valley, viii) results of methodological development on LCA which should benefit viticultural scientists and technicians wanting to use LCA for wine grape production. This work should also contribute to improve multi criteria methods for production processes evaluation.

These results should provide the wine industry the opportunity to increase its awareness of environmental issues and to further increase the environmental quality of grape production processes. The findings could contribute to changes in viticulture towards more environmentally friendly practices. This research could propose new tools for actors in charge of advising the wine sector and enable them to better integrate environmental objectives into the specifications of labelled productions, including PDO, in line with consumers and societal expectations.

BIBLIOGRAPHY

Audsley, E., Alber, S., Clift, R., Cowell, S., Crettaz, P., Gaillard, G., Hausheer, J., Jolliet, O., Kleijn, R., Mortensen, B., Pearce, D., Roger, E., Teulon, H., Weidema, B., van Zeits, H., (2003)

Figure 1

 1 Figure 1 and 2: CV of sugar and anthocyanins contents for 3 to 30 consecutive vintages series, cv. Cabernet Franc, Montreuil Bellay, Loire Valley (INRA EU-1117 in the framework of UMT VINITERA data)

  Comment citer ce document : Renaud, C., Benoit, M., Jourjon, F. (2010). An approach for evaluation of compatibility between grape quality and environmental objectives in Loire valley PDO wine production.

In: Congrès Mondial de la Vigne et du Vin (p. 7 p.). Presented at 33. World Congress of Vine and Wine 8. General Assembly of the OIV, Tbilissi, GEO (2010-06-20 -2010-06-25). Renaud C. et al., 33ème Congrès Mondial de la Vigne et du Vin, Tbilissi -Géorgie -20-27 juin 2010, in press

  Renaud C. et al., 33ème Congrès Mondial de la Vigne et du Vin, Tbilissi -Géorgie -20-27 juin 2010, in press fig. 2 : series CV and average CV per series size (in bold) of anthocyanins content at harvest in Cabernet F berries, Loire Valley

			fig. 1 : series CV and average CV per series size (in bold) of sugar
			content at harvest in Cabernet Franc berries, Loire Valley,
		0,4															0,4
		0,35															0,35
		0,3															0,3
		0,25															0,25
	CV	0,2														CV	0,2
		0,15															0,15
		0,1															0,1
		0,05															0,05
		0															0
		2	4	6	8	1 0	1 2	1 4	1 6	1 8	2 0	2 2	2 4	2 6	2 8	3 0	2	4	6	8	1 0	1 2	1 4	1 6	1 8	2 0	2 2	2 4	2 6	2 8	3 0
							number of years of the series		Renaud et al. 2010						number of years of the series		Renaud et al . 2010

Congrès Mondial de la Vigne et du Vin (p. 7 p.). Presented at 33. World Congress of Vine and Wine 8. General Assembly of the OIV, Tbilissi, GEO (2010-06-20 -2010-06-25).

  Renaud C. et al., 33ème Congrès Mondial de la Vigne et du Vin, Tbilissi -Géorgie -20-27 juin 2010, in press Aubertot J.N., Barbier J.M., Carpentier, A., Gril J.J., Guichard L., Lucas P., Savary S.,Savini I., Voltz M., (2005): Pesticides, agriculture et environnement. Réduire l'utilisation des pesticides et limiter leurs impacts environnementaux. Expertise scientifique collective, synthèse du rapport, INRA et Cemagref (France), 64 p. /agriculture.gouv.fr/sections/thematiques/alimentation/comprendre-informer/ Combris, P., Lecocq S., Visser, M., (1999): Price of Bordeaux and Burgundy wines : is quality important ?, INRA Sciences Sociales v. 12(1) p. 1-3, juillet 99. Ducatel B., Kaytoue M., Marcuola F., Napoli A., Szathmary L. (2010) : Coron : Plate-forme d'Extraction de Connaissances dans les Bases de Données, conférence RFIA (Reconnaissance de Forme et Intelligence Artificielle) -Caen 2010 Escofier B., Pagès J. (1998) Analyses factorielles simples et multiples ; objectifs, méthodes et interprétation. 3 rd edition., éd. Dunod, Paris. 284 p Gazulla C., Raugei M.,Fullana-i-Palmer P. (2010): Taking a life cycle look at crianza wine production in Spain: where are the bottlenecks?, International Journal of LCA (2010) Analyse du Cycle de Vie. 10ème Colloque international annuel du SIFEE, Evaluation, environnement et développement d'une agriculture durable, 20-24 juin 2005, Angers, France Petti L., Raggi A., De Camillis C., Matteucci P., Sára B. and Pagliuca G. (2006): Life cycle approach in an organic winemaking firm : an Italian case-study. 5th Australian Conference on LCA, Melbourne, 22-24 Nov. 2006, Renaud C. et al., 33ème Congrès Mondial de la Vigne et du Vin, Tbilissi -Géorgie -20-27 juin 2010, in press Pizzigallo A.C.I., Granai C., Borsa S. (2006): The joint use of LCA and « emergy » evaluation for Italian wine farms, Journal of Environmental Management 86 (2008) 396-406 Renaud C., Benoît M., Thiollet-Scholtus M., Jourjon F., (2010) a, Evaluation des impacts environnementaux des itinéraires techniques viticoles de production de vins AOP en Val de Loire : démarche d'adaptation de la méthode de l'Analyse du Cycle de Vie (ACV), proceedings VIII International Terroir Congress, June 14th-18th, 2010, SOAVE, ITALY (in press) Renaud C., Benoît M., Jourjon F., (2010) b, Proposal of approach for Evaluation of compatibility between grape quality and environmental objectives assessed by LCA in PDO wine production, Proceedings of 7th International Conference on Life Cycle Assessment in the Agri-Food Sector, September 22 -24, 2010, Bari (Italy), (in Press).

	Brentrup F. Küsters J., Kuhlmann H., Lammel J., (2004): Environmental impact assessment
	of agricultural production systems using the life cycle assessment methodology, I.
	Theoretical concept of a LCA method tailored to crop production Europ. J. Agronomy 20
	(2004) : 247-264
	Boeglin N. Veuillet, D. (2006) : Introduction à l'Analyse de Cycle de Vie (ACV), Note de
	synthèse externe, mai 2005, éd. ADEME
	Brugière F., (2009) : Pratiques culturales sur vignes et pratiques oenologiques : connaissances
	et opinions des Français, Viniflhor-Infos Vins et cidres n°160, Février 2009, p1-10.
	CREDOC, (2009), Baromètre des perceptions alimentaires MAAP/CREDOC 2009
	(synthèse),	9p.,	consulté	le	12/04/10	sur	:
	http:/15:330-337
	Hirczak M., (2007) : La co-construction de la qualité agro-alimentaire et environnementale
	dans les stratégies de développement territorial. PhD Thesis, Université Joseph Fourier,
	Grenoble I, institut de Géographie Alpine, 356p.
	Jolliet O., Crettaz P. (2001) : De la critique à la réalisation d'un écobilan, Ed. EPF de
	Lausanne, Suisse, 121p.
	Jolliet O, Saadé M., Crettaz P. (2005) : Analyse du cycle de vie: comprendre et réaliser un
	écobilan, Ed. Presses polytechniques et universitaires romandes, 235p.
	Lamine, C., (2005) : Santé et qualification des produits. Coopération de scientifiques et
	d'agriculteurs autour de la nutrition méditerranéenne, Natures Sciences Sociétés 13, 403-
	412 (2005)
	LOI no 2009-967 du 3 août 2009 de programmation relative à la mise en oeuvre du Grenelle
	de l'environnement, Journal Officiel de la République Française du 5 août 2009
	Mouron P., Scholz RW, Nemecek T., Weber O. (2006): Life cycle management on Swiss fruit
	farms: Relating environmental and income indicators for apple-growing, Ecological
	Economics 58 (2006) 561-578.
	Payraudeau S., Van der Werf H.M.G. (2005) : Analyse de l'incertitude associée au calcul des
	émissions azotées sur un groupe d'exploitations agricoles dans le cadre de l'application de
	l'

: Harmonisation of Environmental Life Cycle Assessment for Agriculture. Final Report Concerted Action AIR3-CT94-2028. European Commission, DG IV version at 20 august 2003, pp. 101. Comment citer ce document : Renaud, C., Benoit, M., Jourjon, F. (2010). An approach for evaluation of compatibility between grape quality and environmental objectives in Loire valley PDO wine production. In: Congrès Mondial de la Vigne et du Vin (p. 7 p.). Presented at 33. World Congress of Vine and Wine 8. General Assembly of the OIV, Tbilissi, GEO (2010-06-20 -2010-06-25). Comment citer ce document : Renaud, C., Benoit, M., Jourjon, F. (2010). An approach for evaluation of compatibility between grape quality and environmental objectives in Loire valley PDO wine production. In: Congrès Mondial de la Vigne et du Vin (p. 7 p.). Presented at 33. World Congress of Vine and Wine 8. General Assembly of the OIV, Tbilissi, GEO (2010-06-20 -2010-06-25).

ACKNOWLEDGMENTS

Special thanks to Gérard Barbeau, INRA, INRA EU-1117, UMT Vinitera, for providing the 30 year data set for Cabernet Franc, and to Justin Cohen for proof reading of the article.


domain: sdv sde shs

text:
EFFECTS OF AGRICULTURAL PRACTICES ON SPATIAL DISPERSAL PATTERNS OF FOUR GRASSLAND SPECIES

. A generalization of mowing impact according to dispersal modalities was highlighted by our results. Indeed, an effect of mowing on spatial patterns from functional traits connected to dispersion was showed by spatial analysis. For example, dispersal distances of barochorous species such as Ranunculus bulbosus is enhanced by mowing and grazing. In contrast, zoochorous grass (Festuca arundinacea) which have the theoretical capacities to produce expansive lateral spread up to 1 meter was limited in his expansion by cutting and grazing. This study showed that disturbance can play an important role in dispersal and the spatial structure of grasslands species.

Introduction

The effects of agricultural practices on floristic composition of grasslands are well known with a recent interest in plant traits. Plant traits are any morphological, physiological or phenological feature measurable at the individual level, from the cell to the whole-plant level, without reference to the environment or any other level of organization [START_REF] Violle | Let the concept of traits be functional![END_REF]. The identification of plant traits that explain responses of species to grazing or mowing intensity is one of the main tools in management of grazed systems (Weiher et al. 1999) but few studies investigate the management practice effects on plant spatial patterns involved in the maintenance of plant diversity. Spatial distributions in grasslands and meadows were mainly dependent on the vegetation propagation mode and the seed dispersal. Species with structures that favour wind and animal dispersal have better regional local invasion success. At smaller spatial scales, further research is required on the determining factors of dispersal and colonization patterns. Indeed, the natural dispersal capacities of plant can be modified by the effect of agricultural practices. Here, we explore agricultural practices effects on the plant spatial patterns of plant species showing different capacities of dispersion (anemochorous, barochorous and zoochorous sensu [START_REF] Grime | Comparative plant ecology: A functional approach to common British species[END_REF].

Materials and methods

We studied spatial patterns of two common grasses (Festuca arundinacea, Lolium perenne) and two forbs (Ranunculus bulbosus, Taraxacum officinale) choose for their dispersal characteristics and lateral expansion capacities sensu [START_REF] Grime | Comparative plant ecology: A functional approach to common British species[END_REF] (Table 1). F. arundinacea wasmainly dispersed by animals and its theoretical lateral spreadwas up to 1 meter. T. officinale was dispersed by wind and its lateral spread do not exceed 0.10 meter. T. pratense and R. bulbosus were grassland species with unspecialized dispersion mode with a lateral spread limited, respectively, to 0.25 meter and 0.10 meter. We established experimental grids on six permanent grasslands into clay-loamy soil at the experimental installation INRA-SAD at Mirecourt, France (6°81' E, 53°6') in May 2007. Three grasslands were grazed by dairy cows with a stocking rate of 1.5 UGB/ha/an and three were mowed twice a year. One experimental grid (4 x 4 m) was randomly selected in each permanent grasslands and coverage of species was recorded in each 1,600 (10 x 10 cm) quadrats. In order to identify major processes controlling dispersal patterns of four grassland species, presenting several dispersion modalities (anemochorous, barochorous and zoochorous sensu [START_REF] Grime | Comparative plant ecology: A functional approach to common British species[END_REF], we used two spatial analysis: 4TLQV and Tall French Hat Wavelet, adapted to grids sampling. With these methods, when the quadrat variances are plotted against block size, the peaks of these graphs are interpreted as the scale of the mapped phenomena i.e. the size of the patch and the zone of inflection of the curve was the size of the gaps [START_REF] Guo | Interpretation of scale in paired quadrat variance methods[END_REF][START_REF] Perry | A comparison of methods for the statistical analysis of spatial point patterns in plant ecology[END_REF]. All analysis were performed with Passage package [START_REF] Rosenberg | PASSAGE Pattern Analysis, Spatial Statistics, and Geographic Exegesis[END_REF].

Results and discussion

Impacts of mowing and grazing according to dispersal modalities were highlighted by our results (Table 1). Indeed, an effect of mowing and grazing on spatial patterns from functional traits connected to dispersion was showed by spatial analysis. However, the Tall French Hat Wavelett method does not give satisfying results.Dispersal distances of barochorous species Ranunculus bulbosus and unspecialized species Trifolium pratense were enhances by mowing and grazing. The size of the patch, highlighted by the spatial pattern analysis of R. bulbosus, increased and reached a maximum of 1 meter under grazed management (Table 1). In the case of T. pratense, the patch size was greater under grazing conditions than under mowing management (0.90 meter and 0.50 meter, respectively) (Figure 1). The grazing can locally reduce aboveground competition with others species in the community by increasing the availability of light. T. pratense responded by developing rhizomes in grazing conditions probably faster than in mowed grasslands. In contrast, the zoochorous grass Festuca arundinacea which has the theoretical capacities to produce expansive lateral spread up to 1 meter was limited in his expansion by cutting and grazing to patch size around 0.30 meter. The effect of grazing or cutting modified the random theoretical patterns expected by decreasing lateral expansion of F. arundinacea (Table 1). Taraxacum officinale had a theoretical random spatial patterns due to its mainly dispersal agent. Under management, the spatial pattern observed for T. officinale became aggregated and the patch size was higher than its lateral capacities (Table 1) so wind was not effective for the dispersion of seeds. The competitive pressure with surrounding tall grasses like Lolium perenne or Alopecurus pratensis (data not shown) probably limits the T. officinale's dissemination capacities. Figure 1. Spatial patterns for T. pratense in grazed grasslands (a: 4TLQV) and mowed grasslands (b: Tall French Hat Wavelets). The scale of window-width is plotted in units of quadrats (0.1 m).

Conclusions

The analysis of spatial patterns performed in this study did not give similar results and their use must be complementary. The size of the grid seems insufficient because the zone of inflection of the curve is not observed and this does not make possible to obtain the size of the gaps. However, this study showed that agricultural practices could play an important role in dispersal regime and in the spatial structure of grasslands species. Indeed, grazing and the mowing decrease or increase the size of the theoretical spatial patterns according to the dispersal characteristics of considered species.

Table 1 .

 1 Dispersal capacities and spatial pattern analysis for (Festuca arundinacea, Trifolium pratense, Ranunculus bulbosus, Taraxacum officinale) under grazed and mowed management.

	Species	Dispersal	Theoretical	Lateral	4	TLQV	patterns	Tall	Hat	French
		agent	spatial	spread (m)	spatial	(m)	spatial		Wavelet
			patterns (m)	sensu						patterns
				Grime et al.
				1988
					grazed	mowed	grazed		mowed
	F.	zoochorous	random	0.25 -1.00	0.30		0.30	-		-
	arundinacea
	T. pratense unspecialized aggregated 0.10 -0.25 0.90		0.50	-		0.70
	R. bulbosus barochorous	aggregated < 0.10	1.00		0.90	-		-
	T. officinale anemochorous random	< 0.10	0.80		1.00	-		-


domain: math info

text:
Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag. Lower Bounds for Geometric Diameter Problems -p.5/40

The diameter problem

Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

Decision problem

We will give lower bounds for the decision problem associated with the diameter problem.

INPUT: a set P of n points in R d .

OUTPUT: YES if diam(P ) < 1 NO if diam(P ) 1

Lower Bounds for Geometric Diameter Problems -p.6/40

Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag. Lower Bounds for Geometric Diameter Problems -p.7/40

Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

Finding the antipodal pairs

The rotating calipers technique.

Lower Bounds for Geometric Diameter Problems -p.10/40

Finding the antipodal pairs

The rotating calipers technique.

Finding the antipodal pairs

The rotating calipers technique.

Lower Bounds for Geometric Diameter Problems -p.12/40

Finding the antipodal pairs

The rotating calipers technique.

Lower Bounds for Geometric Diameter Problems -p.13/40

Finding the antipodal pairs

The rotating calipers technique.

Lower Bounds for Geometric Diameter Problems -p.14/40 2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

3D-diameter problem

Randomized O(n log n) time algorithm (Clarkson and Shor, 1988).

Randomized incremental construction of an intersection of balls and decimation. 2000).

Deterministic O(n log n) time algorithm (E. Ramos,
These two algorithms compute the diameter of an n-point set in R 3 .

Can we compute the diameter of a convex 3D-polytope in linear time? No, we give an Ω(n log n) lower bound.

Lower Bounds for Geometric Diameter Problems -p.16/40 2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

Model of computation

Lower Bounds for Geometric Diameter Problems -p.17/40 2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

Real-RAM

Real Random Access Machine.

Each registers stores a real number.

Access to registers in unit time.

Arithmetic operation (+, -, ×, /) in unit time.

Lower Bounds for Geometric Diameter Problems -p.18/40

Algebraic computation tree (ACT)

We say that an ACT decides S ⊂ R n if ∀(x 1 , . . . , x n ) ∈ S, it reaches a leaf labeled YES, and

∀(x 1 , . . . , x n ) / ∈ S, it reaches a leaf labeled NO.
The ACT model is stronger than the real-RAM model.

To get a lower bound on the worst-case running time of a real-RAM that decides S, it suffices to have a lower bound on the depth of all the ACTs that decide S Theorem 1 (Ben-Or) Any ACT that decides S has depth Ω(log(number of connected components of S)).

Lower Bounds for Geometric Diameter Problems -p.20/40

Problem statement

We are given a convex 3-polytope P with n vertices.

P is given by the coordinates of its vertices and its combinatorial structure: All the inclusion relations between its vertices, edges and faces.

The cyclic ordering of the edges of each face.

Example: P is given in a doubly-connected edge list.

Problem: we want to decide whether diam(P ) < 1.

We show an Ω(n log n) lower bound. Our approach:

We define a family of convex polytopes.

We show that the sub-family with diameter < 1 has n Ω(n) connected components. We apply Ben-Or's bound. Polytopes P ( β)

The family of polytopes is parametrized by

β ∈ R 2n-1 .
When n is fixed, only the 2n -1 blue points change with β.

Lower Bounds for Geometric Diameter Problems -p.23/40

Polytopes P ( β)

The family of polytopes is parametrized by β ∈ R 2n-1 .

When n is fixed, only the 2n -1 blue points change with β.

Lower Bounds for Geometric Diameter Problems -p.24/40

Notation

Example where n = 3.

a 3 c 1 2 c -1 2 c -1 -3 c 1 -3 b 0 b -2 (β -2 ) b 2 (β 2 ) a -3 c -1 -2 c -1 -1 c -1 0 c -1 1 a 2 a 1 a 0 a -1 a -

Notation

ā := (a -n , a -n+1 . . . , a n ).

A := {a -n , a -n+1 , . . . , a n }. β := (β -n+1 , . . . , β n-1 ). Point sets A and C

B( β) := {b -n+1 (β -n+1 ), . . . , b n-1 (β n-1 )}. b( β) := (b -n+1 (β -n+1 ), . . . , b n-1 (β n-1 )). c := (c -1 -n , c -1 -n+1 , . . . , c -1 n-1 , c 1 -n , c 1 -n+1 , . . . , c 1 n-1 ). C := {c -1 -n , c -1 -n+1 , . . . , c -1 n-1 , c 1 -n , c 1 -n+1 , . . . , c 1 n-1 }. P ( β) := CH(A ∪ B( β) ∪ C).
c -1 -3 c -1 -2 c -1 -1 c -1 0 c -1 1 c 1 -1 c 1 0 c 1 1 c 1 2 c -1 2 c 1 -3 y ψ a -3 a -2 γ a -1 α a 3 a 2 a 1 c 1 -2 2ϕ -ψ x z a 0 = O
Point b j (β j ) z O (1, 0, 0) x y b j (β) β 1 2 jψ (cos(jψ), sin(jψ), 0)
The blue region is parallel to Oxz.

β ∈ [-α, α] Coordinates of points in A, B( β) and C Proof

a i :=    1 2 (1 -cos(iγ)) 0 1 2 sin(iγ)    c s i :=    r cos i + 1 2 ψ r sin i + 1 2 ψ 1 2 sα    b j (β) :=    cos(jψ) -1 2 (1 -cos β) sin(jψ)
Notation: diam(E, F ) := max{d(e, f ) | (e, f ) ∈ E × F }.
Lemma 1 The set

{b j (β) | β ∈ [-α, α] and diam(A, {b j (β)}) < 1}
has at least 2n connected components.

a -3 a 3 a 2 a 1 a 0 b j (β) < 1 < 1 1 a -2 a -1
Lower Bounds for Geometric Diameter Problems -p.31/40

Proof

Proof of Lemma 1: Calculations, until the second-order terms.

Lemma 2

The combinatorial structure of

CH(A ∪ B( β) ∪ C) is independent of β.
We denote

P ( β) = CH(A ∪ B( β) ∪ C). Lemma 3 diam(A ∪ B( β) ∪ C) = diam(A, B( β)).
Lower Bounds for Geometric Diameter Problems -p.32/40

Proof

Definitions:

S n = {(ā, b( β), c) | β ∈ [-α, α] 2n-1 } E n = {(ā, b( β), c) | β ∈ [-α, α] 2n-1 and diam(P ( β)) < 1} Notice that E n ⊂ S n ⊂ R 24n .
Lemma 4 The set S n can be decided by an ACT with depth O(n).

Lemma 5 Any ACT that decides E n has depth Ω(n log n).

Proof: By lemmas 1 and 3, E n has at least (2n) 2n-1 connected components. Apply Ben-Or's bound (Theorem 1).

End of the proof

Theorem 2 Assume that an algebraic computation tree T n decides whether the diameter of a 3-polytope is smaller than 1. Then T n has depth Ω(n log n).

Proof: Take as input graph of T n the the graph of

Hopcroft's problem

P is a set of n points in R 2 .

L is a set of n lines in R 2 .

Problem: decide whether

∃(p, ) ∈ P × L : p ∈ .
An o(n 4/3 log n) algorithm is known. (Matoušek).

No o(n 4/3 ) algorithm is known.

We give a linear-time reduction from Hopcroft's problem to the diameter problem in R 7 .

We first give a reduction to the red-blue diameter problem in R 6 : compute diam(E, F ) when E and F are n-point sets in R 6 .

Lower Bounds for Geometric Diameter Problems -p.37/40 Note that θ(x, y, z) = 1.

For 1 i n p i = (x i , y i , 1) i = (u i , v i , w i ) is the line i : u i x + v i y + w i = 0. Let p i := θ(p i ) and j = θ( j ).

We get

p i -j 2 = p i 2 + j 2 -2 < p i , j > = 2 -2 < p i ,

Proof

Note that p i ∈ j iff < p i , j >= 0.

Thus, there exists i, j such that p i ∈ j if and only if diam(θ(P ), θ(L)) = 2.

θ(P ) and θ(L) are n-point sets in R 6 .

Similarly, we can get a reduction from Hopcroft's problem to the diameter problem in R 7 , using this linearization:

θ(x, y, z) := 1 x 2 + y 2 + z 2 (x 2 , y 2 , y (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

Related work

The red-blue diameter in R 4 can be computed in O(n 4/3 polylog n) (Matoušek and Scharzkopf). It would be interesting to get a reduction from Hopcroft's problem.

Erickson gave reduction from Hopfcroft problem to other computational geometry problems.

Lower Bounds for Geometric Diameter Problems -p.40/40

P

  lies in the intersection of the two balls with radius d(p, p ) centered at p and p .

α

  Geometric Diameter Problems -p.29/40 Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag. is small. ψ = ϕ/n γ = α/n Lower Bounds for Geometric Diameter Problems -p.30/40 Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL(2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

Computing the diameter of a 2D-point set

	Compute the convex hull CH(P ) of P .
	O(n log n) time.
	Find all the antipodal pairs on CH(P ).
	There are at most n such pairs in non-degenerate
	cases.
	O(n) time using the rotating calipers technique.
	Find the diametral pairs among the antipodal pairs.
	O(n) time by brute force.
	Conclusion:
	The diameter of a 2D-point set can be found in
	Comment citer ce document :
	Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006
	: theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887.
	Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL
	(2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

O(n log n) time The diameter of a convex polygon can be found in O(n) time. Lower Bounds for Geometric Diameter Problems -p.15/40 Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (

2

  Lower Bounds for Geometric Diameter Problems -p.25/40

Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

  Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

  Lower Bounds for Geometric Diameter Problems -p.33/40 Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

  P ( β). Denote by U n the ACT of Lemma 4. Plug U n into the accepting leaves of T 8n . It gives an ACT with depth the depth of T 8n + O(n) that decides E n . Apply Lemma 5. Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.

	Related work
	(Chazelle) The convex hull of two 3-polytopes can be
	computed in linear time.
	(Chazelle et al.) It is not known whether the convex
	hull of a subset of the vertices of a 3-polytope can be
	computed in linear time.
	(Chazelle et al.) However, we can compute in linear
	time the Delaunay triangulation of a subset of the
	vertices of a Delaunay triangulation.

Lower Bounds for Geometric Diameter Problems -p.34/40 Lower Bounds for Geometric Diameter Problems -p.35/40 Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag. Diameter is harder than Hopcroft's problem Lower Bounds for Geometric Diameter Problems -p.36/40 Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL

(2006-03-20 -2006-03-24)

. Heidelberg, DEU : Springer-Verlag.

  + y 2 + z 2 (x 2 , y 2 , y 2 ,

		Proof
	θ(x, y, z) :=	1 x 2 √ 2xy,	√	2yz,	√	2zx).

Comment citer ce document : Fournier, H., Vigneron, A. (2006). Lower bounds for geometric diameter problems. In: Latin 2006 : theoretical informatics (p. 467-478). Lecture Notes in Computer Science, 3887. Presented at 7. Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, CHL (2006-03-20 -2006-03-24). Heidelberg, DEU : Springer-Verlag.


H H Han

P E Lauri

C Coutand

Lateral Development Influenced by Position on the Shoot-Reassessment on Apple Shoots Bent during Active Growth and in the Following Winter

Keywords: apple, bending, flowering, branching, organogenesis

The effects of bending on shoot growth and lateral development depend on several factors such as the phenological stage, the duration of bending and the angle of re-orientation. An arching experiment was carried out on five apple cultivars to analyze the effects of the phenological stage at which bending was carried out and the position on the shoot on lateral development. Arching was done in the proximal zone of shoots during spring, when shoots were one third of their final lengths and in the distal zone of shoots after bud organogenesis was completed in the following winter. In all cases, arching was carried out to put shoots under the same mechanical strain. Analyses were done on the arched portion of shoots, with a comparison of the frequencies of laterals in the upper and lower faces of shoots. In both bending treatments, there was a significant increase in the proportion of aborted buds on the lower face, with an increase of sylleptic branches in shoots bent in spring and an increase of inflorescences in shoots bent in winter on the upper face. In shoots bent in winter, inflorescences on the upper face had larger leaves than inflorescences in the lower face. Our results suggested that the effect of branch re-orientation on lateral development may act on both bud organogenesis when bending is carried out during active growth (spring), and bud post-organogenesis when the same manipulation is done during winter before bud break. The interest of branch re-orientation to control branching (intensity and lateral fate) is discussed as an alternative to avoid chemicals.

INTRODUCTION

Shoot bending is known to decrease terminal shoot growth and to alter lateral development, i.e., proportion and possibly final length of the various lateral types (latent, vegetative, inflorescence). Several factors have been shown to influence lateral development, especially genotype, angle of the shoot, and the phenological period during which the manipulation is performed (Lakhoua and Crabbé, 1975). However, in most studies, the level of arching is quantitatively poorly controlled. So that if the "same" arching (e.g., same mass added) is imposed to shoots that exhibit differences in geometrical characteristics (length, diameter), then the shoots are subjected to very different mechanical state. Thus, if differences of sensitivity to arching are found, they can only be due to a different imposed mechanical state (due to genetic variability in shoot geometry) and not to a genetic variability of sensitivity to arching. Biomechanical studies of the effect of mechanical state on shoot growth and branching have demonstrated i) the importance of taking into account shoot geometry for a proper control of the imposed mechanical state, and ii) that plants perceive the level of strain and not of force (Coutand and Moulia, 2000).

This paper is part of a project studying the effects of bending on apple shoot architecture, biomechanics and hydraulics. In our work, we segregate through appropriate bending the genetic variability of sensitivity of cultivars to mechanical state due to arching from the genetic variability due to shoot geometrical differences if arching is uncontrolled. An original biomechanical protocol of arching was designed: the genetic variability of shoot geometry was taken into account and the level of imposed curvature was adapted for each cultivar in order to ensure that all the shoots were subjected to the same mechanical state of strain (i.e., slender shoots were more arched than stouter ones). The objective of the present study was to assess five cultivars for the effects on lateral development of position around the arched part of shoots for shoots bent at two phenological stages, i.e., during active growth (active organogenesis of the axillary production) and in the following winter (after organogenesis was done).

MATERIALS AND METHODS

Five cultivars presenting contrasted shoot shape (e.g., slenderness) and architecture (branching density, frequency of vegetative shoots and inflorescences on 1-year-old wood) were chosen: 'Ariane', 'Braeburn', 'Fuji', 'Gala', and 'Granny Smith'. One-year-old trees, grafted on Pajam rootstock, were planted in a completely randomized design in two adjacent rows in February 2004, in the INRA experimental field in Montpellier, France.

Trees were pruned at planting to leave 3 to 5 buds at the bottom of the scion. The most vigorous 2004-shoot was then selected for the experiment after bud-break.

Arching was carried out by tying down the distal part of shoots in early June 2004 (Spring Bending, SB) and in mid-January 2005 (Winter bending, WB). In SB, the arched zone generally included the whole-shoot, whereas in WB it included the distal half of the shoot. At the time of bending, the length of shoots varied from 37 to 54 cm for SB, and from 125 to 150 cm for WB, depending on the cultivar.

For each treatment, approximately 20 trees of 'Fuji' and 'Braeburn', and 10 trees of 'Ariane', 'Gala' and 'Granny Smith' were planted in a completely randomized design (each tree represented a replication).

In spring 2005, the arched zone of shoots was first determined on SB, including all nodes from the grafting point upwards to the uppermost node, and the same number of node downwards. The same number of nodes was then determined on the arched zone of WB shoots (Fig. 1). Each lateral was characterized by its type and position around the shoot. In the former case, five types were considered: sylleptic (i.e., branch which developed in the same year as bending was carried out, S), latent bud (L), vegetative bud (V), inflorescence (I), and aborted bud (i.e., which began to grow in spring 2005 and soon died, AB). In the latter case, the position around the shoot was designated by dividing the cross-section circumference of the shoot into four quarters. Only the upper quarter and the lower quarter, hereafter referred to as upper (U) and lower (L) face, respectively, were evaluated (Fig. 1). The percentage of each lateral type was then computed considering all laterals on U and L faces.

For data analysis, we compared the percentages of each lateral type between the U and L faces for the two bending treatments and for each cultivar. For inflorescences of WB shoots, the number of leaves more than 2 cm long was determined (sample size was too small in SB shoots). The Kruskal-Wallis non-parametric test was used to compare percentages, and the Newman-Keuls test was used to compare number of leaves of inflorescences (STATISTICA statistical package, StatSoft, France).

RESULTS

An ANOVA revealed that the proportion of lateral types differed significantly among cultivars (data not shown). As explained in the Introduction, as the genetic variability of shoot diameter (which can lead to a variability of mechanical state of the arched branch if the same curvature is imposed) has been compensated by different guide radii in arching treatments, these first results suggested a genetic variability of the sensitivity to strain between cultivars. Further statistical analysis is now required to see if the studied cultivars can be clustered by their level of sensitivity.

Within each cultivar, the comparison of bud types in the upper and lower faces of the arched shoot showed the following results:

(1) In SB shoots, most of the differences between U and L faces were detected for S and AB types. For the five cultivars, there was a higher percentage of S in the U face compared to the L face, and inversely, a higher percentage of AB in the L face, compared to the U face, with significant differences in all cases (Fig. 2).

(2) In WB shoots, most of the differences between U and L faces were detected for I and AB types. For the five cultivars, there was a higher percentage of I in the U face compared to the L face, and inversely, a higher percentage of AB in the L face, compared to the U face (Fig. 3). Differences were significant in all cases except for AB in Gala (P=0.059) and in Braeburn (P=0.157).

(3) Eventually, the number of inflorescence leaves more than 2 cm significantly increased in the U face, compared to the L face for the five cultivars (Fig. 4).

DISCUSSION

Bending significantly altered lateral development. Our results suggested two different mechanisms of lateral growth regulation, depending on the time of bending. Spring bending likely activated a mechanism which stimulated sylleptic branching on the upper face of the arched shoots to the detriment of bud organogenesis in the lower face.

Winter bending activated a post-organogenesis mechanism with the abortion of already formed buds. We are conducting more fundamental research on bending by studying changes in water balance and hydraulics, as suggested by Kim et al. (2004), and with biomechanical analysis of sensitivity to arching among cultivars and relationships between level of applied strain and types of buds. We are also developing applied research to further experiment with timing and duration of bending during the growing season and the effects on vegetative growth and flowering of various cultivars.

In the context of sustainable integrated and organic horticulture, bending may be used as an alternative means to manage branching without chemicals. In spur-bound cultivars, it may be efficient to reduce spur density which is known to have deleterious effects on fruit quality and crop regularity.

Literature Cited

Figures e

Fig.

  Coutand, C. and Moulia, B. 2000. Biomechanical study of the effect of a controlled bending on tomato stem elongation: local strain sensing and spatial integration of the signal. J. of Exper. Bot. 51:1825-1842. Kim, S.H., Shackel, K.A. and Lieth, J.H. 2004. Bending alters water balance and reduces photosynthesis of rose shoots. J. of the Amer. Soc. Hort. Sci. 129:896-901. Lakhoua, H. and Crabbé, J. 1975. Arcure et gravimorphisme chez le Pommier. I. Effets de divers degrés d'arcure sur la forme de la ramification et l'expression de la vigueur. Bulletin Rech. Agron. Gembloux 10:43-54.

Fig. 2 .Fig. 3 .Fig. 4 .

 234 Fig. 1. Quantitative control of arching and determination of the arched zone in shoots bent in spring (SB) and in winter (WB). Arching was started in the apical part of the shoot in order to place the apical bud in a vertical position towards the ground.The arched zone corresponds to the portion of the shoot rolled on the guide; the uppermost bud is located at the middle of the arched zone.

Proc. XXVII IHC-S11 Sustain. through Integr. and Org. Hort. Eds.-in-Chief: R.K. Prange and S.D. Bishop Acta Hort. 767, ISHS 2008

The upper face (U)

The lower face (L)

The upper face (U)

The lower face (L)

The upper face (U)

The lower face (L)

The upper face (U)

The lower face (L)


est destinée au dépôt

Effects of allelic forms of the Potato virus Y (PVY) resistance gene va on infection kinetics and viral population structures

Christelle Lacroix, Michel Tribodet, Jean-Louis Verrier, Camille Kerlan,

Emmanuel Jacquot, Laurent Glais

To cite this version: This plant virus is transmitted by aphids and is worldwide distributed. This pathogen is the most damaging virus affecting tobacco crops. Considering its economical importance and the lack of efficient methods to control aphid transmission, genetic resistance is a solution to limit the PVY spreading in the fields. Three allelic forms (conferring different level of resistance to PVY) of a recessive resistant gene (va) have been described and introduced in numerous cultivars of Nicotiana tabacum. However, such partial resistant hosts can not totally prevent the viral replication in the plants which can consequently result in the selection of virulent variants. Indeed, some variants of PVY able to overcome these resistance sources have been reported in many countries. Hence, the objective of our study is to better characterise the PVY resistance sources and to understand their role in both the emergence and the spread of such virulent PVY isolates. A fully characterized PVY isolate was inoculated to two couples of tobacco near isogenic lines, differing in allelic state at the locus of the va gene. The kinetics of viral particles accumulation during the infection process was recorded in order to determine the impact of the different alleles of the va gene on viral multiplication. Moreover, the molecular analysis of the viral population was performed on different regions of the PVY genome. The nucleotide sequence diversity of each of these genomic regions was compared between inoculated hosts plant in order to determine the impact of the resistant gene va on the structure of viral population. Data related to infection kinetics and molecular changes of viral sequences will be presented.

Effects of allelic forms of the Potato virus Y (PVY) resistance gene va on infection kinetics and viral population structures Abstract N° 851

	VS64 Virus Evolution and Diversity
	Preference: Oral presentation
	Lacroix C. 1 , J-L., Tribodet M. 1 , Verrier 2 , Kerlan C., Jacquot E. 1 , Glais L. 3
	UMR INRA/ENSAR Biologie des Organismes et des Populations appliquée à la Protection
	des Plantes (BiO 3P)
	BP 35327
	35650 Le Rheu Cedex
	hal-02753594

Christelle Lacroix, Michel Tribodet, Jean-Louis Verrier, Camille Kerlan, Emmanuel Jacquot, et al.. Effects of allelic forms of the Potato virus Y (PVY) resistance gene va on infection kinetics and viral population structures. 14. International congress of virology, Aug 2008, Istanbul, Turkey. 2008. 1 INRA-Agrocampus Ouest-Université Rennes1, UMR1099 BiO3P (Biology of Organisms and Populations applied to Plant Protection), F-35653 Le Rheu, France; 2 Imperial Tobacco Group, SEITA, Institut du Tabac, Domaine de la Tour, F-24100 Bergerac, France; 3 FNPPPT (Fédération Nationale des Producteurs de Plants de Pomme de Terre), 43-45 rue de Naples, F-75008 Paris, France;

France Viruses are obligate parasites sharing a high mutation rate when replicated, leading or not to genetic diversity. Indeed, one of the major constraints in the evolution of viral populations is the interaction with the host. Potato virus Y (PVY, Potyvirus genus), a single stranded positive sense RNA virus, infects a wide host range including cultivated Solanaceous species.