Marcus Seidel

Thibault Chervy

Anoop Thomas

Elias Akiki

Robrecht M A Vergauwe

Atef Shalabney

Jino George

Eloïse Devaux

James A Hutchison

Cyriaque Genet

Thomas W Ebbesen
email: ebbesen@unistra.fr

Correction to Vibro-Polaritonic IR Emission in the Strong Coupling Regime

The method of tting the micro-cavity transmission spectrum to derive the cavity absorption spectrum by means of transfer matrix analysis was awed. Consequently, by contrast to our initial conclusions, the polaritonic emission appears thermalized and there is no evidence for polariton emission which is blue-shifted with respect to the polariton absorption. For this reason, the interpretation of the blue-shift as a signature of polariton-polariton interactions is obsolete.

). However, by virtue of

the Kramers-Kronig relations, the relatively strong absorption lines at lower energies (cf.

original Figure 2(a)) inuence the refractive index in the vicinity of the strongly coupled C=O stretching band. Therefore, the simulated free spectral ranges between the cavity and the polariton modes were incorrect. Second, a small aperture was kept inside the Fourier transform infrared (FTIR) spectrometer transmission compartment for both emission and transmission measurements. As a consequence, only a small area of the prepared cavity was sampled. It was not checked which part of the emitting sample was imaged onto the aperture in the transmission compartment. Therefore, it is likely that dierent spots of the same sample were measured in transmission and emission, respectively. A lm thickness inhomogeneity on the order of 10 nm (the polymer lm was about 4 µm thick) can cause a spectral shift of the modes on the order of the initially derived polariton blue-shift (17 cm -1 and 6 cm -1 ) . Both errors added up in a way that the transmission spectrum t yielded a match of emission maxima and reectivity minima at the 1 st and the 3 rd cavity mode, as expected from thermalized emission (cf. original Figure 3 (b)). The emission maxima appeared however blue-shifted with respect to the reection minima (cf. original Figure 3 (d)). It is to note that absorption maxima and reection minima overlap.

In an analogous manner to the procedure described in the original paper, we spin-coated an about 1 µm thick PMMA lm on a 0.5 mm thick silicon substrate. We measured the sample transmission with an FTIR spectrometer and tted it by transfer matrix analysis while optimizing the model of the dielectric function of PMMA. The silicon substrate was treated as an incoherent layer. Its complex refractive index was taken from the literature [START_REF] Chandler-Horowitz | High-accuracy, midinfrared (450 cm -1 ≤ ω ≤ 4000 cm -1 ) refractive index values of silicon[END_REF] and was in good agreement with experimental data. To approximate the dielectric function of PMMA, we started from the Lorentz-oscillator model used in the original paper. Next, we adjusted the imaginary part of the PMMA complex refractive index and nally applied Kramers-Kronig relations to obtain the real part of the refractive index. [START_REF] Törmä | Strong coupling between surface plasmon polaritons and emitters: a review[END_REF] Figure 1 shows the measured transmission spectrum, the t with the originally used simplied dielectric function and the t with the rened dielectric function.

Consequently, we tted again the cavity transmission and emission data originally published. The t of the polaritonic transmission peaks is shown in Figure 2(a). The horizontal black bar denotes the spectral region which has previously been considered (original Figure 2(b)). Subsequently, the polaritonic peaks are modeled well by both dielectric functions.

However, the transmission peaks of the 1 st and the 3 rd cavity mode are only well matched by the rened dielectric function whereas the simulation predicts blue-shifted peaks for the originally used function. Figure 2(b) shows the derived normalized absorption spectra and compares them to the experimentally determined emissivity. The use of the original dielectric function results in a good agreement between the 1 st and the 3 rd cavity mode peak locations, but a larger discrepancy between the measured and simulated lower polariton emissivity peaks. This led to the original conclusion of non-thermal polariton emission. By contrast, the rened dielectric function shows not only a spectral oset for the polariton peaks, but also for the peaks of the bare cavity modes, that is, the whole simulated absorption spec- The clear osets between experimental and simulated 3 rd cavity mode peaks manifest that the originally measured transmittance and emissivity spectra were not directly comparable as the locally sampled cavity lengths were dierent.

To attain consistence between simulations, emissivity and transmittance measurements, we prepared another Fabry-Pérot cavity comparable to the one used to collect the original data. We used a ZnS substrate, sputter-coated an about 10 nm thin Au lm on it, spincoated an about 4 µm thick PMMA layer on top and nally closed the cavity by sputtercoating another about 10 nm thin Au lm. We removed the aperture from the transmission compartment of the FTIR to sample the same cavity area in emission and transmission.

As a consequence, the signal-to-noise-ratio in the emission measurement was reduced, and thus we performed an additional correction for atmospheric absorptions in the FTIR and Figure 4: Transmittance and emissivity in the spectral range from 1400 cm -1 to 2000 cm -1 for (a) the original data (cf. Figure 2) and (b) the recently acquired data (cf. Figure 3). Solid lines represent transmittance spectra, dashed lines emissivity spectra, gray lines experimental data, red lines transfer-matrix simulations with the initially used dielectric function of PMMA and blue lines transfer-matrix simulations with the rened dielectric function. In addition to the funding acknowledged in the original publication, M.S. acknowledges

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Modeling of the PMMA dielectric function. Gray solid line: normalized transmittance spectrum of a 1.05 µm PMMA lm on a Si substrate measured with a FTIR spectrometer. Red dashed line: Model of the dielectric function used in the original paper. Blue dashed line: rened model of the dielectric function including more absorption lines.

  we subtracted the reference spectrum from the signal of the sample and the experimental blackbody spectrum (cf. Eq. (13) of the original paper). Measurement results and simulations are shown in Figure3. As in Figure2(c) and (d), the peaks of 3 rd cavity mode emissivity and simulated absorption were matched. Figure3(a) exhibits again an overlap of simulated and measured polariton emission peaks if the rened dielectric function is used, whereas the original dielectric function predicts blue-shifted emission of the lower polariton. This is highlighted in Figure4where only the spectral range from 1400 cm -1 to 2000 cm-1 is considered like in Figure3(d) of the original publication. The absence of the aperture in the transmission compartment leads to a clearly improved agreement between measured and simulated transmittance spectra as the comparison between the Figures 2(d) and 3(b) demonstrates. The shift between measured and simulated 3 rd cavity mode as well as the linewidth dierence is much smaller in the latter case. The rened dielectric function leads also to a good agreement between measured and simulated transmittance of the polariton modes as Figure 4(b) shows.


Jyoti Lather

Pooja Bhatt

Anoop Thomas

Thomas W Ebbesen
email: ebbesen@unistra.fr

Jino George
email: jgeorge@iisermohali.ac.in

Cavity Catalysis by Cooperative Vibrational Strong Coupling of Reactant and Solvent Molecules

Abstract: Here we report the catalytic effect of vibrational strong coupling (VSC) on the solvolysis of para-nitrophenyl acetate (PNPA) whereby the reaction rate is increased by an order of magnitude. This is observed when the microfluidic Fabry-Perot cavity, in which the VSC is generated, is tuned to the C=O vibrational stretching mode of both the reactant and solvent molecules. Thermodynamic experiment confirms the catalytic nature of VSC of the system. The change in the reaction rate follows an exponential relation with respect to the coupling strength of the solvent indicating a cooperative effect between the solvent molecules and the reactant. Furthermore, the study of the solvent kinetic isotope effect clearly shows that the vibrational overlap of C=O vibrational bands of reactant and the strongly coupled solvent molecules is critical to observe the catalysis in this reaction. The combination of cooperative effect and cavity catalysis confirms the potential of VSC as a new frontier in chemistry.

Strong light-matter coupling offers a unique way of controlling internal reaction coordinates by coupling molecular transitions to the vacuum field (zero-point energy) of a cavity mode. [1][2][3][4][5][6][7] VSC was introduced to couple selectively a vibrational mode, [8,9] which is easily achieved in the liquid state in a microfluidic Fabry-Perot (FP) cavity. [10] Thomas et al., observed the modification of the rate of a C-Si bond breaking process and more recently demonstrated changes to the branching ratio of products by selective VSC of silane derivatives. [3,6] Recently, Hiura et al reported the possibility of accelerating reactions by vibrational ultra-strong coupling of water molecules involved in hydrolysis reactions. [7] In both cases, reactants were directly coupled to cavity modes and the reaction rates could be controlled by moving the physical distance between the mirrors of a FP cavity, i.e. by tuning the coupling to a given vibrational resonance. Recent theoretical studies confirm that potential energy surfaces and reactivity can be modified by coupling to the vacuum field, although the critical role of the solvent is hard to simulate. [11][12][13][14][15][16] VSC condition can be achieved by injecting a molecular liquid into an FP cavity in which the vibrational transition interacts with the cavity mode (Figure 1a) to generate two new eigen states, called vibro-polaritonic states (P+ and P-). The interaction energy (Rabi energy; ℏ𝛺 VR ) is proportional to the transition dipole moment d and the electric field (𝐸) of the electromagnetic mode of the cavity:

ℏ𝛺 VR ∝ 2𝑑 ⋅ 𝐸 × √ 𝑛 ph + 1; 𝐸 = √ ℏ𝜔 2𝜀 0 𝑉 (1)
where 𝜀 0 is the vacuum permittivity, 𝜔 is the vibrational frequency, 𝑉 is the mode volume of the cavity and 𝑛 ph the number of photons involved in the coupling process. When the latter goes to zero, a residual Rabi splitting energy remains even in the dark due to the coupling to the zero-point energy of the cavity. Importantly, ℏ𝛺 VR is proportional to √𝑁 𝑉 ⁄ ~√𝐶 where N is the number and C the concentration of the coupled molecules interacting strongly with the cavity mode. [1][2][3] In this communication, we report the solvolysis of PNPA catalysed by VSC under cooperative strong coupling effect between the reactant and the solvent molecules. In other words, when the solvent and the reactant molecules have the same vibrational bands but only the solvent is at sufficiently high concentration to be strongly coupled to the cavity mode, it increases the reaction rate more than one order of magnitude at room temperature. The FP cavities used in the present experiments were prepared with Au mirrors sputtered on to IR transparent BaF2 windows by following a reported procedure. [10] The Au mirrors were protected with 100 nm of sputtered SiOx. The spacing between the mirrors used for the current study is set to 18 m to couple the C=O stretching mode of PNPA molecules (Figure 2a). Such F-P cavities can hold up to 3 L volume of reacting solution. The non-cavity experiments were carried out in a microfluidic cell made of the same windows without the Au mirrors. See Supporting Information (SI) for further details. The PNPA solvolysis [17][18][19] in this study was carried out under mild basic conditions provided by tetrabutylammonium fluoride (TBAF), as schematically shown in Figure 1b. TBAF in Ethyl acetate (EtOAc) normally follows base catalysed acyl (BAc2) bond breaking mechanism (see SI and Scheme S1). EtOAc was chosen as the solvent because its carbonyl stretching transition overlaps with that of the reactant PNPA (Figure 2b; red traces). Both PNPA and TBAF solutions were prepared separately, mixed outside and injected into the FP cavity. Figure 2. a) Parts of a flow cell micro cavity-QED reactor. b) IR transmission spectra of 10% EtOAc (red trace) in hexane and 100 times magnified 0.1 M PNPA (dotted red trace). Vibro-polaritonic states P+ and P-formed by coupling to the 10 th cavity mode (black trace; pathlength is approx. 18 m) with TMM simulation (dotted black trace). Strong coupling of the C=O stretching mode of neat 12 EtOAc to the 10 th mode of the F-P cavity gives a Rabi splitting of 155 cm -1 , which is equivalent to 4.4 % change in the actual transition energy with P+ and P-at 1840 cm -1 and 1685 cm -1 , respectively (Figure 2b and Figure S2). In the reactive mixture, the PNPA represents only 0.1w% of the mixture and is thus unable to undergo strong coupling to the FP cavity at such low concentrations. [1] One of the questions we address here is whether VSC of 12 EtOAc can nevertheless influence the reactivity of PNPA in such conditions even though it is not a reactant. The major product of the PNPA solvolysis is the para-nitro phenoxide (PNP-) having an intense absorption peak at 407 nm. Since the transparency region of BaF 2 windows extends well in to the UV (ca. 200 nm), the progress of the reaction can be easily monitored by following the temporal rise of PNP-absorption peak as shown in Figure 3a (see also Figure S6). In other words, while the FP cavity is set to couple the C=O vibrational band in the IR, the influence of strong coupling on the reaction rate is being monitored in the UV-Vis region. This condition helps to avoid complications such as filter effects and other issues ) and non-cavity (red circle; 0.18x10 -2 ) for 12 EtOAc. c) Carbonyl stretching modes of pure PNPA (ATR spectrum; black trace); FTIR spectra of 12 EtOAc (blue trace) and 13 EtOAc (red trace) molecules (10 % in hexane). d) The corresponding kinetic traces measured by tuning the cavity ( 12 EtOAc blue circle; 13 EtOAc red circle) and non-cavity ( 12 EtOAc blue empty circle; 13 EtOAc red empty circle); 10 th mode of the cavity overlap with the carbonyl stretching mode of 12 EtOAc and PNPA. The dashed curves are guides to the eye. related to the FP cavity configuration. By having a tenfold excess of PNPA as compared to TBAF (0.1 M vs 0.01M), a pseudo-first order kinetics is observed. Apparent rate constants (kapp) were determined by linear regression method (Figure 3b). [17] In the normal non-cavity, the apparent rate constant (kapp nc ) is on the order of 0.2 x 10 -2 s -1 (Figure 3b). To prepare an ON-resonance cavity, the empty cavity is tuned slowly to the desired pathlength and is kept undisturbed for 30 minutes (Supporting Information). Subsequently, the reaction mixture is injected into the cavity and the kinetic traces are recorded. Under ONresonance condition, in other words when the cavity is tuned to 12 C=O stretching mode of ethylacetate ( 12 EtOAc), the kapp cav increased by more than one order of magnitude (2.5 x 10 -2 s -1 ) compared to the non-cavity as shown in Figure 3b. kapp cav levels off to normal values (kapp nc ) when the cavity is detuned from the C=O mode of 12 EtOAc (the OFF-resonance measurements) as shown in Figure 3d. Please note that the noncavity and the cavity conditions are exactly the same, except the presence of Au mirrors in cavity, and kapp nc is unaffected by small variation in the spacer thickness (blue empty circle in the Figure 3d). Interestingly, the increase in kapp cav follows the vibration envelope of C=O stretching mode of 12 EtOAc molecules that is coupled to cavity mode (Figure 3c andd), following its full width-half maximum (FWHM; 25 cm -1 ). This suggest a cooperative effect between the strongly coupled solvent and the reactant.

In order to confirm this cooperativity effect, we have conducted kinetic isotope effect (KIE) experiments using the 12 C=O ( 12 EtOAc) and 13 C=O ( 13 EtOAc) isotopes with carbonyl vibrational resonances at 1750 and 1706 cm -1 , respectively (Figure 3c). Outside the cavity, the use of 13 EtOAc gives an apparent rate one order of magnitude lower ( 13 kapp = 2.4x10 -4 s -1 ) with respect to the rate with the 12 EtOAc isotope. This large change in the reaction rate can be due to a secondary isotope effect in which the 12 EtOAc is coupled to PNPA carbonyl vibrational state, facilitating external vibrational energy transfer in the system. [20] Please note that the rate determining

step for the BAc2 mechanism is the attack of nucleophile on the electron deficient carbonyl carbon atom. [17][18][19] Very interestingly, under VSC of 13 EtOAc, the reaction rates are not modified. Kinetic action spectra measured as a function of cavity tuning, Figure 3d, shows no change in the rate for the 13 EtOAc solvent system relative to rate outside the cavity, in contrast to 12 EtOAc. This is a confirmation that the VSC of 12 EtOAc is acting cooperatively and perturbing the PNPA internal reaction coordinate so as to affect its bond dissociation energy as will be discussed again further down in agreement with recent theoretical predictions. [21] To clarify how the VSC is affecting the reaction barrier and whether it is truly catalysing the reaction, the temperature dependence of the reaction rate was analysed to extract the thermodynamics activation parameters. As it is immediately apparent from the slopes in Figure 4a, the activation energy drops under VSC. The enthalpy of activation (H ‡ ) calculated from Eyring equation decreases substantially from 53.2 kJ/mol to 7.9 kJ/mol (Figure 4a; Supporting Information), indicating that the transition state (TS) is far more stable under VSC of 12 EtOAc molecules. Another very interesting finding is that the entropy of activation (S ‡ ) also decreases significantly from -70.9 J/K/mol to -206.2 J/K/mol offsetting partially the change in H ‡ . This large decrease in S ‡ indicates that the TS is far more polar under VSC thereby structuring the solvent cage which also decreases H ‡ . In other words the solvent-solute interactions are much stronger under VSC, thereby favouring BAc2 mechanism by stabilizing the intermediates. We then looked into the reaction rate variation with respect to cooperative coupling strength of the 12 EtOAc molecules. To do this we fixed the concentration of PNPA (0.1 M) while varying the 12 EtOAc concentration in a mixed anisole - 12 EtOAc solution. We chose anisole as a cosolvent; the relative solvent polarity difference is only 0.03 compared to EtOAc and the rate is essentially the same in anisole and 12 EtOAc in the absence of VSC (Figure S3) ( 12 EtOAc to reactant ratio is close to 1000, we assume that the vibrational bath is still preserved at the lower concentration of 12 EtOAc). An exponential rise in the reaction rate is observed upon increasing the concentration of 12 EtOAc under strong coupling condition, in other words with the Rabi splitting (Figure 4b). Such an exponential dependence has also been observed for both a slowing desilanation reaction [3] and for an accelerating hydrolysis reaction. [7] This probably points to a more general feature that the activation energy varies linearly with the Rabi splitting in whichever direction the barrier is moving under VSC.

In conclusion, the thermodynamic data shows unequivocally that the reaction is catalyzed under VSC of the solvent. The large decrease in the entropy of activation indicates that the electron density distribution is strongly modified in the TS under VSC resulting in a more polar activated complex. The solvent concentration dependence and the kinetic isotope effect demonstrates that VSC can be transferred from the solvent to the solute as long as their vibrational resonances overlap. This spectral overlap is not in itself enough to transfer VSC from the solvent to the reactant. Clearly the solute-solvent interactions must be strong, e.g. dipolar coupling, to induce the transfer, as has recently been shown in a theoretical study of ensemble induced strong coupling effects on single quantum objects. [21] Other theoretical studies have considered chemical reactivity under VSC in the gas phase and confirm that the reactivity should be modified. [13][14][15][16] In view of the important role of solvation in the TS, further theoretical studies taking into account solvation effects under VSC would be very helpful. On the experimental side, many more classes of reactions need to be studied in order to extract general principles that govern reactions under VSC. The use of cooperative effects as demonstrated here should greatly facilitate this task since it removes the requirement of high concentration of reactants to achieve the strong coupling condition. Action spectra under VSC can be used as a spectroscopic tool to help to elucidate which vibrations play a role in the reaction path. These findings should have large impact on controlling and understanding chemical reactivity through VSC.

Figure 1 .

 1 Figure 1. a) Schematic representation of vibropolaritonic states formed from a molecular vibrational state and a F-P cavity mode. b) The hydrolysis of PNPA in ethyl acetate (EtOAc).The FP cavities used in the present experiments were prepared with Au mirrors sputtered on to IR transparent BaF2 windows by following a reported procedure.[10] The Au mirrors were protected with 100 nm of sputtered SiOx. The

Figure 3 .

 3 Figure3. a) Absorption spectra shows the evolution of PNP -species during the ester hydrolysis. b) Pseudo first order kinetic traces measured at 407 nm for cavity ON-resonance (blue circle; 1.6x10 -2 ), cavity OFF-resonance (blue hollow circle; 0.16x10 -2 ) and non-cavity (red circle; 0.18x10 -2 ) for12 EtOAc. c) Carbonyl stretching modes of pure PNPA (ATR spectrum; black trace); FTIR spectra of12 EtOAc (blue trace) and13 EtOAc (red trace) molecules (10 % in hexane). d) The corresponding kinetic traces measured by tuning the cavity ( 12 EtOAc blue circle;13 EtOAc red circle) and non-cavity ( 12 EtOAc blue empty circle;13 EtOAc red empty circle); 10 th mode of the cavity overlap with the carbonyl

Figure 4 .

 4 Figure 4. (a) Eyring plot for reaction inside the cavity (blue circles) and non-cavity (cell; red circles); (b) Apparent rate constant as a function of Rabi splitting under VSC of 12 EtOAc. Dotted lines are the corresponding linear fitting.

Acknowledgements J.G. would like to thank Department of Chemical Sciences, IISER Mohali for using the facilities; DST-SERB, Core Research Grant (EMR/2017/003455) is also acknowledged. J. L. and P. B. thank IISER Mohali for research funding. TWE acknowledges support of the International Center for Frontier Research in Chemistry (icFRC, Strasbourg), the ANR Equipex Union (ANR-10-EQPX-52-01), the Labex NIE projects (ANR-11-LABX-0058 NIE) and CSC (ANR-10-LABX-0026 CSC) within the Investissement d'Avenir program ANR-10-IDEX-0002-02 and the ERC (project no 788482 MOLUSC). Keywords: Cavity Catalysis • Cooperativity • Vibrational Strong Coupling • Polaritonic Chemistry •


Vincent Claveau
email: vincent.claveau@irisa.fr

Detecting fake news in tweets from text and propagation graph: IRISA's participation to the FakeNews task at MediaEval 2020

This paper presents the participation of IRISA to the task of fake news detection from tweets, relying either on the text or on propagation information. For the text based detection, variants of BERTbased classification are proposed. In order to improve this standard approach, we investigate the interest of augmenting the dataset by creating tweets with fine-tuned generative models. For the graph based detection, we have proposed models characterizing the propagation of the news or the users' reputation.

INTRODUCTION AND RELATED WORK

This paper describes the systems that we developed for the textbased and structure-based MediaEval 2020 Fake News detection challenge. These two subtasks and the datasets are detailed in [START_REF] Pogorelov | FakeNews: Corona Virus and 5G Conspiracy Task at MediaEval 2020[END_REF] and [START_REF] Daniel | FACT: a Framework for Analysis and Capture of Twitter Graphs[END_REF].

Text classification is a common NLP task [START_REF] Kowsari | Text Classification Algorithms: A Survey[END_REF]. Although simple machine learning approaches have shown promising results for fake news detection [START_REF] Maigrot | MediaEval 2016: A multimodal system for the Verifying Multimedia Use task[END_REF], the recent transformer-based architectures, such as BeRT [START_REF] Devlin | BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding[END_REF], have set new standards. Several large pre-trained transformer models are now available; they are known to yield stateof-the-art results on many NLP tasks including text classification [16, inter alia]. We rely on one of these pre-trained models to build our systems. In order to improve this standard approach, we have investigated the interest of augmenting the dataset artificially by generating tweets with fine-tuned generative models (one for each class). These approaches and results are detailed in Sec. 2.

Similarly, classification of data represented as a graph, and in particular node classification, is not new but the recent trend is to use deep learning [START_REF] Hamilton | Representation Learning on Graphs: Methods and Applications[END_REF]. Yet, for the specific domain of fake news detection, other approaches are possible. In particular, it has been shown that the fake news are propagated differently (and faster) than legit news [START_REF] Vosoughi | The spread of true and false news online[END_REF]. The use of node reputation and link-based analysis, as it is done in the detection of spam web pages from the Web graph (such as TrustRank [START_REF] Gyngyi | Link spam alliances[END_REF], an adaptation of PageRank [START_REF] Brin | The Anatomy of a Large-Scale Hypertextual Web Search Engine[END_REF]) is another inspiration for our approaches. Our two approaches are further detailed in Sec. 3.

TEXT-BASED APPROACHES 2.1 Pre-processing

From the tweets still online 1 , the text is extracted and pre-processed as follows. Emojis are transformed into texts [START_REF] Wurster | Emoji Python library[END_REF]. URLs are changed to the fixed string 'URL'. Twitter usernames are removed if they appear once, others are kept and the @ removed. The intuition is that some often cited users may be associated to a specific class. Hashtags are kept (with # removed), and decomposed when they contain a mix of capital and small letters (eg. #CovidHoax is changed in CovidHoax Covid Hoax).

Generating artificial examples

For this task we wanted to investigate the use of generative models in order to artificially augment and balance the datasets. Indeed, the performance of neural language models based on transformers [START_REF] Vaswani | Attention is All you Need[END_REF] makes this task realistic. To do so, we use GPT2 (Generative Pre-Trained Transformers), a model built from stacked transformers (precisely, decoders) trained on a large corpus by auto-regression [START_REF] Radford | Language Models are Unsupervised Multitask Learners[END_REF]. Three GPT2 models -one for each class -are fine-tuned (from the 355M-parameter pre-trained model) with the tweets of the dev set. The amount of tweets available is very small; we stopped the iterations when perplexity reached 0.5. The way this stopping criterion impacts the results would need further investigations, which were not possible due to the limited time of the challenge. For the generation, we randomly picked up tweets and kept the two first words to serve as bootstrap. The temperature, which controls the creativity of the model, was set at 0.7. Here again, we had no time to investigate the impact of this parameter. Approximately 20,000 tweets were generated for each class. Here are some tweets generated for the class '5G conspiracy':

Crude and unproductive! Turn off the 5G in your area and see if that helps. Covid19 is not funny. I hope that the Wuhan government puts an end to this immediately. "Immigrants are the cause of 5G towers, they're the cause of the coronavirus outbreak, they're the covid-19 victims, the 5G towers are the weapon which will eradicate the world population, 5G lays the microchips for the virus, i read somewhere that the 5G was debuting prior to the introduction of the COVID-19 virus to negate some of the hype around COVID-19

Classification models

Our 4 classification variants are based on the RoBerta-large model [START_REF] Liu | RoBERTa: A Robustly Optimized BERT Pretraining Approach[END_REF]. It was preferred over other transformer-based representations because its tokenizer is expected to be more suited for the tweet writing specifics. We have tested models with different classification layers (SVM, logistic regression), with or without fine tuning, and with or without artificial examples. Finally, the submitted runs are the following ones: model 1: tweet embedding from the Roberta model (not fine-tuned), and SVM (RGB kernel); model 2: Roberta model with a linear classification layer, fine-tuned on the task (3 epochs);

Results of text-based detection

The results of our models are given in Tab. 1. When available, in addition to the official score on the test set, we provide Matthews correlation coefficient (MCC), micro-F1 (accuracy) and macro-F1 on the dev data (80% for training, 20% for validation). Note that due to the cost of the artificial example generation and the small amount of data, the GPT2 models are fine-tuned on all the available dev data; we do not have reliable results for models 3 and 4 (generated tweets added to the training set can be very similar to those in the validation set).

From the results, we see that fine-tuning the representation (model 2 vs. model 1) is beneficial. Unfortunately, the artificially generated tweets (model 3 and 4) do not yield the expected improvement. From the confusion matrices, one can see that the class 'other conspiracy' has the poorest results, with tweets being equally labeled as '5G', 'non' or 'other'.

GRAPH-BASED APPROACHES

For the second sub-task, we have proposed two models, based on two different sets of features. They are described in the following subsections, as well as the machine learning algorithms adopted and their results.

Modeling the user's reputation

This set of features aims at taking into account if one of the users posting or propagating the news has already be seen. Each user is indeed associated with a score for each possible label, computed from the numbers of training samples of each class it was associated with. We also take into account the scores of the neighbors of this user, their own neighbors, and so on... In practice, this is implemented with the PageRank algorithm [START_REF] Brin | The Anatomy of a Large-Scale Hypertextual Web Search Engine[END_REF] on the undirected graph with a dumping factor set to 0.8 (optimized by cross-validation). Finally, each sample ends up with one value for each class; these three scores are the features used by the classifier.

Several learning algorithms have been tested (logistic regression, random forests, SVM; as implemented in scikit learn [START_REF] Pedregosa | Scikit-learn: Machine Learning in Python[END_REF]). The optimal settings for their hyper-parameters are grid-searched using 20% of the dev set as validation set. The weight of each sample is adapted according to the inverse of its class proportion ('balanced' strategy). With their optimal settings, the different learning algorithms finally show little differences. For this set of features, the submitted run was produced with a random forest (1,000 trees with a maximal depth set to 5, Out-of-Bag weights used in the prediction).

Modeling the propagation

This set of features is built by considering how the tweet is propagated (without considering the users' reputations). These features can be used even if every involved user has never been seen before and is not connected any known user. The features include (with n 0 the first user tweeting the piece of news): number of nodes in the propagation graph; total number of friends and followers (for all nodes implied), as well as the median, 25% percentile, 75% percentile of followers; number of followers and friends of n 0 ; difference between the number of followers and friends of n 0 ; maximal, minimal, average, median, 25% percentile, 75% percentile of retweet time; times to reach at least 100, 1,000, 10,000 followers and so on up to 200,000 followers. With this set of features, a SVM has been used with the following parameters: standardized features (removed mean and scaled to unit variance), RBF kernel, C=0.9, gamma automatically set with the 'scale' heuristics.

Results of graph-based detection

The results of the systems are given in Tab. 1. The cross-validation and official results are consistent; they both show the advantage of the reputation-based approach, especially when considering micro-F1. The difference between cross-validation and official test score may be explained by a lower amount of already seen nodes in the test set, compared to what was generated by cross-validation. A system exploiting all the proposed features (propagation + reputation) was also tested but obtained no statistical difference with the reputation only features.

For both models, the 'other conspiracy' class is again the most error-prone (proportionally), with an equal amount of the its tweets being classified in the three classes. Overall, for both feature sets, many errors are caused by confusion between the 5G and non 5G conspiracy tweets.

CONCLUSION AND FUTURE WORK

For the detection of fake news based on the text, we have adopted a state-of-the-art approach based on RoBerta. The scores obtained show that there exists a large margin for progress, especially when dealing with close classes (5G vs. other conspiracies). The idea of incorporating artificially generated examples did not result in better performance and still needs some work. First, we may find better ways to set the training and generation hyper-parameters. Secondly, we plan to investigate the use of generative model to expand the sample at inference time.

For the detection based on the structure, we have shown that simple approaches like reputation already offered promising results, even on small datasets with many unseen-before nodes. In addition to this type of approach, we want to explore more recent node representation techniques that make it possible to use deep learning, such as node2vec [START_REF] Grover | Node2vec: Scalable Feature Learning for Networks[END_REF] or subsequent variants.

Table 1 :

 1 Performance of the proposed systems for the textbased and graph-based detection; models are detailed in Sec. 2 and 3.

		cross validation results	official
	model	MCC micro-F1 macro-F1 MCC
	model 1 (text)	0.4654	0.7460	0.5924	0.4680
	model 2 (text)	0.5345	0.7945	0.6253	0.5571
	model 3 (text)	-	-	-	0.4937
	model 4 (text)	-	-	-	0.4888
	reputation (graph)	0.4415	0.7274	0.5900	0.4093
	propagation (graph) 0.3198	0.6051	0.4980	0.3036
	model 3: same as model 2, with artificially generated examples (3
	epochs);
	model 4: same as model 3 (4 epochs).

At retrieval time, respectively

227, 128 and 80 tweets were no longer available for the class 'non', '5G', 'other' in the dev set.


Keywords: Three-dimensional ultrasound, sparse arrays, pulsed wave Doppler, real-time system, coded transmission, pulse compression, ULA-OP

2-D sparse arrays may push the development of lowcost 3-D systems, not needing to control thousands of elements by expensive application-specific integrated circuits. However, there is still some concern about their suitability in applications, such as Doppler investigation, which inherently involve poor signal-tonoise ratios (SNRs).

In this paper, a novel real-time 3-D pulsed-wave Doppler system, based on a 256-element 2-D spiral array, is presented. Coded transmission and matched filtering were implemented to improve the system SNR. Standard sonograms as well as multigate spectral Doppler (MSD) profiles, along lines that can be arbitrarily located in different planes, are presented. The performance of the system was assessed quantitatively on experimental data obtained from a straight tube flow phantom. An SNR increase of 11.4 dB was measured by transmitting linear chirps instead of standard sinusoidal bursts. For a qualitative assessment of the system performance in more realistic conditions, an anthropomorphic phantom of the carotid arteries was used. Finally, real-time B-mode and MSD images were obtained from healthy volunteers.

I. INTRODUCTION

Over the last four decades, ultrasound spectral Doppler has been the method preferred by medical doctors to quantitatively assess blood flow [START_REF] Ph | Doppler ultrasound: physics, instrumentation, and signal processing[END_REF]- [START_REF] Jensen | History and Latest Advances in Flow Estimation Technology: From 1-D in 2-D to 3-D in 4-D[END_REF]. Although traditionally limited to the detection of velocities within a single sample volume, spectral analysis has also been successfully extended to multiple sample volumes aligned along a scan line (multigate spectral Doppler -MSD), for vascular investigations [START_REF] Tortoli | Toward a better quantitative measurement of aortic flow[END_REF].

In recent years, massive research efforts and technological developments have brought two breakthroughs: volumetric (3-D) imaging [START_REF] Provost | 3-D ultrafast doppler imaging applied to the noninvasive mapping of blood vessels in Vivo[END_REF]- [START_REF] Fiorentini | Maximum Velocity Estimation in Coronary Arteries Using 3-D Tracking Doppler[END_REF] and vector Doppler [START_REF] Udesen | High frame-rate blood vector velocity imaging using plane waves: simulations and preliminary experiments[END_REF]- [START_REF] Rossi | High-Frame-Rate 3-D Vector Flow Imaging in the Frequency Domain[END_REF]. Although medical doctors always need some time to fully accept new display modalities, both methodologies are mature for implementation in ultrasound machines. Furthermore, the volumetric morphological view (e.g., of plaques) could finally avoid the unfair assumptions that are often done when using pulsed-wave (PW) Doppler with 2-D scanners [START_REF] Thrush | Peripheral Vascular Ultrasound: How, Why and When[END_REF]. The possible extension of spectral-analysis-based velocity investigation to all points within an entire volume is, thus, of undoubtful clinical interest. Indeed, the support of a 3-D morphological view may facilitate the optimal probe A. Ramalli, E.Boni, C. Giangrossi, P. Mattesini, A. Dallai, and P. Tortoli are with the Department of Information Engineering, University of Florence, 50139 Florence, Italy.

positioning and the rapid identification of regions in which spectral analysis may provide valuable flow information.

3-D imaging is currently possible only through a few highend machines based on expensive 2-D transducer arrays with thousands of elements controlled by application-specific integrated circuits (ASICs) [START_REF] Savord | Fully sampled matrix transducer for real time 3D ultrasonic imaging[END_REF]- [START_REF] Mozaffarzadeh | Receive/Transmit Aperture Selection for 3D Ultrasound Imaging with a 2D Matrix Transducer[END_REF], which relax the system requirements in terms of independent channels. A cheaper alternative is represented by sparse arrays [START_REF] Davidsen | Two-dimensional random arrays for real time volumetric imaging[END_REF], [START_REF] Austeng | Sparse 2-D arrays for 3-D phased array imaging -design methods[END_REF], which can be designed to have the number of active elements equal to the number of channels available in a companion scanner. In general, the design approaches for sparse arrays can be split into two groups: deterministic [START_REF] Austeng | Sparse 2-D arrays for 3-D phased array imaging -design methods[END_REF]- [START_REF] Martínez-Graullera | 2D array design based on Fermat spiral for ultrasound imaging[END_REF] and nondeterministic [START_REF] Haupt | Thinned arrays using genetic algorithms[END_REF]- [START_REF] Diarra | Design of Optimal 2-D Nongrid Sparse Arrays for Medical Ultrasound[END_REF]. Among the latter ones, in [START_REF] Roux | 2-D Ultrasound Sparse Arrays Multidepth Radiation Optimization Using Simulated Annealing and Spiral-Array Inspired Energy Functions[END_REF], [START_REF] Roux | Wideband 2-D Array Design Optimization With Fabrication Constraints for 3-D US Imaging[END_REF], an algorithm based on simulated annealing and broadband simulations was developed. It was shown able to find the set of active elements, which optimize the beam pattern, by considering both the pressure field behavior at different depths and some fabrication constraints. A deterministic approach was followed in [START_REF] Ramalli | Density-tapered spiral arrays for ultrasound 3-D imaging[END_REF], in which the array layout was based on the Fermat's spiral, which guarantees a uniform performance for focused beams steered over a wide range of angles. Moreover, spatial density tapering of elements was proposed to decrease the sidelobe level while increasing the probe sensitivity.

A recent study compared the PW Doppler performance of a full 1024-element gridded array and a sparse 2-D array, which was obtained by selecting 256 elements out of the full array [START_REF] Roux | Wideband 2-D Array Design Optimization With Fabrication Constraints for 3-D US Imaging[END_REF]. The two array configurations were used to transmit focused beams into different directions and to Doppler process the echo-data off-line [START_REF] Mattesini | Spectral Doppler Measurements With 2-D Sparse Arrays[END_REF]. The results have demonstrated that the use of the sparse array only limits the signal-to-noise ratio (SNR), but neither the Doppler spectrum shape nor the detected mean frequency are affected by sparsity.

In this paper, a novel 3-D Doppler system based on a 256element spiral array is presented and shown able to provide, in real-time, multigate spectral Doppler profiles along lines that can be arbitrarily located in a volume. The implementation of coded transmission (TX), together with matched filtering in reception (RX), is also described, and shown capable of partially overcoming the SNR limitation of sparse arrays.

The paper is organized as follows: Section II introduces the hardware used in this study, including a 2-D array probe and the ULA-OP 256 research scanner. The methods used to evaluate the system performance are also reported. The experimental results are described in Sec. III and discussed in Sec. IV. In this work, the ULA-OP 256 research system [START_REF] Boni | Architecture of an Ultrasound System for Continuous Real-Time High Frame Rate Imaging[END_REF] was coupled to a special version of the Vermon matrix array probe (Vermon S.A., Tours, France). The ULA-OP 256 is a hardwarebased open scanner [START_REF] Boni | Ultrasound Open Platforms for Next-Generation Imaging Technique Development[END_REF], which allows implementing custom processing methods by programming computing devices such as field-programmable gate arrays (FPGAs) and Digital Signal Processors (DSPs). As shown in Fig. 1, the special version of the 2-D probe was obtained by sparsely selecting 256 elements out of the original array. It consists of 32 (x-axis) by 35 (y-axis) elements (3.7 MHz, 300 µm pitch, 70% bandwidth), but on the y-direction every ninth row is not connected. The total number of addressable elements is thus 1024. Although not easily recognizable, the selection matches, as much as possible, the layout of a 2-D spiral whose density is tapered with a Tukey window [START_REF] Ramalli | High-Frame-Rate Tri-Plane Echocardiography With Spiral Arrays: From Simulation to Real-Time Implementation[END_REF], [START_REF] Harput | 3-D Super-Resolution Ultrasound Imaging With a 2-D Sparse Array[END_REF]. Each selected element was paired to one channel of the ULA-OP 256 scanner so that it could be individually controlled both in transmission (TX) and in reception (RX).

The scanner software and firmware were modified to permit navigation in the volume of interest. B-mode images, taken on planes defined by a programmable rotational angle, are simultaneously displayed to locate non-isoplanar Doppler lines over the vessels of interest.

In the next paragraphs, the current implementation of the system is detailed.

2) Transmission

For both B-mode and Doppler imaging, the ULA-OP 256 is configured to transmit focused beams with programmable focal depth. No apodization is applied in TX since the spiral layout implemented density tapering. For each Doppler line, either tone bursts or linear frequency modulated (chirp) signals are used in TX to drive each active element with the same 35 V peak amplitude (see Fig. 2). The chirp is 5 µs long, linearly spans a band of 3 MHz centered at 3.7 MHz, and is tapered with a 10% Tukey window. In this way, the resulting -6dB signal bandwidth matches the probe bandwidth (2.7 MHz). The length of the chirp was chosen by considering a tradeoff among SNR gain, depth of the blind zone, and imaging artifacts [START_REF] Chiao | Coded excitation for diagnostic ultrasound: a system developer's perspective[END_REF]- [START_REF] Ramalli | Coded Spectral Doppler Imaging: From Simulation to Real-Time Processing[END_REF]. The tone burst, which is also used for B-mode imaging, includes 2.5 cycles of a sinusoid at 3.7 MHz. The burst is weighted by a Hamming window to obtain the same (-6dB) bandwidth and maximum amplitude of the linear chirp. The Bmode images are obtained by scanning 128 consecutive lines on 64°-wide sectors.

Fig. 3 shows sample one-way fields produced by the system when the tone bursts were transmitted and detected using the HGL008 hydrophone (Onda Corporation, Sunnyvale, CA, USA) moved in a water tank by a home-made 6-axis positioning system. Grating lobes are generally due to the sparsity of active elements, but those visible at x=3 mm on the xy-plane are due to the not connected rows of elements on the y-direction, see Fig. 1.

3) Reception

In RX, the echo signals received after each TX event are band-pass filtered (cut-off frequencies: 0.25 and 10.0 MHz), time gain compensated, and analog-to-digital converted at 78 MHz with 12-bit resolution. Then, they are dynamically beamformed with constant f-number (F# = 2) by the FPGAs onboard the ULA-OP 256. Finally, the beamformed signals are quadrature demodulated and downsampled by the available DSPs to produce up to 512 output samples. The downsampling factor can be adjusted by the user to cover the range of interest.

4) Matched filtering

The ULA-OP's DSPs are also in charge of applying matched filtering to the echo-data obtained in Doppler mode. In order to reduce the computational load, matched filtering is performed on baseband data and in the frequency-domain rather than in the time-domain [START_REF] Yoon | An efficient pulse compression method of chirp-coded excitation in medical ultrasound imaging[END_REF]. Baseband operation is not expected to produce any distortion since the chirp duration is limited to 5 µs and the active aperture is relatively small [START_REF] Misaridis | Use of modulated excitation signals in medical ultrasound. Part I: basic concepts and expected benefits[END_REF], [START_REF] Misaridis | Use of modulated excitation signals in medical ultrasound. Part II: design and performance for medical imaging applications[END_REF]. For each TX/RX event, pulse compression is thus achieved in 3 steps: 2) The resulting complex spectra are multiplied by the coefficients of the matched filter. The frequency response of this filter reproduces the complex conjugate spectrum of the TX signal. When needed, the amplitude response can be weighted by a window that partially mismatches the filter while reducing the side-lobes [START_REF] Chiao | Coded excitation for diagnostic ultrasound: a system developer's perspective[END_REF], [START_REF] Ramalli | A real-time chirp-coded imaging system with tissue attenuation compensation[END_REF], [START_REF] Misaridis | Use of modulated excitation signals in medical ultrasound. Part I: basic concepts and expected benefits[END_REF]. 3) Spectral data are transformed back to the time domain through a 1024-point inverse-FFT and the 512 valid output samples are made available for the next processing stages. It is worth noting that, for a fair comparison, matched filtering was applied to the data of both the tone burst and the linear chirp.

5) B-mode and Doppler processing

For B-mode imaging, the moduli of baseband complex data are computed and log-compressed before being transferred to the host PC. The data are finally scan-converted and displayed in grayscale by the PC real-time interface.

In MSD-mode, the slow-time, baseband, matched filtered samples corresponding to each of 512 different depths along the Doppler line, are FFT-processed by the DSP. The complex moduli of the spectra are then transferred to the host PC. Here they are displayed as color-scale images in which the horizontal axis corresponds to the Doppler frequencies and the vertical axis to the depth of the examined sample volume [START_REF] Tortoli | Toward a better quantitative measurement of aortic flow[END_REF].

The user can also select one of the MSD depths to simultaneously show the corresponding spectrogram as a colorscale image in which the horizontal axis corresponds to time and the vertical axis to the Doppler frequencies.

B. Experimental tests

Different TX/RX strategies, each dedicated to one of the experimental tests that are described in the following paragraphs, were implemented.

1) Assessment of SNR gain

In order to prove the effectiveness of real-time pulse compression in 3-D Doppler mode, experiments were conducted on a homemade flow phantom. This consisted of a straight, rigid, cylindrical tube immersed in a water tank and connected to a hydraulic circuit, through which a bloodmimicking fluid was pushed by a programmable peristaltic pump (Watson-Marlow, Falmouth, UK). Specifically:  The 70-cm long tube, having an inner diameter of 8 mm and 1-mm thick wall, was made of Rilsan ® (Arkema S.A., Colombes, France) -a polyamide and bioplastic member of the nylon family of polymers -characterized by an attenuation coefficient of 2dB/cm/MHz and sound propagation speed of 2600 m/s.  The blood-mimicking fluid consisted of 2.5 g of 10-μm particles of Orgasol ® (Arkema S.A., Colombes, France) -a polyamide powder -suspended in 2 liters of demineralized water with 1 g of surface-active agent for a uniform distribution of particles [START_REF] Ramnarine | Validation of a New Blood-Mimicking Fluid for Use in Doppler Flow Test Objects[END_REF].  The fluid flowed at a steady rate of 280 ml/min, from a reservoir into an expansion tank, then through the straight tube, and finally back to the reservoir. Acquisitions were repeated for 9 different directions of the Doppler line, corresponding to the combinations of the angles 0°, 8°, and 16° in both xz-and yz-plane.

During these tests, as sketched in Fig. 4, manual setting of the probe position was facilitated by two real-time B-mode images: the first one, reconstructed along the plane with 90° rotational angle, was used to intercept the cross-section of the tube; the second one, whose rotational angle was programmed to include the Doppler investigation line, was used to ensure a proper alignment between the tube axis and the focal depth of the Doppler line.

To allow comparing the Doppler SNRs achieved by using different TX signals, the ULA-OP 256 was programmed to interleave, at 1 kHz PRF, the following TX events:

1) Sinusoidal burst TX along a scan line of the B-mode image 1. 2) Linear chirp TX along the Doppler line. 3 Examples of experimental one-way fields produced by the 256-element sparse array. In the left panel, the beam was not steered and was acquired on the plane with rotational angle equal to 0°, i.e. the xz-plane. In the middle and right panels, the beam was steered by 8° on both lateral directions and was acquired on the plane with 45° rotational angle (center) and on a plane parallel to the probe surface at a depth of 25 mm (right).

3) Sinusoidal burst TX along a scan line of the B-mode image 2. 4) Sinusoidal burst TX along the Doppler line. Slow-time Doppler signals were acquired for an interval of 6 s. In this case, data were post-processed by a Matlab ® (The MathWorks, Natick, MA) script that replicates the real-time MSD processing implemented on the ULA-OP 256. The Doppler SNRs obtained with each of the two TX signals were computed as proposed in [START_REF] Ramalli | Coded Spectral Doppler Imaging: From Simulation to Real-Time Processing[END_REF]. Briefly, consecutive MSD frames were averaged so that smooth images, like those in Fig. 5, were obtained. Here, the region of the Doppler spectrum related to the flow (SROI), i.e. the region within the -6dB isolines, which includes 𝑛 spectra, was semi-automatically segmented. Once the position of the walls was manually pointed, an automatic algorithm fitted the borders of the -6dB isolines with a second-degree polynomial curve. The noise region (NROI) was selected in the upper portion of the image, covering 𝑛 =50 depths, where the flow was absent. The SNR was thus estimated as:

𝑆𝑁𝑅 = 10 log 𝑆 𝑁 • 𝑛 𝑁 𝑛 𝑆 (1)
where S and N correspond to the total power measured in 𝑆 and 𝑁 , respectively. Finally, for each acquisition, the SNR gain (GSNR) was computed as the difference between the SNRs obtained with the chirp TX and with the sinusoidal burst TX, respectively.

2) MSD investigation along non-isoplanar lines

In order to prove the capability of assessing blood flow along lines located in different planes, an anthropomorphic phantom [START_REF] Lai | Design of Anthropomorphic Flow Phantoms Based on Rapid Prototyping of Compliant Vessel Geometries[END_REF] was used. Specifically, the phantom mimicked the bifurcation of the carotid artery with stenosis of the internal carotid artery (ICA). The phantom was inserted in the hydraulic circuit so that the carotid bifurcation lied parallel to the probe surface.

As sketched in Fig. 6, during these tests, two real-time Bmode images, crossing at the level of the common carotid artery (CCA), were shown: the first, coincident with the plane at 25° rotational angle, reproduced a longitudinal section including the origin of the external carotid artery (ECA); the second one, coincident with the plane with 0° rotational angle, reproduced a section including the ICA origin.

Two Doppler lines, both focused at ~30 mm depth, were set on the two imaging planes: line A intercepted the CCA, while line B was close to the origin of the ICA. The steering angles, on the xz-and yz-plane, were (𝜃 = -14.5°, 𝜃 = -6.9°) and (𝜃 = -8.6°, 𝜃 = 0.0°) for line A and B, respectively.

The ULA-OP 256 was here programmed to interleave, at 1 kHz PRF, the following TX events: Fig. 4 The reference system and the scanning planes used to facilitate the alignment of the probe with the straight tube. The probe was centered on the origin of the reference system. The first plane, with 90° rotational angle (blue), was used to intercept the cross section of the tube (yellow). The second plane (red), was used to ensure a proper alignment between the tube axis and the focusing point (black dot) of the (solid black) Doppler line, here steered at θxz= θyz=16°. Gray dotted lines represent the projection lines of the tube axis along the main planes.

B-mode images and MSD spectra were shown in real-time on the ULA-OP 256 software interface.

3) In vivo experiments

Two real-time B-mode images, which scan planes at different rotational angles, were made available to facilitate the probe positioning and to allow setting the direction of two Doppler lines during in vivo tests.

The ULA-OP 256 was thus programmed to interleave, at 3 kHz PRF, 6 TX events: In this interleaved mode, the mechanical index (MI), the thermal index for soft tissues at the surface (TISas), and the temperature rise at the probe surface (ΔT) were estimated. The MI was 0.12 and 0.10 for chirp and sinusoidal burst, respectively. The TISas was always lower than 0.01, while ΔT was 4°C, after a 30-minute continuous operation in still air. Then, preliminary acquisitions were performed on the carotid arteries of healthy volunteers.

III. RESULTS

1) Assessment of SNR gain

Fig. 5 shows two MSD images obtained by transmitting the sinusoidal burst and the linear chirp, respectively. The Doppler line was set at 𝜃 = 𝜃 = 16°. Qualitatively, the images do not show a significant difference in the spectrum shape. Also, both spectra show the same artifact due to the saturation of beamformed signals from the second wall of the plastic tube. However, an improved SNR is clearly achieved with pulse compression. Indeed, since both images were normalized to the respective overall maximum intensity, the noise level obtained with the chirp appears considerably lower than that of the sinusoidal burst. Equivalent results were obtained for all tested steering conditions and the estimated SNRs and GSNRs are summarized in TABLE I. On average (see the rightmost column), the estimated SNRs were 19.6 dB for the sinusoidal burst and 31.0 dB for the linear chirp, which corresponded to an average GSNR of 11.4 dB. The MSD profile (panel B) is parabolic-like also here but, compared to the one in panel A, it looks "full" since the Doppler angle was close to 90° [START_REF] Tortoli | Transverse doppler spectral analysis for a correct interpretation of flow sonograms[END_REF] and the spectral broadening was thus high. It is worth highlighting that, in this interleaved setting, a PRF=1 kHz corresponded to a Doppler sampling rate of 250 Hz, which was purposely adapted to get as close as possible to the aliasing limit on panel A and, hence, to exploit the whole available Doppler band.

2) MSD investigation along non-isoplanar lines

3) In vivo experiments

Fig. 8 shows two examples of the ULA-OP 256 interface frozen during real-time operation on healthy volunteers, which were extracted from the supplementary accompanying video clips. In these examples, the bi-planar B-mode volume rate, limited by the PRF (3 kHz), the number of interleaved transmission events [START_REF] Jensen | History and Latest Advances in Flow Estimation Technology: From 1-D in 2-D to 3-D in 4-D[END_REF], and the number of lines per frame (128), was 3.9 Hz, which is quite low but sufficient to support probe positioning. On the other hand, the update rate of MSD profiles was arbitrarily set to 40 Hz, which is high enough for real-time display, but, considering the computational power of the DSP, it could have been increased up to hundreds of Hz.

In the first example , Fig. 8 left, the delta between the rotational angles of the two B-mode images was set to 90°. In this way, the longitudinal and the cross-section of the CCA were scanned. The Doppler line A was steered by 10° within plane A, while line B was set perpendicular to the probe surface.

Both MSD profiles have an M-like shape, which is typical during late systole [START_REF] Tortoli | Interaction between secondary velocities, flow pulsation and vessel morphology in the common carotid artery[END_REF]. In panel B, in particular, a strong clutter from the walls is visible and the spectra look "full", down to 0 Hz, as usual when the Doppler angle is close to 90°. Vice versa, the profiles along the Doppler line A show a wider spectral window, as expected at a lower Doppler angle.

In the second example , Fig. 8 right, the delta between the rotational angles of the two B-mode images was set to 60°. To simulate a non-optimal positioning of the probe, it was slightly shifted with respect to the axis of the CCA, but both Doppler lines were roughly focused on the CCA axis. The two B-mode images show two cross-sections of the CCA, which take the form of ellipses. Both MSD profiles have a parabolic-like shape, as expected during diastole, and show a strong wall clutter. Moreover, they have opposite Doppler shifts: negative along line A and positive along line B, as expected from the schematic view sketched in Fig. 8 center-bottom. Finally, also in this case, both the MSD profiles and the sonograms are "full", due to the almost 90° Doppler angles.

IV. DISCUSSION AND CONCLUSION

In this article, we have presented the first system capable of performing real-time spectral Doppler from any of the points in the volume, scanned by a 2-D spiral array. The system was based on the ULA-OP 256 research scanner and on a prototype spiral probe, designed by selecting 256 elements from a 1024element gridded array. The MSD modality, which represents an extension of classic PW Doppler to multiple aligned sample volumes, has been implemented. We also tested the effectiveness of coded transmission and pulse compression in reception to compensate for the low achievable SNR due to the limited number of elements.

The performance of the system was quantitatively assessed on experimental data acquired from flow phantoms based either on a straight tube and on an anthropomorphic phantom of the CCA. Finally, for a qualitative assessment of the system performance in-vivo, real-time images were collected on healthy volunteers.

Different interleaving sequences, depending on the application of interest, were implemented. For example, the TX sequence for B-mode imaging was interleaved with the transmission of: (1) different Doppler pulses (i.e. a sinusoidal burst and a linear chirp) along the same investigation line, for SNR assessment; (2) chirp Doppler pulses along investigation lines within different scan planes, for a qualitative blood flow assessment in the anthropomorphic phantom and in-vivo. Together with the two B-mode images, used to facilitate probe positioning, two MSD profiles with (Fig. 8), or without (Fig. 7) the spectrograms from selected depths were simultaneously displayed. This capability could be used to observe the flow dynamics along non-isoplanar Doppler lines, e.g. to simultaneously assess the flow before and after a stenosis, an aneurysm, or an aortic stent. Also, it could facilitate the examination of tortuous arteries: the bi-plane scan could ease the optimal probe positioning and the rapid, real-time, setting of the direction of the Doppler lines of interest. [START_REF] Ph | Doppler ultrasound: physics, instrumentation, and signal processing[END_REF][START_REF] Grant | Carotid Artery Stenosis: Gray-Scale and Doppler US Diagnosis-Society of Radiologists in Ultrasound Consensus Conference[END_REF] and MSD profiles (A, B) were obtained as described in the schematic view of the carotid bifurcation phantom in Fig. 6. The dynamic range of B-mode images was 30dB, while that of MSD profiles was 24dB.

In [START_REF] Mattesini | Spectral Doppler Measurements With 2-D Sparse Arrays[END_REF] it was experimentally demonstrated, through off-line calculations, that the use of sparse, rather than full arrays, neither affects the shape nor the mean frequency of the Doppler spectrum, but it impairs the SNR. The results presented in this work have shown the effectiveness of pulse compression in SNR enhancement. Specifically, the use of a linear chirp [START_REF] Ramalli | Coded Spectral Doppler Imaging: From Simulation to Real-Time Processing[END_REF], instead of a sinusoidal burst, has brought to an SNR increase of 11.4 dB (see TABLE I), which was quite stable (standard deviation equal to 0.6 dB) for all tested steering angles. Also, in the tested conditions (B = 2.7 MHz, T = 5µs), the average SNR increase resulted in 11.3 dB, very close to the theoretical value (10 log (𝐵 • 𝑇)) [START_REF] Misaridis | Use of modulated excitation signals in medical ultrasound. Part I: basic concepts and expected benefits[END_REF]. Such gain partially compensated the limited SNR associated with the use of a reduced number of elements (here 256) typical of sparse arrays. Considering that any possible doubling of such number is expected to increase the SNR by 9 dB (6 in TX and 3 in RX) [START_REF] Mattesini | Spectral Doppler Measurements With 2-D Sparse Arrays[END_REF], the pulse compression gain here allowed obtaining a performance better than that achievable with 512 elements excited by standard pulses. In pulsed wave Doppler applications, the SNR could also be increased by exploiting long, narrowband pulses, with conflicting implications on transit time and velocity gradient broadening, respectively. Nevertheless, lengthening the pulses is not advisable in applications where the range resolution is important, e.g. in multi-gate spectral Doppler and color flow imaging. Pulse compression thus represents a good means to achieve high SNR while using wideband, i.e. high resolution, signals.

Even if, in general, the transmission of long linear chirp signals for extended exposure times might rise thermal effects [START_REF] Ramalli | Coded Spectral Doppler Imaging: From Simulation to Real-Time Processing[END_REF], on both probe and skin surfaces, this did not happen in our tests. The relatively low excitation voltage (±35 V) and the sparse distribution of the active elements most likely facilitated heat dissipation. Therefore, the excitation voltage could be further increased, but in our case, we preferred to stay below the maximum voltage limit (±45 V) suggested by the probe manufacturer.

In this paper, a sparse spiral array was associated with a 256channel research system to detect, in real-time, the flow profiles along non-isoplanar investigation lines in phantom (Fig. 7) and in vivo (Fig. 8). The profiles, as expected, show different shapes, depending on the Doppler angle and investigated region. In vivo, in particular, although tissue attenuation further impaired the SNR, the sonograms and the profiles exhibited the expected spectral windows and the same physiological trend that can be observed with linear arrays [START_REF] Tortoli | Interaction between secondary velocities, flow pulsation and vessel morphology in the common carotid artery[END_REF].

All benefits and limitations of 2-D spectral Doppler can be extended to 3-D. For example, quantitative information on blood flow velocity could be, to some extent, obtained through simple angle correction or through vector flow imaging techniques that exploit either the Doppler bandwidth [START_REF] Newhouse | Three-dimensional vector flow estimation using two transducers and spectral width[END_REF], [START_REF] Tortoli | Accurate Doppler angle estimation for vector flow measurements[END_REF], multiple transmission/reception beams [START_REF] Ricci | Real-Time Blood Velocity Vector Measurement Over a 2-D Region[END_REF], [START_REF] Overbeck | Vector doppler: Accurate measurement of blood velocity in two dimensions[END_REF], [START_REF] Dunmire | Cross-beam vector Doppler ultrasound for angle-independent velocity measurements[END_REF], or speckle tracking [START_REF] Holbek | 3-D Vector Flow Estimation With Row-Column-Addressed Arrays[END_REF], [START_REF] Rossi | High-Frame-Rate 3-D Vector Flow Imaging in the Frequency Domain[END_REF].

The results also highlight some limitations of the current system. The MSD images in panels A, B of Fig. 7, present secondary profiles whose depth and frequency are slightly shifted with respect to the main Doppler profile. These profiles can be attributed to the characteristics of the transmitted fields, which, in addition to the main steered beam, also show relatively high (up to -20dB) grating lobes, as visible in Fig. 3. Furthermore:

1) The probe characteristics were not ideal for the investigation of superficial vessels: the central frequency was too low and the aperture size too small (<1 cm) to achieve good spatial resolution.

2) The relatively wide elements and the big average pitch limit the probe steering capability, in terms of reduced sensitivity and increased grating lobe level, respectively. This, in turn, limits the effective size of the region of interest.

3) The navigation system based on two B-mode images, although capable of working at reasonably high frame rates, does not facilitate the detection of the vessels of interest, as a full 3-D rendering could do. For clinical examinations of shallow vessels, wider apertures, linear scans, and higher frequencies would be preferable. The presented configuration might be suitable for the investigation of the carotid artery or the jugular vein as well as for echocardiography [START_REF] Ramalli | High-Frame-Rate Tri-Plane Echocardiography With Spiral Arrays: From Simulation to Real-Time Implementation[END_REF] and abdominal vascular applications. Nevertheless, to make the system suitable for clinical tests, the following features should be included:

1) Integration of in-probe pre-amplifiers to further improve the SNR and penetration depth [START_REF] Boni | On the efficacy of in-probe pre-amplifiers for piezoelectric 2D arrays[END_REF]. 2) A better navigation system, which could include a Cmode display and, possibly, an automatic system to determine the rotational angles of the imaging planes, adapting them to the specific anatomy of the subject (e.g. based on machine learning [START_REF] Østvik | Real-Time Standard View Classification in Transthoracic Echocardiography Using Convolutional Neural Networks[END_REF]). In conclusion, considering the above aspects, the results of this paper are really encouraging and confirm that sparse arrays are a feasible option for the implementation of 3-D imaging/Doppler systems. At a relatively cheap cost, they may allow physicians to simultaneously assess the dynamics of blood flow within an entire volume of interest, at a high temporal resolution, and on multiple non-isoplanar directions simultaneously. Moreover, the 3-D morphological view will provide more degrees of freedom and less room for errors in probe positioning.

Fig. 1

 1 Fig. 1 Layout of the special version of the Vermon matrix array probe. Each selected element (black) was paired to one channel of the ULA-OP 256 scanner.

Fig. 2

 2 Fig.2The excitation signals (left panels) and their power spectra (right panel). On the left panels, the dashed gray lines represent the envelope of the tapering windows.

1 )

 1 Up to 512 (fast-time) beamformed, quadrature demodulated, and downsampled data are transformed, after zero-padding, to the frequency domain through a 1024-point Fast Fourier Transform (FFT).

Fig.

  Fig.3Examples of experimental one-way fields produced by the 256-element sparse array. In the left panel, the beam was not steered and was acquired on the plane with rotational angle equal to 0°, i.e. the xz-plane. In the middle and right panels, the beam was steered by 8° on both lateral directions and was acquired on the plane with 45° rotational angle (center) and on a plane parallel to the probe surface at a depth of 25 mm (right).

1 )

 1 Sinusoidal burst TX along a scan line of the B-mode image 1. 2) Linear chirp TX along the Doppler line A. 3) Sinusoidal burst TX along a scan line of the B-mode image 2. 4) Linear chirp TX along the Doppler line B.

Fig. 5

 5 Fig. 5 Examples of averaged MSD images highlighting the regions of the Doppler spectrum related to the flow (SROI) and to the noise (NROI). The examples refer to the case with 𝜃 = 𝜃 = 16°. On top, the MSD image obtained with the sinusoidal burst; on bottom, the one obtained with the linear chirp.

1 )

 1 Sinusoidal burst TX along a scan line of the B-mode image 1. 2) Linear chirp TX along the Doppler line A. 3) Linear chirp TX along the Doppler line B. 4) Sinusoidal burst TX along a scan line of the B-mode image 2. 5) Linear chirp TX along the Doppler line A. 6) Linear chirp TX along the Doppler line B. B-mode images, MSD profiles, and spectrograms from a selected depth were shown in real-time on the ULA-OP 256 software interface.

Fig. 7

 7 reports a screenshot of the ULA-OP 256 interface obtained during experiments conducted on the carotid artery bifurcation phantom. The sector sketched in Fig. 6 is here shown as a B-mode image in Panel 1. It reproduces a region from the origin of the ECA (on the left) to the bulb in the CCA (on the right). Correspondingly, a slight increase in the vessel diameter can be observed. The (red) Doppler line here intercepted the beginning of the CCA bulb, producing MSD profiles like the one in panel A, showing a parabolic-like shape in the direction of positive Doppler shifts. The B-mode sector shown in Panel 2 reproduces the phantom from the origin of the ICA (on the center-left) to the external wall of the CCA (on the center-right). The (yellow) Doppler line was steered on the origin of the ICA just before the stenosis.

Fig. 6

 6 Fig. 6 Schematic view of the carotid bifurcation phantom, placed parallel to the probe surface at roughly 30-mm depth. B-Mode images were obtained along planes 1 and 2. Doppler lines were steered along directions A and B.

Fig. 7

 7 Fig.7Screenshot of the ULA-OP 256 interface during real-time operation. B-Mode images (1, 2) and MSD profiles (A, B) were obtained as described in the schematic view of the carotid bifurcation phantom in Fig.6. The dynamic range of B-mode images was 30dB, while that of MSD profiles was 24dB.

Fig. 8

 8 Fig.8Two examples of the ULA-OP 256 interface during real-time in-vivo operation on the common carotid artery of healthy volunteers (left and right). B-Mode images (1, 2), MSD profiles and related sonograms (A, B) were obtained as described in the schematic views (center), where the common carotid artery is sketched as a gray cylinder. The dynamic range of B-mode images was 30 dB, while that of MSD profiles was 24 dB.

TABLE I

 I

					ESTIMATED SNR AND GSNR
		𝜽 𝒙𝒛		0°			8°			16°		Avg±Std
		𝜽 𝒚𝒛	0°	8°	16°	0°	8°	16°	0°	8°	16°	values
	SNR [dB]	Sinusoidal burst Linear chirp	19.5 30.4	20.0 31.6	18.8 29.9	21.9 33.2	20.9 32.3	19.2 30.4	19.9 31.1	18.8 31.6	17.2 28.6	19.6±1.3 31.0±1.4
	GSNR [dB]	10.9	11.6	11.1	11.3	11.4	11.2	11.2	12.8	11.4	11.4±0.6