C Saudrais

L Rubbert

L Bonnefoy

R Zhu

H Schneegans

C Baur

U Mescheder

P Renaud

Experimental evaluation of needle tip force sensing associated to tactile feedback for improving needle remote insertion

Keywords: interventional radiology, needle insertion, tactile feedback, force sensing

In this paper, we present an experimental evaluation of tactile feedback for remote needle insertion in soft tissues. A needle with tip force sensing is used to detect changes of tissues and puncture events during insertion. This information is provided to the user during teleoperation by means of a tactile display. Evaluation is conducted by reproducing needle insertion as performed during biopsy procedures in the liver. Needle tip force sensing makes the measurement of tissue change and puncture easier compared to force measurement at the base of the needle. Puncture events are correctly understood by the users. Change of tissue is also satisfactorily detected, which could be an interesting additional information for the user to perform surgical gesture.

Introduction

In interventional radiology, the use of X-ray based imaging devices represents a safety issue for radiologists due to radiations. MRI scanners also have the issue of limited access to the patient due to the bore geometry. Remote manipulation of needle could then improve the conditions for tasks such as biopsy performed by radiologists with these modalities. Radiologists achieve needle insertion relying on images and also insertion forces [START_REF] Elayaperumal | Detection of membrane puncture with haptic feedback using a tip-force sensing needle[END_REF]. Because of the multiple visual sources of information in the operating room that the radiologist has to deal with, remote manipulation with force feedback to inform about the puncture of tissues and the change of tissues are then of interest [START_REF] Schneegans | Fiber Optic Fabry-Perot Interferometry for a Biopsy Needle with Tip Force Sensing[END_REF]. In the following we focus on this objective, considering kidney and liver biopsy procedures. Such procedures consist in local anesthesia at the biopsy needle insertion point, before skin incision. A coaxial biopsy needle is then inserted after deep anesthesia along the planned path. The biopsy needle trajectory is monitored with a medical imaging device when going through abdominal muscle, fat and the organ of interest. When the needle tip reaches the point of interest, the biopsy is performed with a trigger mechanism before extracting the needle carrying the desired tissue specimen [START_REF] Pfeil | Observations And Experiments For The Definition Of A New Robotic Device Dedicated To CT, CBCT And MRI-Guided Percutaneous Procedures[END_REF].

Teleoperation with force feedback to reflect insertion forces during the needle progression is possible, but challenging in terms of control [START_REF] Barbé | User Adapted Control of Force Feedback Teleoperators: Evaluation and Robustness Analysis[END_REF]. An easier approach is to provide to the user only specific events such as the puncture of membranes surrounding tissues like muscle or liver, that also possess different stiffnesses and mechanical properties [START_REF] Elayaperumal | Detection of membrane puncture with haptic feedback using a tip-force sensing needle[END_REF]. In [START_REF] Schneegans | Fiber Optic Fabry-Perot Interferometry for a Biopsy Needle with Tip Force Sensing[END_REF], we showed that we were able to measure in lab conditions the punctures of membranes with great accuracy thanks to a Fabry-Perot load cell placed inside the needle, close to the tip. In [START_REF] Zhu | Mescheder Determination of a tactile feedback strategy for use in robotized percutaneous procedures[END_REF], we investigated how to render information with a tactile feedback using a dynamic Braille display. In this paper, their combination is evaluated experimentally to investigate the capacity of users to understand change of tissues and occurrence of punctures during a needle insertion, and therefore to add to the medical image additional information with tactile feedback.

Methods

Set-up

A 16 G needle (diameter of 1.6 mm) with tip force sensing capability, which has been presented in [START_REF] Schneegans | Fiber Optic Fabry-Perot Interferometry for a Biopsy Needle with Tip Force Sensing[END_REF] is inserted using a linear table (FB075, Nanomotion). To reproduce the biopsy, the needle insertion is performed at constant speed in a phantom composed of 3 layers (Fig. 1). These layers are produced with gelatin, using concentrations of 7%, 45% and 18% [START_REF] Ng | Needle Insertion Forces Studies for Optimal Surgical Modeling[END_REF] to reproduce respectively the bio-mechanical properties, i.e. stiffness, of fat, muscle and organ (liver or kidney). The layers are separated by membranes composed of polyethylene cling film in order to reproduce the faciae existing between the anatomical structures. The signal associated to the membrane puncture can be delivered to the user or not, so that three scenarios can be reproduced with two, one or no membrane between the layers. The phantom is rotated after 3 insertions that are shifted radially by 8 mm, so the insertions are never performed in the same volume of the phantom. 22.5 • rotations are applied, therefore 48 insertions can be performed with a single phantom.

The Fabry-Perrot load cell [START_REF] Schneegans | Fiber Optic Fabry-Perot Interferometry for a Biopsy Needle with Tip Force Sensing[END_REF] located in the instrumented needle is connected to a FISO™ white light interferometer. The signal is then transferred to a PC for signal processing using Labview platform. For some needle insertions, force measurement at the base of the needle is performed for comparison purpose using a force sensor Scaime K1107 mounted between the needle and the linear table. The tactile feedback is provided by means of a so-called tactuator, composed of a Braille display based on a tactile actuator SC5 (KGS Corporation). The tactile display is an array of 8 × 8 dots (25 × 25 mm 2 ) to produce dynamic patterns using an Arduino platform. A push button is also provided to the user to record puncture events. According to the initial results described in [START_REF] Zhu | Mescheder Determination of a tactile feedback strategy for use in robotized percutaneous procedures[END_REF], the following two patterns are being used (Fig. 3): a moving horizontal line which frequency varies with the nature of the gel as detected with the needle tip, and a single ON/OFF signal generated at each puncture detection. The frequency varies proportionally with the measured force between 10 Hz and 25 Hz. In order to set the frequency range, one insertion was used to determine the minimum value of force, associated to 10 Hz, and the maximum value, associated to 25 Hz.

Phantom holder

Needle with tip force sensing capability

Linear table

Fig. 1. The linear table holding the needle with tip force sensing capability and the phantom.

Protocol

The evaluation is performed on 11 healthy subjects (9 male and 2 female subjects) between 22 and 47 years old. Each subject is first introduced to the protocol and the tactile feedback using a prerecorded sequence, in order to get familiar with the dynamic patterns generated with the tactuator. The training phase is two and half minutes long, to keep the learning phase short. Each subject is equipped with noise-canceling headset (Sony WH-1000XM3) and is placed in such a manner he cannot see nor hear the needle progression. Insertion start is indicated to the subject by a visual sign. When the subject considers a membrane puncture occurred, he presses the push button. In addition, he mentions orally if a tissue change occurs. After each insertion, the subject leaves the room keeping the noise canceling headset while the next insertion settings are prepared.

In order to avoid learning of the sequence by the subject, the insertion sequences are generated randomly, modifying two parameters. First, the insertion speed is set to 2 mm/s or 4 mm/s (S=1 or S=2), so the time to go through a layer is not necessarily constant between two experiments. Second, the presence of the number of membrane (up to two) is not always reflected to the subject. Puncture of the first membrane (M1=0 or M1=1) and the second membrane (M2=0 or M2=1) are varied between two experiments. A total of 8 combinations of conditions S, M1, M2 exists. For each subject, 3 insertions are achieved choosing randomly a set of conditions. The subject is only aware of the number of layers in the phantom, and the possible presence of membranes.

Results

Needle tip force sensing performances

In Fig. 4, the force measurements as functions of the needle progression are represented for insertions at speeds of 2 mm/s (3 insertions) and 4 mm/s (3 insertions). The membrane punctures M1 and M2 are recorded synchronously for all measurements as expected.

The evolution of the tip force is not dependent on the speed and needle insertion depth whereas the proximal force profiles exhibit different slopes. Using the tip force, it is quite simple to discriminate the nature of the layers. On the contrary the proximal force measurement is dependent on the needle velocity, so it is difficult then to discriminate the layers. In addition, after noise signal filtering, membrane puncture appears clearly on the tip force measurement, while for the first membrane it can be seen that the peak of proximal force measurement is hardly visible.

Experimental evaluation

The Table 1 provides the results of the experimental evaluation with the tip force sensing needle (distal). The experiment has been performed on two different days with thus two different phantoms, but with the same gel compositions. The first 7 subjects starting from the left column of the table did the experiment the first day in a row, and the 4 remaining on the second day in a row. As a summary, 65 out of 66 membrane puncture detections (98%) have been successfully performed. 59 out of the 66 frequency changes (89%) have been successfully detected.

Discussion

With the considered instrumented needle, the ability to measure the force at the tip of the needle is proven to be clearly an added-value to build force feedback during needle insertion, as also observed in [START_REF] Elayaperumal | MR-compatible biopsy needle with enhanced tip force sensing[END_REF]. In fact, the insertion profile of the force measurement at the distal end of the needle allows us to detect in a simple way the puncture during the whole insertion. The phantom was here based on homogeneous layers. It will be interesting to further investigate force measurements with this design of needle based on Fabry-Perot interferometry, and how to make the signal processing robust to signals collected in in vivo conditions. The approach we propose to reflect to the user events related to the needle progression is quite simple. We actually limit the number of information sent to the user, providing only one piece of information related to the nature of tissue and another one related to the occurrence of membrane puncture. As one can see, the absence of transition detection occurs equivalently for both transition (T12 and T23) and are not correlated with the absence or presence of a membrane (M1 or M2). The evaluation results are excellent (98%) for the puncture detection which is very encouraging in terms of safety improvement during teleoperated needle insertion as the tactile feedback comes as a complementary information to the visual feedback provided by the medical imaging device. Puncture information to take a decision about needle progression could be sufficient, as they have a priori knowledge about the anatomy. However, the feedback about change of tissue seems also feasible, and it could be a valuable complementary source of information if unexpected changes occur. 1 2 2 1 1 1 1 2 1 2 1 2 1 2 1 2 1 2 2 2 1 2 1 1 1 2 1 2 1 2 2 2 1 M1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 Settings M2 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 M1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 M2 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Sex M M M M M M M F F M M Subject
1 T12 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 Results T23 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Table 1. Results of the experimental evaluation. The highlighted column can be interpreted as follows. The male subject is 23 years old. The first insertion has been set to an insertion speed of 4mm/s (speed #2), simulating an absence of membrane M1 between the first and second gel layers, by not sending a signal to the tactuator, but with a membrane M2 between the second and third gel layers. The results are split in two parts: membrane puncture detection, and change of tissue. In case of the non-occurrence of membrane M1 puncture, the subject did not press the push button, which was correct [START_REF] Schneegans | Fiber Optic Fabry-Perot Interferometry for a Biopsy Needle with Tip Force Sensing[END_REF]. In case of membrane puncture, the ON/OFF pattern has been sent to the tactuator and the subject pressed the push button which was also correct [START_REF] Schneegans | Fiber Optic Fabry-Perot Interferometry for a Biopsy Needle with Tip Force Sensing[END_REF]. The second part of the evaluation is the ability to detect a change of tissue which is interpreted by an increase or decrease of the frequency of the moving line pattern. For the change between the first and second layers (T12 with no membrane M1) the subject did not detect any change (0). However, for the second change between the second and third layers (T23 with membrane M2), the subject did detect the change (1).

Conclusion

In this paper, the interest of needle tip force sensing capabilities in remote needle insertion was presented and discussed as well as its experimental evaluation in combination with tactile force feedback. The interest of needle tip force sensing is demonstrated by comparing the insertion profiles of distal versus proximal force sensing when inserted in a phantom. Based on the profile of tip force measurement, puncture and changes of tissues could be well established and reconstructed as a tactile information with two distinct dynamic patterns. The experimental evaluation on 11 subjects with a phantom demonstrates that it is possible to detect puncture event which could improve the safety during remote needle insertion. Other information as the change of tissues which seems understandable through a tactile feedback could be a crucial information to avoid critical zones.

Acknowledgements

This work was supported by the INTERREG Upper Rhine program from the ERDF (European Regional Development Fund), SPIRITS project (interreg-spirits.eu), and also by Investissements d'Avenir program (Robotex ANR-10-EQPX-44, Labex CAMI ANR-11-LABX-0004). The authors thank Sensoptic SA for the work on needle with tip force sensing capabilities and Help Tech GmbH for providing the Braille display.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Experimental set-up during evaluation with subject.

Fig. 4 .

 4 Fig. 4. Distal and proximal needle axial force measurement evolution with respect to the insertion depth at speed 2mm/s and 4mm/s in three various gels separated by membranes.


Zhaohui Huo

Vasilica-Adriana Badets

Helen Ibrahim

Michel Goldmann

Hualong Xu

Tao Yi

Corinne Boudon

Laurent Ruhlmann
email: lruhlmann@unistra.fr

Synthesis and Characterization of Bisthienylethene-Porphyrin Photoswitchable Copolymers

Keywords: Electropolymerization, Porphyrin, Bisthienylethene, Polymer, Photocyclisation

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

Introduction

Diarylethenes are photochromic materials with promising potential for the development of photonic devices such as optical switches due to their reversible photocyclization reaction [1][2][3] . Specifically, bisthienylethene (BTE) derivatives display thermally irreversible, fast-switching, high quantum-yield and fatigue resistant photoisomerization reactions. The photocyclization reaction are most of the times accompanied by the change of other physical-chemical properties such as refractive index, optical rotation or luminescence. Switchable supramolecular self-assemblies based on the interaction between pyridine group containing bisthienylethene unit (BTEPy) and carboxylic acids showed fluorescent enhancement both in solution and also in the solid state [4] .

In addition, in the presence of metal ion such as Zn 2+ , the photochromism from the open to the closed-ring form was strongly enhanced [5] . A bisthienylethene iridium (III) complex coordinating to the photochromic diarylethene derivative BTEPy was described. (BTEPy)2Ir(acac) showed excellent near-infrared photochromic properties such as thermal stability and fatigue resistance accompanied by efficient quenching of phosphorescence emission by the closed form of the bisthienylethene moiety [6] . Furthermore, bisthienylethene-based iridium(III) complex was used as a phosphorescence probe for monitoring living cells [7] .

Porphyrins get excited at a wavelength where the open form of BTE is transparent. Moreover, the spectral overlap between the emission band of porphyrin and the closed form of BTE provides a mean to regulate the luminescence via the photoisomerization reaction [8] . The ability to control the excitation wavelengths of porphyrins and their intense luminescence far into the visible domain led to intense research of porphyrin-dithienylethene hybrids. Most of the examples cited here are based on covalent or coordinative bonds between the two molecules [9,10] . Coordination complex between Ru porphyrin and BTEPy was prepared showing optical switch which phosphoresces at 730 nm instead of fluorescing and consequently emits light energy far beyond the photochemically active absorption bands. The emission intensity can be modulated by photochemically switching between open and closed forms [11] . Synthesis of photochromic hybrid, where porphyrin macrocycles are attached to the ends of the bisthienylethene backbone was also described. The luminescence intensity of the porphyrin is significantly governed by the state of the bisthienylethene photoswitch. The photoisomerization reaction was carried out under illumination at 313 nm and the non-fluorescent closed form was obtained while in the open form, the porphyrins display significant fluorescence intensity at 655 nm when excited at 430 nm [8] . In bisthienylethene-bridged diporphyrins, the close attachments of the porphyrin to the bisthienylethene induced loss of its photochromic reactivity, probably through the intramolecular energy transfer quenching. However, the appropriate selection of a spacer between the bisthienylethene and porphyrin guarantees the photochromic reactivity of the bisthienylethene moiety that can reversibly control the fluorescence of the porphyrin subunit [12] . Additionally, Moore's group prepared bisthienylethene-porphyrinfullerene triad (BTE-porphyrin-C60) as an electron-transfer switch, which showed no significant porphyrin fluorescence in either open or closed forms [13] . These properties make from BTE a very good candidate for the development of responsive surfaces that currently receive widespread interest in applications such as microfluidic devices, sensors, organic devices and electronics [3] . The common approach to get these responsive surfaces is to incorporate a stimuli responsive unit into a polymer while keeping the functionality undisrupted. The incorporation of BTE into polymers while keeping its thermally irreversible photochromism has been widely reported in the literature. We distinguish here the polymers obtained by the electropolymerisation of subunit of BTE backbone from polymers obtained via incorporation (e.g. in polystyrene [14] or poly(methyl methacrylate) [15] ) or other chemical reactions (e.g. click chemistry [16] ). The electropolymerisation of bifunctional diarylethene substituted with methoxystyryl [17] , bis-tertiophene or bis-bithiophene [18,19] and 2,5-dithienylpyrrole [20] were reported. G. Zerbi et al. synthesized a thiophene backbone photochromic polymer, whose thermal stability was surprisingly higher than that of the monomer [21] . Reaction of 2,3-bis (2,5-dimethyl-3-thienyl)-N-allyl maleimide with methyl methacrylate (MMA) gave photochromic copolymer with quite high cyclization and ring opening quantum yields, even for the copolymers in the film. The switching stability of the photochromic copolymer was observed a least during over 200 open to closed cycles [22] . Several homopolymers from 1,2-bis(3-thienyl)cyclopentene derivatives were also synthetized using ring-opening metathesis polymerization methods [23] . These homopolymers retained their photochromic properties both in solution and in the solid state. But the photochromic properties in solution diverged from those of its monomer. It is probably due to the decline in rotational freedom of the C-C bonds between the thiophene and cyclopentene rings because of the rigidity of each end of the photochromic skeleton joining the cross-linked polymer backbones. Free rotation around these bonds is indispensable to orient the orbits for the electrocyclic ring closing reaction. In the case of the polymer based on bis-tertiophene, reversible switching of conductivity within diarylethene-based redox-active polymer films was observed [19] . Singlet oxygen generation [24] , photo-patterning [25] and quenching of electron transfer from a singlet state excited porphyrin to a fullerene was also modulated by the photocyclisation reaction [26] . In this view, we present here a copolymer obtained by the electropolymerization of a porphyrin unit and BTE (Scheme 1). It is important to note that the polymer is not obtained via the direct electropolymerization of a moiety of BTE, as most of the BTE containing polymers published so far. Moreover, our material is not a simple association of one unit of porphyrin with BTE, as most of the examples cited above; it consists of a porphyrin copolymer with BTE included in the backbone and not as a pendant group.

Results and Discussion

Electroynthesis of the Poly-BTEPy-ZnOEP copolymers

Scheme 1 presents the electropolymerization process. The principle of electropolymerization of zinc octaethyl porphyrin in the presence of pyridine containing spacers have been developed by our group and multiple examples have been published so far [27- 29] . The process involves the formation of a porphyrin dication by raising the electrode potential to positive values (step V in Figure 1, above 1 V vs. SCE). This high electrophilic dication undergoes a nucleophilic attack from pyridine substituted compounds. In the present work, we have tested this process using pyridine substituted diarylethene (BTEPy, Scheme 1). Figure 1 shows the electropolymerization process that was optimized with respect to the scan direction and lower potential limit that is either -1.3 V or 0 V vs. SCE. In the anodic scan, peaks corresponding to the formation of a first porphyrin radical cation (step IV into Figure 1) followed by the peak of the porphyrin dication (step V) and finally by the peak corresponding to the oxidation of isoporphyrin (step VI) are observed. In the cathodic scan down to -1.3 V (Figure 1A) peaks corresponding to the reduction of the intermediate isoporphyrin and of the pyridinium reduction (peaks *, I, II and III) are observed. The first one (peak *) could correspond to the reduction of the isoporphyrin and the three others (peaks I, II and III into Figures 1 and3) could correspond to the reductions of the pyridinium spacers formed between each porphyrin ring and BTE. Peaks I and II are irreversible while peak III is reversible. The last wave (peak III) probably corresponds to the simultaneous reduction of the pyridinium groups substituted in 5 and 15 mesopositions of the porphyrin (bi-substitution in positions 5 and 15, i.e. trans-substitutions) while the first signals (peaks I and II, observed at -0.52 V and -0.75 V vs. SCE) probably corresponds to the reduction of pyridinium group in 5 and 10 meso-positions (in the case of bi-substitution in positions 5 and 10, i.e. cis-substitutions). Indeed, in the case of cis-substitutions, mutual interaction between the two pyridinium substituents can be observed leading to two successive one-electron reduction steps for py + -BTE-py + spacers instead of only one (two electron reduction step). Indeed, when we use ZnOEP, the four meso-positions (positions 5, 10, 15 and 20) are free, and the nucleophilic attack can occur on each of them. Thus, "zigzag" polymers can be obtained. Further details about these species can be found in our previous publications [30,31] . It is important to notice here that in Figure 1A the electropolymerization leads to an increase of the current with each scan while in Figure 1B the opposite is observed. In the second case, the obtained copolymer is less conductive but also more linear (with bi-substitution mainly in positions 5 and 15, i.e. trans-substitutions). For this reason, the electropolymerization between 0 and 1.8V was chosen and all the results are presented for this copolymer (further called Poly-BTEPy-ZnOEP). The electrochemical behavior of BTEPy alone (in its open and closed form) is described in Figure 2. For the open form an irreversible oxidation and an irreversible reduction are observed at 1.47 V and -1.16 V respectively. For the closed form the electrochemical processes are shifted toward more negative potentials, rendering the oxidation of this form easier to perform. If the oxidation of BTEPy would be encountered during the electropolymerization, the ability to perform photoswitchable reactions might be altered. For this reason, the open form was selected for performing the electropolymerization.

Cyclic voltammetric investigations of the films

Figure 3 shows the electrochemical behavior of the final copolymer Poly-BTEPy-ZnOEP and Table 1 contains a summary of peak position for all the species present in the copolymer or as standalone species. Inside the copolymer, specific peaks of pyridinium (py + ) reduction are observed. No signals of the BTEPy (included in the copolymer) are observed because the oxidation and reduction process are largely diminished once the species is entrapped in the polymer. The electropolymerization process was followed also via an electrochemical quartz crystal microbalance in order to measure the deposited amount. Figure 4 shows the increasing deposited mass with each scanning cycle. A total value of 3.2 µg.cm -2 was deposited after 50 scanning cycles.

Film morphology (atomic force microscopy)

The deposited film was also studied by scanning atomic force microscopy (AFM) (Figure 5). From Figure 5, it can be seen that the deposit shows packed aggregates. Tightly packed aggregated coils of the copolymer appear on the surface with an average diameter of ca. 200-300 nm. The deposited thickness varies with the number of scans, reaching 10 nm after 50 scanning cycle. The rms surface roughness of the Poly-BTEPy-ZnOEP film has been estimated at 3.3 nm (calculated from an area of 1 µm 2 ). The presence of tightly packed aggregated may be due to - interactions, in particular between porphyrin macrocycles.

X-ray photoelectron spectroscopy (XPS)

The copolymer films were also investigated by X-Ray photoelectron spectroscopy (Figure 6). XPS data revealed the presence of BTEPy in the final copolymer due to signal of sulfur S 2p3 at 165.0 eV, along with signals characteristic to the ZnOEP based copolymer described elsewhere [30][31] .

The analysis of the survey spectra of Poly-BTEPy-ZnOEP confirms the presence of the porphyrin subunits (Zn 2p3 at 1022.8 eV, C 1s, 285.6 eV and N 1s peaks). The N1s peaks reveal the presence of two chemically different nitrogen atoms. The contributions at 402.4 eV and 399.6 eV are attributed to the iminic nitrogen and to the reduced pyridinium respectively. Furthermore, the signals of phosphorus 2p3 (136.6 eV) as well as fluorine 1s (687.2 eV) correspond to the PF6 -counter-anion also present in the copolymer.

UV-visible spectroscopy and photoisomerization reaction

The optical properties of Poly-BTEPy-ZnOEP were recorded during UV-Vis experiments. Figure 7A presents the UV-Vis spectra as a function of the number of scanning cycles while Figure 7B shows a comparison between the UV-Vis spectra of ZnOEP alone, BTEPy alone as well as the polymer as obtained on ITO electrodes and the polymer dissolved in dimelthylformamide. Table 2 contains a summary of the absorption bands. It is important to notice that the Poly-BTEPy-ZnOEP displays mainly the specific band of the porphyrin when immobilized on ITO and it displays also the specific band of BTEPy while dissolved in DMF.

Please note that a quantitative quenching of the emission of the porphyrin for Poly-BTEPy-ZnOEP has been measured. The most important information of this paper is the ability of BTEPy to undergo its specific photoisomerization reactions inside the copolymer backbone (Scheme 2). Figure 8 shows the changes of UV-Vis spectra under the illumination at a wavelength of 300 nm followed by an illumination at a wavelength higher than the appearance of bands around 640 nm and 410 nm and the decrease in the initial band around 360 nm (Figure 8B). The ability of BTEPy alone to perform the photoisomerization reactions was also measured during the UV-Vis experiments performed in the same condition (Figure 9), proving that BTE behavior is not altered by attached pyridine. A model mixture ZnOEP/BTEPy (1/1) for a solution comparison has been also studied in DMF showing similar behavior than for BTEPy alone in solution has been observed as expected (Figure 10). Nevertheless, it is worthwhile to mention here that the copolymer Poly-BTEPy-ZnOEP cannot perform the photoisomerization reactions while immobilized onto ITO electrode. This result diverges with homopolymers obtained from 1,2-bis(3-thienyl)cyclopentene [23] which retain their photochromic properties both in solution and in the solid state. It can be explained by the presence of - interactions as well as electrostatic interactions between the pyridinium and the PF6 - counteranions in the copolymer (aggregated coils observed by AFM, Figure 5). Note that it takes about 30 minutes to perform the photoisomerization reactions from the open to closed form and reach the plateau in the case of Poly-BTEPy-ZnOEP polymer. In the case of BTEPy, the time required for the photocyclisation under the same experimental conditions was 5 minutes. This result can easily be explained for the polymer by the decrease in rotational freedom around the C-C bonds between the thiophene and cyclopentene rings because of the rigidity of each end of the photochromic skeleton joining the cross-linked polymer backbones, namely the porphyrins and the pyridinium. High reversibility of the interconversion openclosed form has been observed during repetitive switching cycles consisting of alternating UV-visible and visible irradiation (Figure 8F) and no spontaneous cycloreversion can be observed at room temperature.

Conclusion

In conclusion, we have demonstrated here the possibility to obtain a porphyrin based copolymer including bisthienylethene units.

The copolymer is able to perform photoswitchable isomerization reactions, proving that the incorporation of BTEPy was successful. This is a proof of concept and further associations of porphyrin and BTEPy are currently under development in our group.

Experimental Section

Most common laboratory chemicals were reagent grade, purchased from commercial sources and used without further purification. The zinc-β-octaethylporphyrin (ZnOEP) was purchased from Sigma-Aldrich. The pyridine substituted diarylethene, (1,2-Bis[2-methyl-5-(4-pyridyl)-3-thienyl]cyclopentene, abbreviated BTEPy) was synthesized according to the litterature [4] . 1 H NMR (400 MHz, CDCl3) δ (ppm) 8.51 (d, 6 Hz, 4H, pyridyl α-H), 7.33 (d, J=6.4 Hz, 4H, pyridyl β-H), 7.21 (s, 2H, thienyl C-H), 2.84 (t, 4H, -CH2-), 2.10 (m, 2H, -CH2-), 2.01 (s, 6H, -CH3). Voltammetric data have been recorded with a standard threeelectrode system using a PARSTAT 2273 potentiostat. Electropolymerizations have been carried out under an argon atmosphere using a 0.1 mol/dm 3 solution of 0.1 mol/dm 3 TBAPF6 in 1,2-C2H4Cl2/CH3CN (7/3) containing 0.25 mmol/dm 3 of ZnOEP and 0.25 mmol/dm 3 of BTEPy (Scheme 1) between 0 or -1.3 and 1.8 V vs. SCE. Single-side coated indium-tin-oxide (ITO, SOLEMS, 25-35 Ω/cm 2 ) electrodes with a surface area of 1 cm 2 were used as working electrode, and a platinum wire as auxiliary electrode. The reference electrode was the saturated calomel electrode which was electrically connected to the solution by a junction bridge filled with electrolyte. For each copolymer, the number of iterative scans (n) was 20. After electropolymerization, the modified working electrodes were washed with CH3CN and then with CH2Cl2 in order to remove the monomers and the conducting salt present on the deposited films. The electrochemically deposited films were dissolved and removed from ITO electrode with DMF. The operation is repeated 6 times. UV-vis absorption spectra were recorded with a single beam Hewlett-Packard HP 8453 diode array spectrophotometer operated at a resolution of 2 nm. A QCA-922 (SEIKO EG&G instrument) system combined STAT 3 was used for simultaneous electrochemical quartz crystal measurement (EQCM) and cyclic voltammetric measurements. The electrochemical cell was assembled in a glove box using an ITO AT-cut quartz crystal resonator (mirror finished, resonant frequency: 9.08 MHz ± 50 kHz, A = 0.2 cm2, SEIKO EG&G., LTD) as working electrode, a platinum wire as counter electrode, and a Ag/AgCl wire as a quasi-reference electrode. The solution used for the electropolymerization here is the same as the one used for electropolymerization of the copolymers with the larger ITO electrode. Iterative scans were conducted at a scan rate of 100 mV•s -1 at room temperature with simultaneous recording of the quartz resonance frequency. The change of the quartz resonance frequency (Δf) was converted into the mass change (Δm) by applying Sauerbrey's equation (eq 1):

∆f = -2f0 2 ∆m/A(µ.ρ) 1/2 (1)
where f0 is the resonant frequency of the fundamental mode, ρ is density of the crystal (2.684 g/cm3), A is working area (0.2 cm2) of the ITO quartz crystal resonator, μ is shear modulus of quartz (2.947×1011 g•cm -1 •s -2 ). XPS experiments were carried out on a RBD upgraded PHI-5000C ESCA system (Perkin-Elmer) with MgKR radiation (h=1253.6 eV) or Al KR radiation (h= 1486.6 eV). In general, the X-ray anode was run at 250W and the high voltage was kept at 14.0 kV with a detection angle at 54°. The pass energy was fixed at 23.5, 46.95, or 93.90 eV to ensure sufficient resolution and sensitivity. The base pressure of the analyzer chamber was about 5×10-8 Pa. The sample was directly pressed to a self-supported disk (10 x 10 mm) and mounted on a sample holder then transferred into the analyzer chamber. The whole spectra (0-1100 eV) and the narrow spectra of all the elements with higher resolution were both recorded by using RBD 147 interface (RBD Enterprises, U.S.A.) through the Auger Scan 3.21 software. Binding energies were calibrated by using the containment carbon (C1s = 284.6 eV). The data analysis was carried out by using the RBD Auger Scan 3.21 software provided by RBD Enterprises or XPS Peak 4.1 provided by Raymund W.M. Kwok (The Chinese University of Hongkong, China). Atomic force micrographs (AFM) measurements have been conducted directly on the ITO surfaces using a Dimension 3100 (Veeco) in the tapping mode under ambient conditions. Silicon cantilevers (Veeco probes) with a spring constant of 300 N/m and a resonance frequency in the range of 120-139 kHz have been used. The scanning rate was 1.0 Hz. Irradiation was performed using a 300 W Xe arc lamp (Lot, Quantum design) with intense focused output beams (50 mm beam diameter) equipped with a water cell filter to absorb the IR radiation. A spherical reflector collects the output from the rear of the lamp and focuses it on or near the arc for collection by the condenser. One condenser is positioned for compensating focal length change due to dispersion and to produce a beam converging to the photochemical cell. Filter at 300 nm and long pass filter at λ > 435 nm have been used. According to the supplier, the irradiance of the lamp from 435 nm to 800 nm was around 50 mW.m -2 .nm -1 .

Scheme 1

 1 Scheme 1 General electropolymerization scheme of ZnOEP with BTEPy.

Figure 1 .

 1 Figure 1. Cyclic voltammograms recorded A) between -1.30 V and +1.80 V vs. SCE and B) between 0.0 V and +1.80 V vs. SCE during the electropolymerization of 0.25 mmol/dm 3 ZnOEP with 0.25 mmol/dm 3 BTEPy in CH3CN/1,2-C2H4Cl2 (3/7) in the presence of 0.1 mol/dm 3 NBu4PF6. Working electrode: ITO. (←) Start of the scan. S =1 cm 2 ; scan rate: 0.1 V/s.

Figure 2 .

 2 Figure 2. Cyclic voltammetry of BTEPy in the open form (black curve) and closed form (dotted red curve under illumination at λ=330 nm) in CH3CN/1,2-C2H4Cl2 (3/7) with 0.1 mol/dm 3 NBu4PF6. (←) Start of the scan. Working electrode: ITO, S =1 cm 2 ; scan rate: 0.1 V/s.

Figure 3 .

 3 Figure 3. Cyclic voltammograms of Poly-BTEPy-ZnOEP (obtained after 50 scans, between 0.00 V and +1.80 V) in CH3CN/1,2-C2H4Cl2 (3/7) with 0.1 mol/dm 3 NBu4PF6. (←) Start of the scan. S =1 cm 2 ; scan rate: 0.1 V/s. Peak #: Fc/Fc + internal reference. Peak *: reduction of the isoporphyrin.

Figure 5 .

 5 Figure 5. Tapping mode AFM topography of A) and B) Poly-BTEPy-ZnOEP films (obtained after 50 scans, between 0.00 V and +1.80 V) and section analysis of the aggregate marked by a cyan line for B). C) Thickness measured by AFM versus different numbers of iterative scans.

Figure 4 .

 4 Figure 4. A) Consecutive cyclic voltammograms and electrochemical quartz crystal microbalance measurements for the first 20 scans during the electropolymerization of 0.25 mmol/dm 3 BTEPy with 0.25 mmol/dm 3 ZnOEP in CH3CN/1,2-C2H4Cl2 (3/7) in the presence of 0.1 mol/dm 3 NBu4PF6. Working electrode: ITO (A = 0.2 cm 2 ) deposited on a 9.08 MHz AT-cut quartz crystal. v = 100 mV s -1 . B) Mass change (Δm) calculated from Sauerbrey's equation versus the number of scan n.

Table 1 .

 1 Electrochemical data for ZnOEP, BTEPy and Poly-BTEPy-ZnOEP. 11 * (190), -0.52 irr (peak I) , -0.75 irr (peak II) , -0.85 (peak III) (92) Peak *: reduction of the isoporphyrin intermediate. a Potentials in V vs. SCE were obtained from cyclic voltammetry in 1,2-C2H4Cl2 with 0.1 mol/dm 3 NBu4PF6. Scan rate = 100 mV s -1 . Working electrode: ITO, S=1 cm 2 . b Open form of BTEPy. Potentials in V vs. SCE were obtained from cyclic voltammetry measured in the dark in CH3CN with 0.1 mol/dm 3 NBu4PF6. Scan rate = 100 mV s -1 . Working electrode: ITO, S=1 cm 2 . c Potentials in V vs. SCE were obtained from cyclic voltammetry in CH3CN/1,2-C2H4Cl2 (3/7) with 0.1 mol/dm 3 NBu4PF6. Scan rate = 100 mV s -1 . Working electrode: ITO, S=1 cm 2 . The given half-wave potentials are equal to E1/2 = (Epa+ Epc)/2. Under bracket: △Ep = |Epa-Epc|.

Figure 6 .

 6 Figure 6. XPS spectra of the modified ITO electrodes with Poly-BTEPy-ZnOEP obtained after 25 iterative scans between 0.00 and +1.80 V vs. SCE. (A) Global XPS spectra, (B) C 1s, (C) N 1s, (D) P 2p3, (E) Zn 2p3, (F) F1s, (G) S 2p3.

Figure 8 .

 8 Figure 8. A) UV-vis absorption spectral changes of Poly-BTEPy-ZnOEP (open-ring form to PSS) in DMF under different irradiation time by light at λ = 300nm and B) the corresponding differential spectra. C) Absorbance evolution at λ = 650 nm during the process A) and D). D) UV-vis absorption spectral changes of Poly-BTEPy-ZnOEP (PSS to open-ring form) in DMF under different irradiation time by light λ > 435 nm and E) the corresponding differential spectra. F) Absorbance evolution at λ = 650 nm during repetitive cycles to convert Poly-BTEPy-ZnOEP from open to closed form.

Figure 7 .

 7 Figure 7. A) UV-vis absorption spectra of Poly-BTEPy-ZnOEP (obtained after n iterative scans, between 0.00 V and +1.80 V) on ITO. B) UV-vis normalized absorption spectrum of Poly-BTEPy-ZnOEP (obtained after 25 iterative scans) onto ITO electrode (green line) or in DMF solution (blue line) compared to ZnOEP (black line) and BTEPy (red line) in DMF.

2 .

 2 Scheme 2. Open to closed interconversion of Poly-BTEPy-ZnOEP.

Figure 9 .

 9 Figure 9. UV-vis absorption spectral changes of BTEPy (open-ring form to PSS) in CH3CN under different irradiation time by light λ = 330 nm and B) the corresponding differential spectra. C) UV-vis absorption spectral changes of BTEPy (PSS to open-ring form) in DMF under different irradiation time by light λ > 435 nm and D) the corresponding differential spectra. C = 1.5.10 -5 mol/dm 3 .

  Compound closed-Poly-BTEPy-ZnOEP is stable at room temperature, but can be reverted back to open-Poly-BTEPy-ZnOEP by visible irradiation (Figures 8DE).The differential spectra show the disappearance of bands around 640 nm and 410 nm. It confirms the photoisomerization from the to the open form. However, the recovering the initial band around 360 nm is partial. It must be also noticed that a slight decrease of the bands associated to the ZnOEP porphyrin (Soret and Q bands) are observed during illumination (Figure 8E) which may indicate the formation of the radical ZnOEP • porphyrin which breaks the aromaticity of the macrocycle inducing the decrease of the intensity of the bands associated to the porphyrin These results suggest that during the photoisomerization reaction from the closed to the open form, the radicals formed can be at least partially delocalized to the porphyrin macrocycle (Scheme 2).

Figure 10 .

 10 Figure 10. UV-vis absorption spectral changes of the mixture ZnOEP + BTEPy (open-ring form to PSS) in DMF under illumination at λ = 330 nm during 10 minutes and B) the corresponding differential spectrum. C = 0.375.10 -5 mol/dm 3 . Blue curve: t = 10 minutes (BTEPy in closed form). Red curve: t = 0 min (BTEPy in open form).

Table 2 .

 2 UV-visible spectral data for ZnOEP and BTEPy in DMF, Poly-

	BTEPy-ZnOEP on ITO and in DMF. In brackets: molar extinction coefficient (ε
	/10 3 dm 3 •mol -1 •cm -1 ).
	Compound	Soret	Q bands/nm	π-π * Band/nm
		band/nm
	ZnOEP	408 (672.3)	538 (34.3)
			674 (37.7)
	BTEPy			283 (21.3),
				320 (14.4)
	Poly-BTEPy-ZnOEP (ITO)	425	554, 588
	Poly-BTEPy-ZnOEP (DMF)	421	547, 586

Acknowledgements

We thank CNRS, the Université de Strasbourg (France), Université Paris-Descartes (Paris, France), Sorbonne Université (Paris, France), and Fudan University (Shanghai, China) for funding of this work. The authors are grateful to the CNRS for constant financial support. We also thank the Oversea Study Program of Guangzhou Elite Project (GEP) for the Ph.D. grant of Zhaohui Huo. This work was also supported by Fund of senior visiting professor of Fudan University.

Conflict of Interest

The authors declare no conflict of interest The synthesis of a new diarylethene-porphyrin photoswitchable copolymer via the electropolymerization of zinc octaethyl porphyrin and pyridine substituted diarylethene is reported. The incorporated diarylethene maintains its reversible photochromism upon the UV-Vis radiation with multiple cycles of ring-opening and closing.

Entry for the


Ora Matushansky

Locatives are not cases: Evidence from Lak

Keywords: Case, locative cases, Nakh-Dagestanian, Lak

The generativist view of cases as features of an NP reflecting a relation to another constituent is incompatible with locative cases, which both encode semantic relations and stack in ways that indicate an independent syntactic projection. I will argue that Lak locative cases are best treated as nominal suffixes with axial semantics, like top in tabletop.

Introduction: Case, locative cases, and Lak

Case is usually defined as a system of marking a relation established between an NP and another element in the structure, as in [Blake 1994:6]: "Case is a system of marking dependent nouns for the type of relationship they bear to their heads". In the generative syntax Case has been implemented as a feature (or a feature bundle) on the noun phrase that varies in function of what that noun phrase establishes an (agreement) relation with (a functional head in a certain configuration for structural cases, the theta-assigner for inherent cases). 1 As is easy to see, this basic view is incompatible with semantic cases, of which locative cases are a principled subpart. In this paper I will argue that the so-called "locative cases" of Lak are in fact contentful morphemes.

Lak (lbe, a Nakh-Dagestanian language of Northeast Caucasus) has a rich system of locative affixes. While [Муркелинский 1971] advances the hypothesis that these affixes are postpositions, they are far more usually described as cases ( [Жирков 1955, Казенин 2013, Тестелец 2019], etc.). The locative specification of a noun phrase is constructed, as is usual for this group of languages, by the combination of a "series" marker (indicating the spatial relation) and a "mode" marker (indicating the type of movement or lack thereof). The spellout of locational affixes is agglutinative (1): all dynamic (directional, or "mode") suffixes are added on top of the essive (locative, "series") ones. The affixes are attached to the noun in its oblique form (indicated by the suffixal augment to be discussed below), while adjectives, demonstratives, etc., are not marked for case ([Жирков 1955:45]).

(1) a. q:at-lu-v(u) inessive, I-a house-OBL-IN in the house [Жирков 1955:36] b. q:at-lu-vu-x intranslative, IV-a house-OBL-IN-TRS through the house [Жирков 1955:36] c. q:at-lu-lu-x subtranslative, IV-f house-OBL-UNDER-TRS across under the house [Жирков 1955:37] This highly agglutinative nature of Nakh-Dagestanian case systems (see [Mel'čuk 2006[START_REF] Daniel | Case marking in Daghestanian: limits of elaboration[END_REF][START_REF] Radkevich ; Radkevich | On Location: The Structure of Case and Adpositions[END_REF][START_REF] Казенин ; Казенин | Синтаксис современного лакского языка[END_REF][START_REF] Тестелец | Именные локативные формы в дагестанских языках[END_REF]], among many others) has led [START_REF] Comrie | The great Dagestanian case hoax[END_REF]] to conclude the locative sub-domains of this case system should not be viewed as a list of cases on a par with the core cases of Indo-European languages and structural case.

(2) Lak locative cases essive allative elative translative versative

a. -v(u) 'in' ø -n -a(tu) -x -maj b. -j 'on' ø -n -a(tu) -x -maj c. -lu 'under' ø -n -a(tu) -x -maj d. -x 'behind' ø -n -a(tu) -x -maj e. -č'a 'near' ø -n -a(tu) -x -maj f. -c' 'next to' ø -n -a(tu) -x -maj at to from via towards
In fact, as already noted in [van Riemsdijk, Huybregts 2002], locative case composition follows the usually assumed syntax for paths [START_REF] Jackendoff ; Jackendoff | The base rules for prepositional phrases[END_REF][START_REF] Jackendoff ; Jackendoff | Semantics and Cognition[END_REF][START_REF] Jackendoff ; Jackendoff | Semantic Structures[END_REF][START_REF] Koopman ; Koopman | The Syntax of Specifiers and Heads[END_REF], den Dikken 2003], etc.): paths are constructed on the basis of places, as shown in (3). The fact that the static (essive) mode in Lak does not have an overt suffix (1a) supports this intuition. One view of Lak (and generally, ND) locative systems is that the locative affixes are in fact the functional heads Place 0 and Path 0 in (3), i.e., adpositions ( [Муркелинский 1971] for Lak, [van Riemsdijk, Huybregts 2002] for Lezgian). 3 If, however, they are regarded as cases, i.e., as features of the noun phrase ( [Жирков 1955, Казенин 2013, Тестелец 2019], etc.), several problems arise.

As is obvious from both its semantics and its morphology, a dynamic case, such as a sublative, consists of two sub-features: [sub] 'under ' and [trans] 'through' reflecting the features of Place (under) and of Path (through). Supposing the structure in (4), in order for the two features to be realized agglutinatively in the order in (1c), it is necessary to assume that they are ordered already on the NP. In other words, we need a structured case-feature bundle, and its structure has to reflect the order of assignment. The need for this structure appears to be successfully resolved under the view (e.g., [START_REF] Caha ; Caha | Case Movement in PPs[END_REF][START_REF] Caha ; Caha | The case hierarchy as functional sequence[END_REF][START_REF] Caha ; Caha | The German locative-directional alternation[END_REF]) where each case corresponds to some functional projection KP on top of an NP. Under this view, there is no case-feature assignment, there is selection for a certain KP, and the specific morphemes -lu 'under' and -x 'via' are realizations of the relevant KPs:

([Radkevich 2010:4] without reference; [Магомедбекова 1967:61]: Akhvakh essive is marked with -e-alternating with -i-).

3 Lak has "postpositions" that are distinct from "case markers", we will return to this issue in section 2.3. The same questions arise, however: how come the order of the two KPs reflects the order of the functional P-heads assigning the relevant cases? Note that if the semantics of 'under' and 'through' is present at KSUB 0 and KTRS 0 , respectively, the question arises of how these K-heads are different from adpositions.

It seems therefore reasonable to hypothesize with [Муркелинский 1971] that Lak locative cases are actually adpositions. It turns out, however, that this solution is insufficient.

Lak locative affixes as heads rather than features

As discussed above, Lak locative suffixes have clear semantic import, which is not the case for prototypical cases, such as dative or genitive. 4 Treating them as cases, i.e., as reflections of another element in the derivation, would entail postulating at least nine phonologically null prepositions with different semantics (the five localizing ones and the four non-stative modes).

It would also mean the existence in the language of several cases that can only be assigned by these null prepositions: thus, for instance, the elative suffix -a does not occur anywhere except on top of some localizing affix (as well as of certain locative adverbials, like šava 'home' or lagma 'around', on which see [Жирков 1955:127, Муркелинский 1971:246]). It seems unreasonable to have a case assigned by only one null morpheme. In addition to these logical arguments, we also have some morphosyntactic reasons against treating Lak locative suffixes as cases.

Versative

The versative "mode" suffix is special in two ways ( 5)-( 6). Firstly, unlike the allative, elative and translative suffixes, it combines with allatives rather than with essives. Secondly, it contains a class marker agreeing with the absolutive argument ( [Жирков 1955:39-40, Муркелинский 1971:87]), which is most often also the subject of motion.5 This kind of agreement also characterizes some other Lak spatial expressions, including šava 'home' (which can be lexically specified to bear uninterpretable class features).

(5) a. oʻrč' q:at -lu-vu-n-Ø-aj lavgunni.

boyI.ABS house -OBL-IN-ALL-AGRI-VERS went

The boy went towards the inside of the house.

b. ssil ninu q:at -lu-vu-n-n-aj durcunni.

sister.GEN=ERG motherII.ABS house -OBL-IN-ALL-AGRII-VERS brought

The sister brought the mother inside the house. [Жирков 1955:42] (6) a. oʻrč' aqu -Ø-vu-n-Ø-aj lavgunni.

boyI.ABS garden -OBL-IN-ALL-AGRI-VERS went-AGRI

The boy went towards the garden.

b. š:arrsa aqu -Ø-vu-n-n-aj largunni.

womanII.ABS garden -OBL-IN-ALL-AGRII-VERS went-AGRII

The boy went towards the garden.

c. baˁrč aqu -Ø-vu-n-m-aj lavgunni. calfIII.ABS garden -OBL-IN-ALL-AGRIII-VERS went-AGRIII

The calf went towards the garden. [Муркелинский 1971:66] On the assumption that inflectional affix ordering by default reflects the order of syntactic merge, the position of an agreement affix indicates that the versative is not a feature on an NP but an independent functional head. Indeed, other forms of the NP do not agree, so the class agreement marker cannot be a property of the NP itself. If the versative suffix were not an independent head, the class marker would have to appear on an additional functional head (i.e., the versative adposition assigning it). However, the class marker is located between the versative suffix and the NP, while the putative versative P 0 would necessarily appear either on the left or on the right periphery, leading to an incorrect order:

(7) a. *[FP n- [NP q:at-lu-vu-n- aj]] if P is right-branching PVERS 0 III house-OBL-IN-ALL-VERS b. *[FP [NP q:at-lu-vu-n- aj-] n] if P is left-branching house-OBL-IN-ALL-VERS PVERS 0 III
We conclude that the versative affix must be an independent functional head. The fact that it combines with allatives rather than with essives can then be explained in two ways: either as case-assignment (if the versative P 0 assigns the allative case) or as semantic role (if the versative is regarded as a non-intersective modifier of the allative). Under the latter view, the semantics of versative would be defined as in (8): taking a set of paths p and returning another set of paths, r, such that there exists in that set a path, p, that r is part of yet does not include its endpoint. In Lak, however, independent evidence may be provided in favor of the former hypothesis.

(8) [[VERS]] = λp  D path, t . λr  D path . p  p . r  p  ENDPOINT (p)  r,
where the endpoint of a path is defined as in [START_REF] Zwarts | Vector space semantics: a model-theoretic analysis of locative prepositions[END_REF] One problem with ( 8) is that it does not extend to the related language Avar, where, as noted by [Тестелец 2019:40], the same suffix may combine with allative (yielding the versative, 'towards') or with elative (yielding the directive elative, 'from the direction of'). In this latter case the starting point rather than the endpoint would have to be excluded. 6 This strongly suggests that semantically the versative/terminative suffix combines directly with the locus rather than with the corresponding paths, and independent evidence may be provided in favor of this hypothesis.

Mode markers

There is evidence that unlike other mode suffixes, allative (-n) is a case-marker. Firstly, as discussed above, it can be embedded ( 5)-( 6), and it is the only mode with this ability. Secondly, as noted by [Бокарев 1948:63, Жирков 1955:39], the allative case in Lak is syncretic with the dative:

(9) a. butta-l duš-ni-n lu lavsunni.

dative father.OBL-ERG girl-OBL-DAT book.ABS gave The father gave the girl a book. [Жирков 1955:41] b. oʻrč' q:at -lu-vu-n uvx:unni.

allative boyI.ABS house -OBL-IN-ALL entered-AGRI

The boy entered the house. [Жирков 1955:41] The assumption that the "allative" is actually the dative solves the versative issue: the versative can be straightforwardly defined modally as a set of paths that would end at its locus argument in the normal course of events, while the allative use of the dative can be assumed to arise from case-assignment by the verb. 7 The elative ('from') and the translative ('via') markers, on the other hand, seem most reasonably analyzable as postpositions, as suggested by [Муркелинский 1971]: while we see no independent evidence for or against this view, treating them as cases necessitates the postulation of the corresponding null postpositions, which seems like a less economical solution.

Series markers

The major argument against treating series markers as cases is the fact that they feed derivational processes: as illustrated in (10), they appear in complex nouns formed with the location suffix -alu-( [Жирков 1955:33, Абдуллаев, Эльдарова 2000:27]). 8 Similar nominalizations in Russian (e.g., primorje 'seaside', from pri 'by, near' and more 'sea') are derived from locative PPs.

(10) a. lamu-x-alu bridge BEHIND AREA the area beyond the bridge

b. vi-v-alu inside IN AREA the interior

A possible objection could be that Lak postpositions combine with the NP in the genitive case, whereas series markers combine, like the core cases, with the so-called oblique stem, derived with a root-specific augment (glossed as OBL in (1), ( 5), ( 6), ( 9)) or even suppletive, as in (9a): the absolutive form for 'father' is ppu ( [Жирков 1955:43]).

This objection is easily met, as this oblique stem is also what is used in compounds ( 11)-( 12) ( [Жирков 1955:41, Муркелинский 1971:124]), which entails that it is simply the Elsewhere form. 7 Alternatively, a null dative-assigning null preposition can be hypothesized. The choice between the two solutions would be determined by the possibility of having an allative NP inside a noun phrase, as in the road to Paris.

8 It should be noted that what looks like genitive case morphology can be found in compounds, e.g., in numeral-containing compounds like trëxnogij 'three-legged', from tri 'three' and noga 'leg' in Russian. Yet here the genitive ending seems to be a marker of the specific configuration rather than a derivational suffix and alternates with the usual compound linker o/e (e.g., odnonogij 'three-legged', from odin 'one', or tysʲačenogij 'thousand-legged', from tysʲača thousand'). [START_REF][END_REF] Irrespective of the status of this augment, stative locative forms can be reasonably assumed to have the syntax of compounding, with Lak series markers viewed as bound nominal roots (like the English -ware in silverware or -top in tabletop, rooftop, etc.). From the point of view of their semantics, they can be assimilated to axial parts ( [START_REF] Svenonius ; Svenonius | The emergence of Axial Parts[END_REF][START_REF] Svenonius | [END_REF]), which [START_REF] Matushansky | Tops and bottoms: axial nominals as weak definites[END_REF] argue to be nouns denoting locations rather than entities. Essive forms can therefore be nominal compounds with the semantics of loci (places): their syntax is that of locative adjuncts (or arguments), though they also exhibit nominal properties (see [START_REF] Matushansky ; Matushansky | The case of restricted locatives[END_REF]] for the hypothesis that both denotations are available for a noun).

If the stative locative "series" create nouns, it is unsurprising that these derived nouns can be case-marked with dative. The fact that they are marked with no other case is explained by the fact that they cannot appear in argument positions (where entity-denoting NPs would be required).

Independent support for this view comes from the so-called "spatial postpositions" in Lak: freestanding morphemes with the same spatial semantics and often, a similar phonological form:

(13) Lak postpositions ( [Жирков 1955:50,129, Муркелинский 1971:247]) "series markers" "postpositions" -v(u) 'in' viv 'inside' -j 'on' jalu 'in top of' -lu 'under' lu 'underneath' -x 'behind' maq 'behind' qiriv 'at the back of' -č'a 'near' č'arav 'nearby, beside' -c' 'next to' čulux 'close by'

Four out of the six series markers are transparently connected to the corresponding "postpositions": most clearly, the superessive jalu consists of the "series" marker j-'on' combined with the aforementioned nominalizer -alu-used to create names of locations ( [Муркелинский 1971:103])).

Just like the locus-denoting compounds that we have hypothesized above, all these "postpositions" combine with the mode suffixes (e.g., vivu-naj 'towards the inside', viv-atu 'from the inside'), yet with no other "cases" of Lak. Just like nouns, they all assign genitive case to their complements, which can always be omitted (and then these "postpositions" would function as spatial adverbials with a deictic or anaphoric reference point, cf. the English behind). Like series markers, they lend themselves to temporal meanings (e.g., maq can also mean 'after'), further supporting the hypothesis that they belong to the same semantic domain.

All these facts can be explained if these "postpositions" are free locative nouns (e.g., č'arav 'side', jalu 'top'), while the "series markers" (-v, -j) are their bound counterparts. Both denote in the locative domain and are therefore incompatible with argument positions.9

Summary

We have offered evidence against treating Lak locative affixes as cases. For the versative marker, the fact that it agrees with the absolutive argument strongly suggests that it is an independent syntactic head, and the position of the class marker further shows that it is the affix itself that realizes this head.

The semantics of the versative argues that it combines with a location rather than a path, contrary to what its morphosyntax suggests: the allative marker that the versative requires is unlikely to encode the allative semantics. However, given that the allative and the dative are syncretic in Lak, it seems reasonable to assume that allative is in fact dative. The other "mode" suffixes, the elative and the translative, can be readily analyzed as postpositions.

The remaining class of locative suffixes, the so-called "series" suffixes, have been argued to be bound nominal counterparts of locative nouns denoting axial parts. Evidence for this view comes from both the existence of purely spatial nouns (adverbs, in traditional terminology) and from the ability of both bound and free localizers to be marked with the dative case. While in other languages (e.g., Chalcatongo Mixtec [START_REF] Brugman ; Brugman | The use of body-part terms as locatives in Chalcatongo Mixtec[END_REF], see also [START_REF] Svorou ; Svorou | The Grammar of Space[END_REF]), Kîîtharaka [START_REF] Muriungi ; Muriungi | Categorizing adpositions in Kîîtharaka[END_REF])) axial nouns have been shown to mix nominal properties with locative semantics, referring in both domains, it is only in Lak that they would be assumed to have a purely locative semantics.

Analysis

Putting together what has been suggested so far, Lak stative locative suffixes can be described as phrasal affixes: from the semantic standpoint they combine with entire noun phrases, even though morphologically they form a nominal compound with the head noun. The nominal head (N 0 ) is marked oblique as the nonabsolutive default. The versative adposition (with its unvalued class feature) takes NP Place as its complement, to whose head it assigns dative case: As is easy to see, the structure and the derivation would be the same if we were DAT to assume that the inessive suffix -v(u) 'in' is a P 0 rather than an N 0 . The problem with this alternative would be the status of the allative/dative suffix: as adpositions cannot be case-marked, -n 'to' would have to be a contentful postposition, with the subsequent issues for the semantics of the versative as discussed above.

Finally, the hypothesis that locative morphemes can be a type of nominal heads forming a compound with the GROUND nominal explains the peculiar syntax of Lak locative affixes and supports adding a new route to the grammaticalization cline in [START_REF] Lehmann ; Lehmann | Grammaticalization: synchronic variation and diachronic change[END_REF]]: adpositions can also develop from axial part nouns. The case of Lak, whose locative suffixes seem to occupy an intermediate position between functional (P 0 ) heads and lexical axial parts would be a case in point.

Further questions: the approximative series

Zhirkov claims an additional incomplete locative case, the approximative (aka, apudlocative) one with the interpretation similar to the Russian u 'at/by':

(16) a. q:at-lu-x̂ [Жирков 1955:37] house-OBL-APPROX by the house b. q:at-lu-x̂:-un house-OBL-APPROX-ALL towards the house As a further point of similarity to the Russian u 'at/by', [Муркелинский 1971:86] calls this case the possessive one and claims that the general ablative case š:a 'from' (treated by Zhirkov as being outside the locative paradigm) is formed from it, with the reduplicated x̂: turning into š: by a more general phonological process and a regarded as the elative suffix. The same analysis is proposed in [Бокарев 1948:63], hypothesizing that the original meaning of this case was 'before'. If these analyses are right, the full locative paradigm should look as follows:

(17) Lak locatives The connection between the apudlocative and the possessive meanings has also been explored in [START_REF] Matushansky ; Matushansky | Intersecting location and possession[END_REF]], noting the same drift in languages as diverse as Russian (u 'at/by'), Hebrew (ecel 'chez', 'near/at' in Biblical Hebrew) and Dutch (bij 'at/by').

Potential objection: vacuous locatives

One potential argument against treating Lak locative suffixes as adpositions rather than cases is that locative forms can be used in non-locative senses. Thus [Тестелец 2019] considers the dative/allative syncretism in Lak or Avar or the genitive-elative syncretism in Bezhta and Hunzib as evidence for treating both as cases (see also [Бокарев 1948], [Казенин 2013]; as well as [Forker 2010] for Tsez, [Ганенков, Ландер 2011] for Dargwa), similar conclusions can be drawn from the use of superessive as an instrument, as in ( 18)). b. rik'-ira-x murx̂ buvtunni. [Жирков 1955:43] axe-OBL-POST tree.ABS cut.PAST He cut the tree with an axe.

This counter-argument, however, is rather weak, as regular adpositions (e.g., the English to for many datives) may introduce core arguments and l-selected PP complements (as in depend on) have as little or as much of the semantics of the preposition as do quirky objects. The fact that even "complex prepositions" may acquire non-compositional meanings ((19a) in both Russian and English, see also [START_REF] Marelj | Mistaking for: testing the theory of mediated predication[END_REF]] on for and in in non-verbal predication) and introduce arguments ((19b) in Hebrew) further shows that the semantic distinction is rather nebulous. We conclude that Murkelinsky's hypothesis cannot be rejected on semantic grounds and emphasize once again that the proposal advanced here (differing from Murkelinsky's only in the assumption that locative suffixes are nominal rather than adpositional) is motivated in this difference by the necessity to deal with the allative/dative case in versatives. 10

  2

  q:at-lu-vu-n-Ø-aj in (5a) can in a variety of ways. The versative adposition [φ]-aj might be a phonological clitic and cliticize to the essive-cum-dative suffix vu-n. The syntactic structure remains intact.Alternatively, the oblique-marked noun head-moves into the dative-marked locative nominal head N 0 Place, yielding a complex head (house-in):The resulting complex can head-move into the versative head (14c) or merge with it by any of the known morphosyntactic mechanisms like m-merger or Lowering (14d); the only difference is in the label:

(

  18) a. žul kolxoz-ra-vu traktor-da-x ğaj učajs:ar. [Бокарев 1948:62] our kolkhoz-OBL-IN tractor-OBL-POST till In our kolkhoz they till with a tractor.

One variant of this view (e.g., [Toman 1994, Watanabe

2006]) is that Case is not a property of the noun phrase (NP, DP) but rather of a special functional projection KP taking that noun phrase as a complement. For our purposes this makes no difference.

Such is not always the case in ND languages: in Akhvakh and Tindin essives are marked

Though, as shown by[START_REF] Cysouw | Reconstruction of morphosyntactic function: Nonspatial usage of spatial case marking in Tsezic[END_REF][START_REF] Daniel | Case marking in Daghestanian: limits of elaboration[END_REF], locative cases may have non-spatial uses approaching them to core structural cases, the same is true of adpositions (cf. on in depend on).

On agreeing adpositions, focus particles and adverbials in languages of the same area see[Кибрик 1999:182-183, 376, 410-412,

[608][609][610][611][612][613][614][615][616][617][618][619][620] on Tsakhur,[START_REF] Bond | Agreement domains and targets[END_REF],[START_REF] Polinsky | Agreement between arguments? Not really[END_REF], etc., on Archi, [Rudnev 2020] on Avar, among others.

Furthermore, as also noted by Testelets, the Avar directive elative does not exclude the starting point, which suggests that it subsumes the elative it is based on and only receives its non-initiative interpretation pragmatically: when the starting point is known to be excluded, bare elative is used and directive elative is used otherwise. We leave the precise interpretation of the versative and of the directive is an issue for future research.

Lak has other locative adverbials that only have locative cases([Жирков 1955:129], see[START_REF] Daniel | Case marking in Daghestanian: limits of elaboration[END_REF] for the same phenomenon in Bagvalal), e.g., x̂:ič' 'in front', daˁniv 'between', as well as some toponyms([Муркелинский 1971:103]).


Several issues to discuss: ➢ evidence for this view ➢ (accounting for the) variation ➢ relation to other "complex prepositions" ➢ cross-linguistic coverage

Elevator pitch: (a) there are no "complex prepositions" (b) PNPs are not a uniform category (c) variation is determined by a cluster of properties (the presence/lack of an article, of P1 and P2, modification and possessivization restrictions)

Caveat: not all PNPs have the structure in (4), see Philippova [to appear] for the evidence that dative PNPs like (5) involve a possessive PP complex [START_REF] Matushansky | To PPs in their proper place[END_REF]):

(5) a.

Ona posmotrela v-sled emu.

Russian, [START_REF] Philippova | Prepositional repercussions in Russian: Pronouns, ellipsis and comparatives, Ben-Gurion University of the Negev. Parameters of nominal deficiency in complex prepositions[END_REF] she looked in-step him.DAT She stared after him (watched him go).

b.

Maša bežala na-vstreču im. Masha ran on-meeting them.DAT Masha was running to meet them halfway.

Following [START_REF] Corver | Bij Marie in de nek[END_REF][START_REF] Broekhuis | Inalienable possession in locational constructions[END_REF][START_REF] Broekhuis | Inalienable possession in locational constructions: an apparent problem[END_REF][START_REF] Matushansky | To PPs in their proper place[END_REF], Matushansky 2021, and Philippova [to appear The lexical NP im 'them.DAT' here is not a dependent inside the PP

DECOMPOSING PNPS

It seems obvious that PNPs consist of several different parts. Two points of contention: ➢ the nature of the inner lexical part ( §2.1, noun for us, the functional head AxPart for [START_REF] Svenonius | The emergence of Axial Parts[END_REF][START_REF] Svenonius | Spatial P in English[END_REF] and a lot of follow-up work [START_REF] Muriungi | Categorizing adpositions in Kîîtharaka [01/10[END_REF][START_REF] Pantcheva | Persian preposition classes[END_REF][START_REF] Fábregas | Axial) parts and wholes[END_REF][START_REF] Takamine | The Axial Part Phrase in Japanese[END_REF][START_REF] Botwinik-Rotem | A closer look at the Hebrew Construct and free locative PPs: The analysis of mi-locatives[END_REF][START_REF] Roy | Complex prepositions[END_REF], Romeu 2014, etc.)) ➢ internal constituency ( §2.2) and variation ( §2.3)

On the nominal core of PNPs

Main evidence: the fact that N1 is so very often a lexical noun: direction/richting/napravlenie 'direction ', dessus/verx 'top', etc. Parameters of nominal deficiency in complex prepositions, Toulouse (September 30-October 1, 2021) It combines with a preposition (P1)

It has nominal syntax, like the article (or a possessive):

(7) a.

The chamber pot can be found at the foot of the bed.

M&Z b.

The grandfather clock is to the left of the wardrobe.

The determiner shows gender and number agreement with N1 and undergoes the en/au alternation (see [START_REF] Cornulier | A peeking rule in French[END_REF][START_REF] Zwicky | French prepositions: no peeking[END_REF][START_REF] Miller | The principle of phonology-free syntax: four apparent counterexamples in French[END_REF], Matushansky 2015, a.o.) characteristic of the interaction of the P+D complex with gender in French:

(8) a. Coordinating PNPs with the same P1 can in principle be possible only for a small subset of PNPs (for semantic reasons)

For cardinal points, potential cases of such coordination is structurally ambiguous in English: Possessivization (15), which breaks the linear sequence P1-N, can also be taken as evidence

Variation

The syntax of PNP sequences is not uniform Major points of variation [START_REF] Quirk | Complex prepositions and related sequences[END_REF][START_REF] Melis | La préposition en français[END_REF], Stosic and Fagard 2019, etc.) Alice did a solo on the saxophone. ?She did not realize it was out of tune. b.

The government acted in the light of his suggestions. ?It was very clear.

With PNPs pronominalization of just the nominal core is simply impossible

Invariability

Weak nouns resist modification and retain their number (usually, singular):

(24) resistance to modification Ziggy played (the) guitar. Parameters of nominal deficiency in complex prepositions, Toulouse (September 30-October 1, 2021)

(30) a. in (the) light of, for (the) sake of, at (the) risk of b.

sous (le) prétexte de, à (la) hauteur de [START_REF] Fagard | La formation des prépositions complexes : grammaticalisation ou lexicalisation ?[END_REF] For weak nouns, it is easy to see item-specific variation within the same semantic field:

(31) bare/definite variation With PNPs the N is usually metaphorically or metonymically shifted, rather than enriched:

(37) a. at the back of axial information only b. au pied de at+the foot of at the foot of The enriched interpretation is one of the reasons why modification of weak nouns is severely limited (more on this below) Parameters of nominal deficiency in complex prepositions, Toulouse (September 30-October 1, 2021) The change in meaning is not a special property of PNPs or PPs, as it is also found in idioms, including those with weak nominals (38).

(38) a.

adding insult to injury b.

think/*act out of the box

The change can be predictable (see Lauwers 2014a on sous)

Distributional restrictions

A noun is weak only with certain governors (prepositions or verbs):

(39) a. in bed vs. *on bed b.

play the piano vs. kick the piano (40) à/*de côté de, sous/#sur la botte de

The question remains how the combination of a preposition and a weak nominal is licensed (as both are needed), but is this so different from the question of how idioms are licensed?

SYNTACTIC CORRELATES OF SEMANTIC WEAKNESS

Main point: semantic irregularity does not entail irregular nominal syntax (it's unidirectional)

The presence of the article

The existence of near-minimal pairs shows that the choice between the presence and the absence of an article in PNPs is a low-level property of the weak noun in the context of the appropriate licenser:

(

Modification

PNPs differ with respect to their ability to have a modified nominal core For some PNPs, like for some weak nouns and semi-idiomatic PPs, modification is possible (though restricted):

The presence of an overt article makes modification more likely, but this may be because the class of PNPs is not defined and what is a PNP with an article for one would be a regular PP for another Parameters of nominal deficiency in complex prepositions, Toulouse (September 30-October 1, 2021)

(44) a. en prise (directe) avec in grip (direct) with in (close) contact with b. at (great/considerable/tedious/epic) length c.

go to (public) school Some require an adjective:

(45) a. on *(good) terms with b.

at *(great/public/considerable) expense

In general, only adjectives yielding degree interpretation or kind-level adjectives are possible:

(46) a. at great/*unforeseen expense b.

by (*late/*sheer/*big) car c.

in (sore/desperate) need of We don't know what makes modification possible for some PNPs and semi-idiomatic PPs, but the constraints seem similar

CONCLUSION AND FURTHER QUESTIONS

Main claim: PNPs are syntactically regular except for the missing article. This property they share with weak nouns, which most frequently appear in semi-idiomatic PPs

There is no insight in treating PNPs as a syntactic class

The hypothesis that the nominal core of PNPs is a weak noun is consistent with the lack of an article (in some PNPs), resistance to modification and number change, non-referentiality and special interpretation

Additional insights might come from PPs without an article (cf. [START_REF] Baldwin | In search of a systematic treatment of determinerless PPs[END_REF] The special meaning and special syntactic properties need to be encoded in the noun but take into consideration the surrounding context. Similar issues have been tackled in the treatment of idioms by the Distributed Morphology framework (starting with [START_REF] Marantz | Cat" as a phrasal idiom: Consequences of late insertion in Distributed Morphology[END_REF], who notes that idiomaticity does not change composition)

Archaic and unpredictable case-marking

Dutch lacks (except on pronouns) both case-marking and the feminine-masculine distinction (the two genders are neuter and common). However, some remnants of both are retained in PNPs and fossilized PPs:

( What is crucial in ( 48) and ( 49) is that the special form of the preposition is historically a P-D amalgam (like the French du or the German am)

The form of the noun is also case, but these could also be fossil words

This non-cliticized article takes these forms also with other prepositions (and the inflection is also found on demonstratives and adjectives in some fixed expressions):

(50) a. aan de-n lijf-e on the-MSG body-E personally b.

in de-r minn-e (schikken) in the-FSG love-E reach an agreement to reach an amicable agreement Given the existence of the mechanism ensuring a special allomorph in some PDN sequences, can the zero article be a special case of its application?

Against the nominal nature of the lexical core

Russian: n-augmentation of 3 rd -person pronouns only happens after prepositions [START_REF] Yadroff | The origin of prepositions[END_REF]Franks 2002, Philippova 2018 Philippova 2018: n-forms reflect the categorial feature [Prep], variation is due to whether the PNP is analyzed as a morphologically complex P-head or as a syntactic combination of an active P-and N-heads (p. 58) If PNPs involve a noun, why are n-forms possible? Possible answers:

(i) the genitive-marked lexical NP is actually a PP with a genitive-assigning null P (which may also be subcategorized for by comparatives, also taking n-forms) (ii) the feature [Prep] is assigned by the outer preposition (P1), and N is not a barrier for this case-assignment (unlike a regular N, but like noun-like cardinals)

In approaches the weak noun has special syntax, but the specialness is very different

APPENDIX: NON-DIAGNOSTICS FOR CONSTITUENCY

Apparent PN coordination:

(54) a. se mettre du côté et au niveau du genou blessé REFL put.INF of+the side and at+the level of+the knee wounded to place at the side and on the level of the wounded knee c. {avec/sans} l'aide de with/without the+help of with/without the help of This suggests that P1 is a preposition with its regular properties NB: The general invariability of outer prepositions is not a counterargument: it is a property of expressions with fixed meaning independently to PNPs (cf. in/out of love vs.in/#out of stitches) 7.

  Parameters of nominal deficiency in complex prepositions, Toulouse (September 30-October 1, 2021)

( 18 )

 18 the area [to the east of the river and (*the) north of the railway] a.to the [east of the river and north of the railway] mostly likely not this structure b.[to the east of the river] and [north of the railway] situated north of Z and south of W.

( 21 )

 21 Dominique a complété son projet à l'aide de l'ordinateur, et Dominique has completed their projet to the+help of the+computer, and Frédérique aussi. Frédérique also Dominique completed their projet with the help of the computer, and Frédérique too. The help that the computer has rendered in the two cases may be very different A bare PNP varies under a quantifier: (22) Elke aannemer werkte in opdracht van de overheid. Dutch each contractor worked in order of the government Each contractor worked by order of the government. Wide scope is impossible, suggesting that this is not an indefinite Anaphora removes the weak interpretation: (23) resistance to pronominalization Aguilar-Guevara and Zwarts 2010 a.

  to the red radio on the picnic table.

(

  25) a. ? in the bright light of his suggestions b. ? to the cold north of the city Most PNPs, like most weak nouns, are singular, yet plural ones are also possible. The change in number removes the "weak" interpretation: (26) a. If you get lost in the mountains, walk down. b. If you get lost on the mountain, walk down. no weak reading (27) a. sous les auspices de, aux alentours b. ? sous l'auspice de, *à l'alentour (28) resistance to pluralization a. Bob and Mary went to the hotels/#the hospitals. b. ? in the lights of these suggestions, at the risks of minor inflections c. op het gebied van A en B 'in the area of A and B' Dutch d. ? op de gebieden van A en B 'in the areas of A and B' Number-neutrality characterizes most shifted interpretations 3.3. Alternation with a bare NP Only a few weak nouns or PNP nouns can alternate, and the choice is often conditioned by dialect or register: (29) a. Mary went to (the) hospital. b.

  top and in front of the recycling bin Alternative analysis: right-node raising(Abbott 1976, Bachrach and Katzir 2009, a.o.RNR can be combined with a shared P1: (56) obéir sous la botte et la férule des pauvres Lauwers 2014a obey under the boot and the rod of+the poor to obey under the heel and the rod of the poor This also explains cases of coordination of a PNP and a P (Stosic and Fagard 2019): (57) intervenir [à cause de et malgré] la complexité de la situation intervene.INF at cause of and despite the complexity of the situation to intervene because of and despite the complexity of the situation Coordination of nominal cores does not seem to be possibleThe outer preposition (P1) can vary in function of direction, mode, or polarity: blessé Parameters of nominal deficiency in complex prepositions,Toulouse (September 30-October 1, 2021)

P2 forms a constituent with the lexical NP to the

	Parameters of nominal deficiency in complex prepositions, Toulouse (September 30-October 1, 2021)
	Any theory not treating N as a noun has to account for its nominal syntax
	We do not deny that PNPs can evolve into prepositions (cf. Noailly 2006, but also Fagard and
	De Mulder 2007, Le Draoulec and Rebeyrolle 2021):
	(12) a.	une mise en scène style Bob Wilson
		a staging		style Bob Wilson
		staging in the Bob Wilson style
	b.	histoire de se	faire	une idée
		en tête history of REFL make.INF an idea du train in head.F of.the train the matter of getting an idea	French, Roy 2006b
	in the front section of the train But they are not prepositions (cf. Place République) unlike the real preposition chez
	b. 2.2. Constituency au to.the.M foot.M of the+tree pied de l'arbre
	at the foot of the tree PNP sequences can't be treated as constituents to the exclusion of the lexical NP
	c. The inner preposition (P2) can be repeated across conjunction (for some PNPs, like (13), from in ons midden
	Fagard and De Mulder 2007):
	(13) Je travaille à	l'aide	de	jeux de rôles et de Gestalt-thérapie.
	I work at/to DEF+help of/from game of roles and of Gestalt-therapy
	I work using roleplay and Gestalt-therapy.
	(9) a. This means that exclusion of P1 and N1: po povodu + GEN Russian along occasion.DAT
	on the occasion of (14) à l'aide [PP2 de jeux de rôles et de Gestalt-thérapie]
	b. The combination of P2 and the following NP also pass other constituency tests: v-pered-i + GEN
	in front LOC in front of (locative) (15) possessivization (only if P2 is de or its equivalent)
	c. a. b. in front (10) a. a son v-pered-0 at/to 3SG.POSS unbeknown insu unbeknown to him/her in Jans richting in Jan's direction in Jan's direction à l' insu de c. v moem napravlenii	French Dutch French Russian
		at/to DEF unbeknownst of/from in my direction
		unbeknownst to in my direction
	b. (16) R-pronominalization by dint of
	c. a.	onder het mom van im Hinblick wor.auf/dar.auf	Dutch German, Trawiński 2003
		under DEF guise of in+the view WO+on/DA+on
		under the pretext of in terms of what/of it
	…this is unproblematic in view of the existence of fossil words (Aronoff 1974, aka cranberry b. in lijn er.mee
	words, Richter and Sailer 2003): freestanding morphemes appearing only in one particular
	environment or a few:
	(11) a.	kith and kin
	b.	mettle (in high mettle, test/prove/show (one's) mettle, on (one's) mettle)
	Historically the nominal core of PNPs is clearly a noun. What is its synchronic status?
	➢	Svenonius 2006, 2010: AxPart (a functional head)
	➢	Matushansky and Zwarts 2019: weak nouns
	➢	the PNP view: ?

Dutch in our.N middle.N in our midst

In languages with case-marking the noun shows case morphology (which can be irregular, as in (9b), see also section 5.1): ACC to the front of (directional)

It can even be modified (e.g., in the general direction of), on which more below While the distribution of the noun may be limited to the PNP in question…: Dutch in line R+with in accordance with it Dislocation (Seppänen et al. 1994) seems to work in English and Dutch: (17) a. Of which proposal do they seem to be in favor? b. Met welk voorstel zijn ze in tegenspraak? with which proposal are they in conflict With which proposal are they in conflict? Parameters of nominal deficiency in complex prepositions, Toulouse (September 30-October 1, 2021)

  Philippova 2018: in (53) a possessive pronoun is possible as well, but it is not the case that all PN[P]s have all three options There are no PN[P]s that allow only n-forms Parameters of nominal deficiency in complex prepositions,Toulouse (September 30-October 1, 2021)

				):
	(51) a.	datʲ	ej/*nej
		give.INF her.DAT
	b.	po	nej/*ej
		along her.DAT
	(52) a.	znatʲ	ego/*nego
		know.INF him.DAT
	b.	bez	nego/*ego
		without him.DAT
	And it also happens with PNPs without an overt P2 (i.e., those where the lexical NP surfaces in
	the genitive):
	(53) a.	v ramkax	nego/ego	Philippova 2018:55
		in framework.PL.LOC it.GEN
		in its framework
	b.	vozbuždenie v otnošenii nego/ego ugolovnogo dela
		initiation	in relation he.GEN criminal.GEN case.GEN
		initiation of a criminal case with respect to him