H Dannerbauer

E Daddi

G E Morrison

B Altieri

P Andreani

H Aussel

S Berta

A Bongiovanni

A Cava

J Cepa

A Cimatti

H Dominguez

D Elbaz

N Förster Schreiber

R Genzel

C Gruppioni

B Horeau

H S Hwang

E Le Floc'h

J Le Pennec

D Lutz

G Magdis

B Magnelli

R Maiolino

R Nordon

A M Pérez García

A Poglitsch

P Popesso

F Pozzi

L Riguccini

G Rodighiero

A Saintonge

P Santini

M Sanchez-Portal

L Shao

E Sturm

L Tacconi

I Valtchanov

UNVEILING FAR-INFRARED COUNTERPARTS OF BRIGHT SUBMILLIMETER GALAXIES USING PACS IMAGING

Keywords: Galaxies: high-redshift -Galaxies: individual (GN13 alias HDF850, 4) -Galaxies: starburst -Cosmology: observations -Infrared: Galaxies -Submillimeter: galaxies 1, introduction

We present a search for Herschel-PACS counterparts of dust-obscured, high-redshift objects previously selected at submillimeter and millimeter wavelengths in the Great Observatories Origins Deep Survey North field. We detect 22 of 56 submillimeter galaxies (39%) with a SNR of ≥ 3 at 100 µm down to 3.0 mJy, and/or at 160 µm down to 5.7 mJy. The fraction of SMGs seen at 160 µm is higher than that at 100 µm. About 50% of radio-identified SMGs are associated with PACS sources. We find a trend between the SCUBA/PACS flux ratio and redshift, suggesting that these flux ratios could be used as a coarse redshift indicator. PACS undetected submm/mm selected sources tend to lie at higher redshifts than the PACS detected ones. A total of 12 sources (21% of our SMG sample) remain unidentified and the fact that they are blank fields at Herschel-PACS and VLA 20 cm wavelength may imply higher redshifts for them than for the average SMG population (e.g., z > 3 -4). The Herschel-PACS imaging of these dust-obscured starbursts at high-redshifts suggests that their farinfrared spectral energy distributions have significantly different shapes than template libraries of local infrared galaxies.

Several hundred dust-enshrouded high-z sources have been selected through submm/mm imaging with bolometer cameras like SCUBA, LABOCA, AzTEC, MAMBO (e.g., Bertoldi et al. 2007;Coppin et al. 2006;Dannerbauer et al. 2002Dannerbauer et al. , 2004;;Hughes et al. 1998;Perera et al. 2008;Pope et al. 2006;Smail et al. 2002;Weiß et al. 2009).

The large beam size in the (sub)millimeter (e.g., MAMBO: 11 ′′ ; SCUBA: 15 ′′ ; LABOCA: 19 ′′ ) hampers the identification of these so-called Submillimeter Galaxies (SMGs; see for a review Blain et al. 2002) based on bolometer data only.

The most obvious choice for obtaining the subarcsecond accurate positions of the dust continuum is (sub)millimeter interferometric continuum observations (e.g., Dannerbauer et al. 2002Dannerbauer et al. , 2008;;Younger et al. 2007). However the slow mapping speed of (sub)millimeter interferometers does not allow us to study a large number of sources. The most suitable tool for counterpart identification is interferometric observations at radio wavelengths. About 50% -80% of these submm/mm sources have been identified, mainly based on radio observations, and the peak of the redshift distribution of the radio-identified SMG population lies at < z >= 2.2 (Chapman et al. 2005). However, the effect of the bias toward the true redshift distribution introduced by the radio selection technique is still under debate, as SMGs even beyond z = 4 have been already detected by the VLA at 20 cm (e.g., Capak et al. 2008;Coppin et al. 2009;Daddi et al. 2009a,b;Knudsen et al. 2010;Morrison et al. 2010;Schinnerer et al. 2008). The sample of unidentified SMGs could be either spurious sources or lie at extreme redshifts but no systematic studies on this subsample of SMGs have been conducted so far.

The launch of the Herschel observatory (Pilbratt et al. 2010) promises a different perspective of SMGs than provided by radio observations only and offers a higher mapping speed than (sub)mm interferometric observations. Deep PACS (Poglitsch et al. 2010) imaging at 100 µm and 160 µm on the Great Observatories Origins Deep Survey North (GOODS-N) will sample the FIR emission of these dust-enshrouded high-z objects and enable us to study in detail their far-infrared spectral energy distribution (SED), redshift distribution, dust temperatures (Chanial et al. 2010;Elbaz et al. 2010;Magnelli et al. 2010) and dust masses (Santini et al. 2010). In absence of interferometric observations at mm and cm wavelengths, the Herschel-PACS beamsize at 100 µm (160 µm) of 6.7 ′′ (11.0 ′′ ) provide a more accurate location of the dust emission than the bolometer data taken with SCUBA, AzTEC, MAMBO or LABOCA.

In this letter we discuss our search for PACS counterparts at 100 µm and 160 µm, explore the diagnostic potential of Herschel-PACS for the counterpart identification and compare it with the widely used identification approach using VLA observations. In comparison, the Spitzer-MIPS 70 µm and 160 µm imaging of the GOODS North region performed by Huynh et al. (2007) in the pre-Herschel era detected at relatively high significance only two (one) out of 30 SMGs at 70 µm (160 µm), at rather low redshifts (z = 0.5 and z = 1.2). The FIR observations presented here will enable us to study a significant sample of SMGs in the far-infrared wavelength regime.

far-infrared association of submillimeter galaxies

PACS observations of the GOODS North region at 100 µm and 160 µm were taken during the Herschel Science Demonstration Phase in autumn 2009 and are part of the Guarantee Time extragalactic PACS survey 'PEP: The PACS Evolutionary Probe' (PI: D. Lutz). The final images achieve 3σ sensitivities of ∼ 3.0 mJy and ∼ 5.7 mJy at 100 µm and 160 µm respectively. Berta et al. (2010) describe in their appendix the Herschel-PACS observations, data reduction and the blind extraction of PACS sources with SNR≥ 3. Lutz et al. (in prep.) will present the fluxes of PACS sources. The PACS images are aligned on the GOODS imaging products. Complementary to the Herschel PACS observations, we use for this work data from the VLA at 1.4 GHz (Morrison et al. 2010) and Spitzer-MIPS at 24 µm (Dickinson et al., in prep.).

In the past years, several groups surveyed the GOODS North region using the bolometer cameras SCUBA, AzTEC and MAMBO (Borys et al. 2003;Greve et al. 2008;Hughes et al. 1998;Perera et al. 2008;Pope et al. 2005;Wang et al. 2004). These observations discovered about 150 SMGs at 850 µm, 1.1 and 1.2 mm. Robustly identified VLA and MIPS 24 µm counterparts are already known in the literature for SCUBA and AzTEC sources (Chapin et al. 2009;Pope et al. 2006). In addition, Greve et al. (2008) presented VLA counterparts for 11 out of 30 MAMBO sources.

We search for Herschel-PACS counterparts of SMGs that are either detected with a SNR of ≥ 4 or detected by at least two different surveys. 56 SMGs fulfill this criterion which should assure a robust SMG sample to work with. Our sample14 consists of 36 SCUBA, 12 AzTEC and 8 MAMBO sources and for 15 SMGs spectroscopic redshifts (SMG spec ) have been already obtained. We match our SMG sample with the PACS 100 µm and 160 µm blind catalogue and search for counterparts within a radius of 5.5 ′′ for MAMBO sources, 7.5 ′′ for SCUBA sources and 9 ′′ for AzTEC sources. As a sanity check of the blind catalogue, we inspected by eye the search region in the PACS imaging. The search circles that we have applied correspond to the beam size (FWHM) of the different bolometric datasets and should guarantee that no reliable associations to SMGs will be missed. We also searched the VLA 1.4 GHz map and the MIPS 24 µm images for counterparts at the SMG positions.

We calculate the corrected Poissonian probability p that an association of SMGs within the search radius is a chance coincidence. This approach (see for details Downes et al. 1986) corrects the simple Poissonian probability of a detected association for the possibility of associations of different nature but similar probability. The derived probability of PACS and MIPS association is based on raw number counts in GOODS North. We search for VLA counterparts of SMGs down to 3σ. However, the VLA source catalogue (Morrison et al. 2010) is only reliable down to 20 µJy (∼ 5σ). Therefore, we assess the reliability of VLA counterparts relying on published number counts (e.g., Fomalont et al. 2006). Similar to previous studies, we define following quality criteria for assessing the robustness of identified candidate counterparts. We classify association of SMGs with p ≤ 0.05 as secure and with 0.05 < p ≤ 0.10 as possible counterparts.

We uncover PACS secure or possible counterparts for 22 SMGs, corresponding to a PACS identification rate of 39% of our whole SMG sample, see also Table 1 for details. Our PACS identification rate of 39% is lower than the rate of 54% found by Magnelli et al. (2010). The reason is that Magnelli et al. (2010) focus on already radio-identified SCUBA and AzTEC sources with spectroscopic redshifts mainly. The top panel of Fig. 1 displays the (sub)millimeter-PACS separation of our association. We did not find evidence of systematic offsets. We find PACS counterparts at a mean (sub)millimeter-PACS positional offset of ∆ (submm)mm-P ACS100 = 5.0 ′′ ± 2.1 ′′ and ∆ (submm)mm-P ACS160 = 4.9 ′′ ± 2.0 ′′ . This is consistent with a typical submm/mm position error of about 3 ′′ to 5 ′′ and strengthens our choice of the FWHM of the bolometric data as search circle for PACS counterparts. The top panel of Fig. 1 shows clearly a dominance of secure counterparts. Given this statistical approach, associations with offsets much larger than the average might not always be correct. We detect 20 (16) SMGs at 160 (100) µm and classify 15 (12) of them as secure and 5 (4) as possible counterparts. The number of PACS counterparts at 160 µm is higher than at 100 µm. This is expected as the 160 µm measurements lie close to the FIR peak. We note that based on the corrected Poissonian probability p each PACS detection within the bolometer beam (our search circle) is classified as associated SMG counterpart. Typical PACS fluxes of these dust-obscured high-z sources range between 4.0 mJy to 34.9 mJy at 100 µm and 5.0 mJy to 65.0 mJy at 160 µm.

We have 43 (28 are secure; 15 are possible) radioidentified SMGs in our sample, about 50% of them are seen at PACS wavelengths. Vice-versa, only one PACS association (secure) is undetected at 1.4 GHz, see detailed discussion of GN13 (alias HDF850.4) at end of Section 3. One-third of PACS detected SMGs have at least two VLA counterparts.

diagnostic potential of pacs observations of submillimeter galaxies

About twice as many SMGs are identified by the VLA than by PACS. VLA observations are more sensitive for sources at redshifts up to z = 4. None of the well-known, spectroscopically identified SMGs at z = 4 -GN20, GN20.2a/b and GN10 (Daddi et al. 2009a,b;Dannerbauer et al. 2008;Wang et al. 2007Wang et al. , 2009) ) -have been significantly detected in our PACS imaging, see middle panel in Fig. 1. Another highly promising z ≥ 4 candidate, HDF850.1 (Cowie et al. 2009;Dunlop et al. 2004;Hughes et al. 1998) is also not seen by PACS. However, all these SMGs have radio counterparts. Focusing on our spectroscopic subsample of 15 sources, SMG spec , we find a trend that the fraction of SMGs detected at PACS bands decreases with redshift (see middle panel in Fig. 1), being explained by the fact that PACS fluxes drop with increasing redshift. No source beyond z = 2.00 (GN06) at 100 µm and z = 2.58 (GN04) at 160 µm is significantly detected by PACS. However, we do not find evidence that the PACS detection rate of SMGs correlates with the SCUBA flux density (Fig. 1). In addition, VLA observations provide subarcsecond accurate positions which are essential for the proper identification in the optical and near-infrared bands and follow-up spectroscopic observations. PACS cannot deliver positions at these accuracies. To summarize, ultra-deep VLA observations still remain the best and most effective approach to identify SMG counterparts, even up to redshift z = 4.

Using only radio, 850 µm and 24 µm flux densities, Daddi et al. (2009a) derived accurate (∆z/(1 + z) ∼ 0.1) radio-IR photometric redshifts for SMGs. Motivated by this work, we apply the radio-IR photometric redshift code presented in Daddi et al. (2009a) and calculate photometric redshifts by adding our PACS measurements to existing SCUBA, MIPS 24 µm and VLA 1.4 GHz flux measurements of our SMG sample. Naively we would have expected to improve the accuracy of the radio-IR photometric redshifts by adding FIR measurements shortwards to the IR dust peak. In Fig. 2 we show the results of our attempt using template libraries of local galaxies (Chary & Elbaz 2001). In the left panel we show photometric redshifts (adapted from Daddi et al. 2009a) based on radio, MIR and submm observations for SCUBA counterparts with known spectroscopic redshifts in GOODS North which agree fairly well. In the right panel we show photometric redshift estimates adding the PACS measurements to our previous measurements in the radio, MIR and submm. Clearly the obtained accuracy decreases and these photo-z estimates are poorer. Omitting certain measurements (e.g., MIPS 24µm and/or VLA 1.4 GHz) gives even worse results. We obtain similar results by using template libraries from Dale & Helou (2002) and the average SED constructed by Micha lowski et al. ( 2010) of 73 spectroscopically identified SMGs (Chapman et al. 2005). This result means that most likely the far-infrared properties of SMGs are different from templates built to describe local galaxies. These observed differences arise most probably from the fact that SMGs are colder than local ULIRGs of same luminosity (Chanial et al. 2010;Chapman et al. 2005;Elbaz et al. 2010;Magnelli et al. 2010). Further investigations are needed to fully exploit the Herschel-PACS imaging in order to obtain accurate photometric redshifts.

We already know the spectroscopic redshift for 15 SMGs in our sample. However, in absence of spectroscopic redshifts for most of our sources, searching for correlations between observed properties is essential for constraining the nature, redshift and evolution of SMGs. We explore if flux ratios involving PACS 100 µm and 160 µm measurements can be used as a rough redshift indicator. Fig. 3 displays the results of our analysis. The PACS color (S 160 µm /S 100 µm ) of SMGs does not vary with redshift and is consistent with the prediction of models and observed SEDs from Chary & Elbaz (2001), Micha lowski et al. ( 2010), Armus et al. (2007) and Pope et al. (2008). The PACS colors seem to be slightly redder than predicted by the various models and may indicate a difference between the observed FIR-SED of SMGs and templates describing fairly well local infrared galaxies. The composite rest-frame SED for the SMG spec (Fig. 3) subsample shows their diversity in the far-infrared. Their far-infrared colors are different from the template SEDs, most notably for the local luminous infrared galaxies. This may explain our finding reported above that we are not able to obtain accurate IR-radio photometric redshifts by including PACS measurements.

The PACS fluxes are redshift dependent, whereas the (sub)millimeter flux density at z ≥ 1 is not (due to the negative K-correction; e.g., Blain et al. 2002), thus one would expect to see a trend between (sub)mm/PACS flux ratio for both PACS bands (see also the predictions based on different templates in Fig. 3). Indeed, we find a fairly clear trend both for S 850 µm /S 160 µm respectively S 850 µm /S 100 µm versus spectroscopic redshift for the SMG spec subsample15 over the whole redshift range spanned by our SMGs from z ∼ 1 -4. We conclude that the (sub)mm/PACS flux ratio seems to be a useful albeit crude redshift indicator and may help to se- In the left panel we show photometric redshifts based on radio, 850 µm and 24 µm flux densities measurements for SMG counterparts with spectroscopic redshifts in GOODS North (adopted from Daddi et al. 2009a). There is a fairly good agreement. In the right panel, we show photometric redshift estimates including PACS measurements which are less reliable. lect/mark SMGs at very high-redshifts. We explored also VLA/PACS and PACS/MIPS 24 µm flux ratios versus redshift but did not observe any correlation, being consistent with the fact that VLA, MIPS 24 µm and PACS fluxes drop with increasing redshift. Based on this finding, we investigate the (sub)mm/PACS ratio for the remaining 41 SMGs without any reliable redshift. This analysis shows that PACS-detected SMGs tend to have lower flux ratios than the PACS-undetected SMG sample (Fig. 3). This trend seems to be more prominent for the S 850 µm /S 160 µm flux density ratio. Our analysis may indicate that indeed as previously discussed PACSundetected SMGs could tend to lie at higher redshifts and the (sub)mm/PACS flux ratio could be a crucial tool to select the very high-z tail of the SMG population.

The previous analysis bridges with the discovery that 12 out of 56 SMGs (21%) in our sample are blank fields both at PACS and radio wavelengths. The nature of these sources is still not clear. These SMGs could be either spurious sources which is mainly assumed, or at redshifts higher than z > 4. Indeed, how reliable are these (sub)mm sources detections? The sample consists of seven submillimeter and five millimeter selected sources (of the latter population, one is seen by AzTEC and four by MAMBO). We checked each source for its reliability. The mm sources are selected with SNR ≥ 4. Four of the seven SCUBA galaxies are listed in both Pope et al. (2006) and Wang et al. (2004). The fact that Pope et al. (2006) and Wang et al. (2004) used (nearly) the same SCUBA data, but performed independent data reduction and source extraction, is giving more weight to the reliability of these detections. As a sanity check we inspected the SCUBA and MAMBO galaxies in the AzTEC 1 mm map. Our analysis suggests that most of these sources are reliable. One of them has a SNR ∼ 9 at 850 µm. However, we note that only mm interferometric observations will reveal unambiguously the reliability of these sources. Their non-detection both at radio and PACS wavebands in combination with its (sub)mm/PACS flux ratio may suggest that these sources could lie at higher redshifts than the typical SMG population (e.g., z > 3 -4).

We conclude this work by presenting the identification of an SMG counterpart having a PACS but no VLA detection. Daddi et al. (2009a) suspected that the source at z spec = 0.457, about 7 ′′ away from the SCUBA position, could not be the correct counterpart of GN13 alias HDF850.4 (Hughes et al. 1998;Pope et al. 2006). We detect a faint (4.2σ), secure counterpart at 100 µm, being very close to the bolometer position (∼ 0.6 ′′ ). Its reliability is fortified by a 200 µJy strong, secure counterpart at 24 µm. Using the flux ratios S 850 µm /S 100 µm = 0.38 and S 850 µm /S 160 µm > 0.37 as a coarse redshift indicator suggests a redshift of z ∼ 1 -2.5. PACS has been developed by a consortium of institutes led by MPE (Germany) and including UVIE (Austria); KUL, CSL, IMEC (Belgium); CEA, OAMP (France); MPIA (Germany); IFSI, OAP/OAT, OAA/CAISMI, LENS, SISSA (Italy); IAC (Spain).

This development has been supported by the funding agencies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Germany), ASI (Italy), and CICYT/MCYT (Spain). We thank Alex Pope and Lee Armus for providing SEDs of SMGs and local ULIRGs.

Fig. 1 .

 1 Fig. 1.-Top panel: Histogram of distance between the submm/mm position from the bolometric map and PACS positions of associated FIR sources at 100 µm (left) and 160 µm (right). Black and gray indicate secure and possible PACS counterparts. Middle panel: We show the redshift distribution for our SMG sample with spectroscopic redshifts (gray) and overplot our PACS detections at 100 µm (green) respectively 160 µm (red). Lower panel: We show the SCUBA flux distribution of our SMG sample (gray) and overplot our PACS detections at 100 µm (green) respectively 160 µm (red).

Fig. 2 .

 2 Fig. 2.-Comparison of spectroscopic and photometric redshifts.In the left panel we show photometric redshifts based on radio, 850 µm and 24 µm flux densities measurements for SMG counterparts with spectroscopic redshifts in GOODS North (adopted fromDaddi et al. 2009a). There is a fairly good agreement. In the right panel, we show photometric redshift estimates including PACS measurements which are less reliable.

Fig. 3 .

 3 Fig. 3.-Left Panels: From top to bottom we plot the flux ratios S 160 µm /S 100 µm , S 850 µm /S 160 µm and S 850 µm /S 100 µm versus redshift for SMGs with spectroscopic redshifts. Template SEDs of a local LIRG with L IR ≈ 1 × 10 11 L ⊙ (blue-solid line), a local ULIRG with L IR ≈ 1 × 10 12 L ⊙ (black-solid line) and a HyLIRG with L IR ≈ 1 × 10 13 L ⊙ (red-solid line), all from Chary & Elbaz (2001), and an average SMG (black-dashed line, Micha lowski et al. 2010), are shown for comparison. Average SEDs including Spitzer-IRS spectroscopy of local ULIRGs (blackdashed-dotted line, Armus et al. 2007) and SMGs (black-dotted line, Pope et al. 2008) are shown as well. The histograms present the distribution of SMGs without spectroscopic redshifts (bluefilled), lower limits of flux ratios are displayed by the pink-empty histogram. For the S 160 µm /S 100 µm flux ratio we show the upper limit as gray-empty histogram. The pink (gray) arrow underlines the limits. Right Panels: From top to bottom, we plot the composite rest-frame SED -IRAC 3.6 µm (pink), MIPS 24 µm (blue), PACS 100 µm (green), PACS 160 µm (green), SCUBA 850 µm (gold), VLA 20 cm (red) -of our spectroscopic SMG sample normalized on SCUBA, VLA and PACS 160 µm fluxes. Template SEDs of ULIRGs and SMGs are shown for comparison. Both data points and templates are normalized on an SMG with a SCUBA flux of 8 mJy at z = 2.2.

Fig. 4 .

 4 Fig. 4.-From left to right and top to bottom we show the 50 ′′ × 50 ′′ IRAC 3.6µm, MIPS 24 µm, PACS 100µm and PACS 160µm images of the field of GN13 alias HDF850.4(Hughes et al. 1998;Pope et al. 2006), north is up and east to the left. The 7.5 ′′ search radius circle at the nominal SCUBA position of GN13 (magenta cross) is drawn. Green (red) circles represent PACS 100µm (PACS 160µm) ≥ 3σ detections and the white square a VLA source.Daddi et al. (2009a) suggested that the counterpart at z = 0.457 in South-West direction ∼ 7 ′′ away from GN13 is a mis-identification. We propose the PACS 100 µm detection on top of the nominal SCUBA position (magenta cross) as new counterpart at z ∼ 1 -2.5.

In case that an SMG is detected at submm and mm bands, we give preference the SCUBA detection and include it in our sample. For mm-only detected sources we list, if available, the AzTEC otherwise the MAMBO detection.

For SCUBA sources fromPope et al. (2006) we use the deboosted flux. The same we do for AzTEC and MAMBO sources. We converted the AzTEC and MAMBO mm flux densities into SCUBA flux densities by assuming a flux ratio of S 850 /S 1 mm of 2.5 for a ULIRG-like SED at redshift z ∼ 2 -3.

We thank an anonymous referee for useful comments that improved our manuscript. We acknowledge the funding support of the ERC-StG grant UPGAL 240039 and ANR-08-JCJC-0008.


Adrien Barton
email: adrien.barton@gmail.com

William Duncan
email: william.duncan@roswellpark.org

Fumiaki Toyoshima

Jean-François Ethier
email: ethierj@gmail.com.

First Steps Towards an Ontology of Belief

Keywords: Belief, disposition, process, plan, intention, information content entity, aboutness, quality 1.!Introduction Belief, disposition, process, plan, intention, information content entity, aboutness, quality

This paper presents first steps towards a formalization of beliefs. It argues for the multiple nature of beliefs: the term "belief" can refer to a mental process of taking something to be the case, or to a disposition realized by such a mental process. The categorical basis of a disposition-belief has as part the concretization of an information content entity, which is in a relation of aboutness with the entities concerned by this belief.

Introduction

Belief is a central construct in several artificial intelligence models of agency -such as the Belief-ef ef Desire-Intention (BDI) model [START_REF] Wooldridge | Reasoning about rational agents[END_REF]; an ontological formalization of beliefs would therefore be highly valuable. For example, we might want to formalize patient's beliefs underlying their adherence or non-adherence to medication prescriptions [START_REF] Ethier | Improving the Semantics of Electronic Prescriptions with a Realist Ontology[END_REF] (e.g. beliefs about a medication's efficacy). Currently, the Mental Functioning Ontology (MF [START_REF] Hastings | Representing mental functioning: Ontologies for mental health and disease[END_REF]), an OBO Foundry candidate [START_REF] Smith | The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration[END_REF], classifies belief as a Mental disposition, without further analysis (but see the recent [START_REF] Schulz | Towards an ontology of religious and spiritual belief[END_REF]). This paper will present why it makes sense to classify belief as a disposition, and argues that there is also another kind of belief, namely occurrent belief. ef ef It should also be possible to extend this account to other ontological frameworks formalizing dispositions, such as UFO [START_REF] Guizzardi | Dispositions and causal laws as the ontological foundation of transition rules in simulation models[END_REF] -a foundational ontology tailored for general conceptual modeling languages.

The term "belief" is polysemous. Suppose that Mary believes that amoxicillin cures bronchitis. The term "Mary's belief" may refer to the content of Mary's belief, ef ef or it may also refer to an entity in Mary's mind. The philosophical literature standardly takes the former entity to be a proposition, and the latter entity to be a cognitive attitude towards this proposition. The ontological nature of propositions is a highly complex topic, and we will not delve into it in this paper, building instead in section 3 upon information content entities ("ICE"), as defined by the Information Artifact Ontology (IAO [START_REF] Smith | Aboutness: Towards foundations for the information artifact ontology[END_REF]). As a matter of fact, there are several ontologies based on the theory of ICEs, such as the Prescription of Drugs Ontology (PDRO [START_REF] Ethier | Improving the Semantics of Electronic Prescriptions with a Realist Ontology[END_REF]), where an ontology of belief would be useful. We will first show in section 2 that beliefs in the second sense have both a dispositional and occurrent nature. We will suggest here first steps in developing a formalization in OWL (and point to some insufficiencies of this language to formalize beliefs). In the remainder of the paper, universals or classes will be italicized and capitalized, and names of particulars will be written in bold.

2.!The Dual Nature of Beliefs

In the Basic Formal Ontology (BFO [START_REF] Arp | Building Ontologies with Basic Formal Ontology[END_REF]), a realizable entity is as an entity that is manifested or exhibited during some process, but continues to exist even when it is not participating in a process (where a process is a temporally extended entity, whose existence depends on at least one material entity). Realizable entities are further specialized into dispositions and roles. Dispositions are realizable entities "that exists because of certain features of the physical makeup of the independent continuant that is its bearer" (such as being flammable), whereas roles exist because the bearer is in special physical, social, or institutional circumstances (such as being an employee). Given this, we classify beliefs in BFO as a subtype of dispositions. My belief that amoxicillin cures bronchitis exists even when sleeping -that is, even when I am not consciously thinking it -and exists in virtue of the physical makeup of my neuronal system.

Next let us consider how beliefs (as dispositions) are realized. A proposal [START_REF] Schwitzgebel | Belief[END_REF] is that beliefs are dispositions to physically perform certain kinds of actions (that is, dispositions to behave in a certain way). My belief that amoxicillin cures bronchitis, then, is realized when I perform the action of taking amoxicillin when I have bronchitis.

This approach, however, does not seem to account for the nature of beliefs. I can have a belief that amoxicillin cures bronchitis even if I'm totally paralytic and able to take To answer this objection, one might argue that beliefs are dispositions to act if further conditionalized: my belief that amoxicillin cures bronchitis is a disposition to take amoxicillin if I have bronchitis and I am not paralyzed. However, this proposal only seems to capture the practical dimension of beliefs (how they relate to action), not how they relate to the purely theoretical attitude of taking some state of affairs to be the case. Consider the fictional counter-example of a supernatural spirit with no power of action at all, who would have many beliefs about the world (e.g. that the sea is mostly composed of water, etc.), but no disposition to act.

Thus, following a classical philosophical distinction [START_REF] Schwitzgebel | Belief[END_REF][START_REF] Mumford | Dispositions[END_REF], we hold that dispositional beliefs are not realized by physically performing actions, but by some occurrent mental process that we call "occurrent belief", namely the cognitive process of taking it to be the case that amoxicillin cures bronchitis. For example, Jones may believe that amoxicillin is helpful to cure his bronchitis, but this (dispositional) belief is not being continuously activated (or said differently, realized) in his mind. At t 1 (see figure 1 below), he deliberates whether he should take amoxicillin, and his dispositional belief is realized by a process of him taking amoxicillin to be helpful to cure his bronchitis. His dispositional belief is then realized a second time at t 2 by a similar process. Thus, a person may have a dispositional belief that amoxicillin cures bronchitis even when sleeping or unconscious. We can then suggest the following definitions:

•! Dispositional belief: A disposition that can be realized in an occurrent belief.

•! Occurrent belief: A MF:Mental process of taking something to be the case.

The difficulty here would be to analyze what it means to take something to be the case, which might involve a cognitive attitude towards a proposition -two complex notions. This will remain out of scope of this paper, which will instead analyze how beliefs can be articulated with IAO's theory of ICEs.

3.!Information Content Entities and Beliefs

In the following, we will use single quotes such as in 'amoxicillin' to refer to an ICE instance. ICEs are about something (see [START_REF] Smith | Aboutness: Towards foundations for the information artifact ontology[END_REF] and the two senses of aboutness they introduce, at the level of reference and the level of compound expression). For example, the ICE 'aspirin' on a drug product monograph is an ICE that is about the class of aspirin drug products. Following Smith and Ceusters [START_REF] Smith | Aboutness: Towards foundations for the information artifact ontology[END_REF], an ICE is concretized by one or several instances of a specific subclass of BFO:Quality named Information Quality Entity (IQE). For example, if Dr. Jones writes the word "amoxicillin" on a white paper, the ICE 'amoxicilin' that refers to the active ingredient amoxicilin is concretized by some qualities inhering in the mereological sum of ink molecules on this paper. Not all qualities of the ink are relevant from an informational point of view: for example, writing the dot on the "i" slightly more to the left or to the right is not relevant in this sense. According to IAO's theory, ICEs might also be concretized by a neuronal configuration. There is an important distinction between ICEs and IQEs. IQEs specifically depend on their bearer; that is, an instance of an IQE exists only as long as the unique entity it depends on exists. On the other hand, ICEs generically depend on their bearer: they can be copied or migrate on another bearer.

We hypothesize that a belief involves the concretization of an ICE in one's brain: if I believe that amoxicillin cures bronchitis, my brain must carry some associated information. For example, let's define 'Amoxicillin cures bronchitis' as ICE 1 , and 'L'amoxicilline soigne les bronchites.' (the French translation) as ICE 2 . Thus, if I believe that amoxicillin cures bronchitis, my brain may bear ICE 1 or ICE 2 2 . However, having ICE 1 (or ICE 2 ) concretized in one's brain does not imply that the person believes that amoxicillin cures bronchitis. Suppose that John holds at t 0 the belief 0 that amoxicillin does not cure bronchitis, but after attending to a conference on the topic, holds at t 1 the belief 1 that amoxicillin does cure bronchitis (note that holding belief 1 is stronger than simply not holding belief 0 anymore). At t 0 , some ICE such as ICE 0 'Amoxicillin does not cure bronchitis' is concretized in John's brain by IQE 0 , and he holds a belief attitude towards it. At t 1 , ICE 0 might still be concretized in his brain occasionally (as it was presumably concretized in your brain when you read the sentence), but he does not hold a belief attitude towards it. Said differently, a mental representation of some information does not imply a belief in the veracity of the represented information. I can have a mental representation of the statement 'the Earth is flat' (and thus, I can have the ICE 'the Earth is flat' concretized in my brain), even if I do not believe it. To connect a belief with its informational content, we will compare the qualities underlying the former with the qualities underlying the latter. Barton et al. [START_REF] Barton | The identity of dispositions[END_REF] define the "categorical basis" of a disposition as the quality (or sum of qualities) in virtue of which this disposition obtains (and which therefore inheres in a part of the disposition's bearer named by BFO the "material basis" of this disposition [START_REF] Arp | Building Ontologies with Basic Formal Ontology[END_REF]). For example, the categorical basis of a glass' fragility is constituted by some features of its molecular structure. Thus, the categorical basis of a belief is a sum of qualities of a brainnamely, those qualities in virtue of which this belief exists. The connection between belief 0 and its informational content ICE 0 can be formalized by stating that the quality IQE 0 concretizing ICE 0 in John's brain is a part at t 0 of the categorical basis of his belief 0 .

Figure 1 illustrates how our formalization can be used to relate a belief to the object(s) of this belief. ICE 1 , for example, is about the class Amoxicillin and the class Bronchitis (at the level of reference, cf. [START_REF] Smith | Aboutness: Towards foundations for the information artifact ontology[END_REF]). Therefore, belief 1 can be connected to the classes Amoxicillin and Bronchitis by stating that belief 1 has as categorical basis a sum of qualities that have as part IQE 1 , and IQE 1 is the concretization of ICE 1 that is about the class Amoxicillin and about the class of Bronchitis3 .

4.!Conclusion

In this paper, we have put forth the beginnings of a theory for representing two important ways that we understand beliefs: dispositional beliefs and occurrent beliefs. A dispositional belief exists even when we are not actively thinking it, and when we are actively thinking about a belief, we engage in an occurrent belief process during which we take something to be the case. Dispositional and occurrent beliefs are related using BFO's realized in relation: an instance of a dispositional belief is realized in an instance of an occurrent belief.

Our analysis left open whether a dispositional belief could be causally active even if it is not realized. For example, I may believe that (ceteris paribus) massive objects accelerate towards the Earth. This belief certainly has a causal influence on some of my actions, even when I do not consciously deliberate about it. As a consequence, if one endorses a purely dispositional theory of causation, a dispositional belief is realized in an occurrent belief whenever it is causally active, even when the person having this belief does not consciously deliberate about it.

To relate our dispositional beliefs to the entities that are targets of our beliefs, we incorporate IAO's theory of ICEs, which enables us to e.g. relate belief 0 and belief 1 with the classes Amoxicillin and Bronchitis. A theory of proposition would be helpful to proceed further and be able to relate beliefs not only with the entities they concern, but also with their substantial content, such as the propositions "Amoxicillin does not cure bronchitis" (related to belief 0 ) and "Amoxicillin cures bronchitis" (related to belief 1 ) -the former being especially complex to analyze in a realist ontology, as it does not describe a state of affairs that obtains.

Finally, the present account has defined beliefs independently of practical rationality, that is, independently of any intention to act on it. However, beliefs do frequently play a role in motivating action. Future work should also examine how dispositional beliefs can lead to an intention to act, by being realized by an occurrent belief that is part of a plan making process, that leads to an OBI:Plan (as formalized by the Ontology for Biomedical Investigations [START_REF] Bandrowski | The ontology for biomedical investigations[END_REF]).

Figure 1 :

 1 Figure 1: Relevant classes and instances (Bronchitis is omitted)

This shows how a theory of proposition would help to complement this account, as those two ICEs arguably express the same proposition.

Note that ICE1 is also about the state of affairs of amoxicillin having a disposition to cure bronchitis (in the sense of aboutness at the level of compound expression[START_REF] Smith | Aboutness: Towards foundations for the information artifact ontology[END_REF]). This is however presently not easily formalizable in OWL. Also, relating a particular such as ICE1 with classes such as Amoxicillin and Bronchitis is not easily formalizable in OWL, although one could use the inverse relation of is_about to solve this difficulty[START_REF] Barton | What is a risk? A formal representation of risk of stroke for people with atrial fibrillation[END_REF].

Adrien Barton acknowledges financial support by the CIHR-funded Quebec SPOR Support Unit. William Duncan acknowledges partial support from the Roswell Park Comprehensive Cancer Center Biomedical Data Science Shared Resource that is funded in part by Cancer Center Support Grant NCI P30CA16056.


Malika Auvray
email: mail.auvray@isir.upmc.fr

Multisensory and spatial processes in sensory substitution

Keywords: Sensory substitution, Blindness, Brain plasticity, Rehabilitation technologies, Learning

Sensory substitution devices aim at compensating sensory deficits by converting stimuli coming from a deficient sensory modality (e.g., vision) into stimuli accessible through another modality (e.g., touch or audition). Studies conducted with these devices revealed the central nervous system to be very plastic. Various laboratories have conducted studies investigating such plasticity by means of behavioural and brain-imaging techniques. At the ISIR Laboratory, we focused on the factors underlying the learning of sensory substitution devices, their adequacy to the target population, and we explored ways of improving their design by the use of crossmodal correspondences and by taking into account individual differences in the used reference frames. We also investigated the nature of the experience with sensory substitution. In particular, we suggested moving beyond positions reducing experience to that of a single sensory modality. Rather, sensory substitution is considered as a multisensory experience, involving not only visual, but also auditory or tactile processes as well as cognitive processes. In this framework, individual differences do have an influence on the extent to which the different sensory modalities influence the experience with the devices.

I. Introduction

Sensory substitution devices were developed with the aim of compensating one or several functions of a deficient sensory modality by converting stimuli that are normally accessed through this deficient sensory modality into stimuli accessible by another sensory modality. For instance, these devices can convert visual information into sounds or tactile stimuli. Sensory substitution devices have broad applications such as sensory rehabilitation and perceptual augmentation. For instance, visual-to-tactile (e.g., Bach-y-Rita et al., 1969;[START_REF] White | Seeing with the skin[END_REF] and visual-to-auditory (e.g., [START_REF] Hanneton | The Vibe: A versatile vision-to-audition sensory substitution device[END_REF][START_REF] Meijer | An experimental system for auditory image representations[END_REF] conversion systems were designed in order to assist blind and visually impaired individuals.

Numerous devices were designed to compensate other deficits, such as proprioceptive deficits (e.g. see [START_REF] Danilov | Efficacy of electrotactile vestibular substitution in patients with peripheral and central vestibular loss[END_REF][START_REF] Diot | Sensory substitution for balance control using a vestibular-to-tactile device[END_REF]. In the field of perceptual augmentation, these devices were developed in order to gain access to visual information, either when there is an excess of visual information to process, such as when driving a car (e.g., [START_REF] Ho | The multisensory driver: Implications for ergonomic car interface design[END_REF] or when conditions of perception are degraded, as can be the case for those involved in firefighting [START_REF] Carton | Tactile distance feedback for firefighters: design and preliminary evaluation of a sensory augmentation glove[END_REF] or military operations [START_REF] Jones | Vibrotactile pattern recognition on the arm and back[END_REF].

In what follows, the focus will be on visual-to-tactile and visual-to-auditory devices, designed for the rehabilitation of visual deficits. Most of them consist of a tiny camera, either hand-held or embedded in glasses, recording the external scene in real time. This scene is then converted into sounds or tactile stimuli. The translation codes can be very diverse. In most visual-to-tactile devices, the translation code is analogical. For instance, a visual circle can be translated into a circular pattern of tactile stimuli. In some devices, non-analogical codes have also been used, for instance in order to convert distance into vibrations (e.g., [START_REF] Farcy | Electronic travel aids and electronic orientation aids for blind people: Technical, rehabilitation and everyday life points of view[END_REF][START_REF] Maidenbaum | The "EyeCane", a new electronic travel aid for the blind: Technology, behavior & swift learning[END_REF][START_REF] O'brien | Perception of distance-to-obstacle through time-delayed tactile feedback[END_REF]. The code used in visualto-auditory devices translates several dimensions of the visual signal into dimensions of the auditory signal. For instance, the vOICe [START_REF] Meijer | An experimental system for auditory image representations[END_REF] translates vertical position into frequency, horizontal position into time scanning, and visual brightness into auditory loudness. Other visual-to-auditory devices convert colour information using different orchestral instruments (e.g., the See ColOr; [START_REF] Bologna | On the use of the auditory pathway to represent image scenes in real-time[END_REF]the EyeMusic, Levy-Tzedek et al., 2014).

Studies conducted on sensory substitution devices revealed the central nervous system to be very plastic. Behavioural studies have investigated performance across a variety of tasks. In particular, studies have revealed that these devices allow their users to perform localisation tasks (e.g., [START_REF] Levy-Tzedek | Cross-sensory transfer of sensory-motor information: visuomotor learning affects performance on an audiomotor task, using sensory-substitution[END_REF][START_REF] Proulx | Seeing 'where' through the ears: effects of learning-by-doing and long-term sensory deprivation on localization based on image-to-sound substitution[END_REF], shape recognition (e.g., Arno et al., 2001;Auvray et al., 2007Auvray et al., -a, 2007-b;-b;[START_REF] Pollok | Image-to-sound conversion: Experience-induced plasticity in auditory cortex of blindfolded adults[END_REF]Striem-Amit et al., 2012b), and navigation tasks [START_REF] Chebat | Navigation with a sensory substitution device in congenitally blind individuals[END_REF]2015). Brain-imaging studies have shown that the use and practice of visual-to-tactile [START_REF] Ptito | Cross-modal plasticity revealed by electro-tactile stimulation of the tongue in the congenitally blind[END_REF]; see also [START_REF] Kupers | Transcranial magnetic stimulation of the visual cortex induces somatotopically organized qualia in blind subjects[END_REF]visual-to-auditory (e.g., Striem-Amit andAmedi, 2014) devices result in increased activation in blind people's visual cortex (for reviews, see [START_REF] Proulx | Multisensory perceptual learning and sensory substitution[END_REF][START_REF] Ptito | The pluripotent visual cortex in congenital blindness[END_REF]. It should however be mentioned that one study directly compared activation longitudinally [START_REF] Kim | Tactile-auditory shape learning engages the lateral occipital complex[END_REF]. The results did not reveal increased activation, but rather a change in functional connectivity. This result might suggest that the observed cross-modal recruitment of the visual cortex during the use of sensory substitution devices can be due to unmasking or existing computations through non-visual inputs already there prior to devices' use (e.g. [START_REF] Ptito | Cross-modal plasticity revealed by electro-tactile stimulation of the tongue in the congenitally blind[END_REF]Striem-Amit et al., 2012-c).

Interestingly, the visual brain areas activated during a task with a visual-to-auditory device correspond to those that are activated for the same task performed visually. For instance, when congenitally blind participants are required to recognize human silhouettes with the visual-to-auditory conversion device The vOICe, this activates visual cortex extrastriate body-selective area, which responds more strongly to images of human body than to other types of objects (Striem-Amit and Amedi, 2014). Another example is the activation of visual word form area (VWFA) when congenitally blind participants are asked to recognize letters with The vOICe (Striem-Amit et al., 2012-b). This led the researchers in this group to think of the brain as having a flexible sensory-independent, task-selective supramodal organization rather than a sensory-specific one (Amedi et al., 2017;[START_REF] Heimler | Origins of task-specific sensoryindependent organization in the visual and auditory brain: neuroscience evidence, open questions and clinical implications[END_REF].

Ever since their inception in the sixties, sensory substitution devices proved to be fruitful tools to investigate questions in the fields of philosophy of perception, experimental psychology, and studies of brain plasticity. However, in spite of their potential and the perspectives they open, sensory substitution devices remain under-used to date. Thus, one of the major challenges for scientists working in the field of rehabilitation is to favour the use of aid devices by impaired people. The limited success of sensory substitution devices can be explained by insufficiencies in the analyses of what is sensory substitution, insufficiencies in the understanding of impaired people's perceptual specificities, and deficiencies in the design of the devices. To overcome these insufficiencies, the research conducted in the lab lies both upstream and downstream of the design of sensory substitution devices. In particular, as will be detailed in the next sections, it involves a conceptual understanding of the nature and possibilities offered by sensory substitution devices, studies of the factors underlying learning processes, and the possibility of improving their design by using crossmodal correspondences and taking into account individual differences in the used reference frames.

II. Conceptual understanding of sensory substitution

One important question raised is: to which sensory modality does the perception with a sensory substitution device belong? Two opposite theses were initially put forward: the dominance thesis (e.g., Keeley, 2002) according to which perception with a sensory substitution device remains in the substituting modality (touch or audition), and the deference thesis (e.g., [START_REF] Hurley | Neural plasticity and consciousness[END_REF][START_REF] Noë | Action in Perception[END_REF][START_REF] O'regan | Why Red Doesn't Sound Like a Bell. Understanding the Feel of Consciousness[END_REF] according to which perception switches to the substituted modality (vision). The deference thesis has opened the door to over-optimistic claims involving the idea that users of visual-to-tactile substitution devices would become able to "see with the skin" [START_REF] White | Seeing with the skin[END_REF] or to "see with the brain" (Bach-y-Rita et al., 2003). These optimistic claims have been echoed to the wider audience, including potential users of these devices: sensory substitution devices have been advertised

as "helping the blind see with their ears" [START_REF] Jacobson | 2 0 1 4 ) . App helps the blind "see" with their ears[END_REF] or "rewiring brains to see with sound" [START_REF] Trivedi | Sensory hijack: rewiring brains to see with sound[END_REF]. My collaborators and I suggested that it is time to go beyond the dominance versus deference debate, and that perception with a sensory substitution device goes beyond assimilation to either the substituting or the substituted modality. According to this view, sensory substitution should be understood as being vertically integrated on preexisting capacities that involve the substituting and the substituted sensory modalities, as well as cognitive processes (see figure 1). To go deeper into the defended view, the dominance versus deference debate remains based on an implicit perceptual equivalence which we suggest to identify as a perceptual assumption. The influence of this perceptual assumption is visible in the fact that researchers accept or target equivalences between using a sensory substitution device and the exercise of a sensory modality. In other words, the perceptual assumption considers that sensory substitution follows what occurs with canonical cases of perception through one of the typical sensory modalities that is as specialized channels for transducing external information. To us, this perceptual assumption has led to a confirmation bias in the interpretation of the results.

The results of existing studies have been filtered out of the negative evidence, or data fitting less well with this assumption, while the remaining evidence has been seen as confirming the equivalence between using a sensory substitution device and perceiving through one of the canonical senses. Furthermore, the experimental protocols themselves are built with the perceptual assumption in mind which, in turn, constrains or limits the kind of data that can be gathered. As will be detailed below, our aim was to stress the limits of the perceptual models and the perspectives that can be opened by alternative models.

We first discussed the dominance versus deference debate by having recourse to the criteria that have been used for the taxonomy of our sensory modalities [START_REF] Auvray | Perception with compensatory devices. From sensory substitution to sensorimotor extension[END_REF]. These criteria involve sensory organ, stimuli, properties, qualitative experience, behavioural equivalence, dedication, and sensorimotor equivalence. The reviewed criteria did not allow favouring the dominance or the deference theses, and most of them appeared as a matter of degree or a matter of interpretation. We subsequently argued that the evidence leads to an alternative view, according to which the experience after sensory substitution is a transformation, extension, or augmentation of our capacities rather than being equivalent or reducible to an already existing sensory modality. We developed this view by comparing sensory substitution devices to other "mind enhancing tools" such as pen and paper, sketchpads or calculators. In particular, we built on the transformative view of mind enhancing tools (e.g., [START_REF] Clark | Natural-born cyborgs: Minds, technologies, and the future of human intelligence[END_REF]Menary, 2006) according to which they do transform cognition in a qualitative way. In this sense, these tools not only facilitate established cognitive processes, they can also allow for the appearance of novel cognitive operations, which simply would have been impossible without them.

This view was subsequently refined to include the cognitive processes at stake (see [START_REF] Deroy | Reading the world through sensory substitution devices[END_REF][START_REF] Jacobson | 2 0 1 4 ) . App helps the blind "see" with their ears[END_REF]. In particular, we argued that learning to use a sensory substitution device should not be thought of as occurring horizontally. Experience with sensory substitution devices is built up from existing sensory modalities and this relation is of interdependence or crafting. We used an analogy with dual-route models of reading (e.g., [START_REF] Coltheart | Serial processing in reading aloud: evidence for dual-route models of reading[END_REF], according to which, learning to use a sensory substitution device is no longer to be thought of as being merely a matter of perceptual learning or adaptation, but as the building of a parallel access to cognitive and spatial representations that get grafted onto some pre-existing perceptual-cognitive route. To summarize, sensory substitution is treated here as involving both perceptual and cognitive processes, which take into account integration of the novel information with the existing perceptual-semantic route.

While developing this view, it appeared necessary to take into consideration alternative views on sensory substitution and in particular the claims that long-term use of sensory substitution devices may induce forms of synaesthesia in practised users (e.g., [START_REF] Proulx | Synthetic synaesthesia and sensory substitution[END_REF][START_REF] Ward | Visual experiences in the blind induced by an auditory sensory substitution device[END_REF][START_REF] Ward | Sensory substitution as an artificially acquired synaesthesia[END_REF]. We proposed to clarify the debate by dissociating the substituted information from the associated phenomenology and to verify for each, if they fulfil the criteria used to define congenital synaesthesia (i.e., inducer-concurrent pairing, idiosyncrasy, automaticity of the process, consistency over time). Our analysis highlighted that comparing the two is not straightforward. Indeed, defending SSD-use as being synesthetic involves giving an account of why one or several criteria to define synesthesia can be loosened in some cases without weakening the understanding and definitions given to congenital synesthesia. In addition, our theoretical analyses suggest that whatever the criteria, experience with a sensory substitution device appears to be closer to cross-modal correspondences than to synaesthesia [START_REF] Auvray | Patrolling the boundaries of synaethesia: A critical appraisal of transient and artificially-acquired forms of synaesthetic experiences[END_REF].

Finally, we built on the vertical integration model in order to investigate the predictions that can be made from this model [START_REF] Arnold | Individual differences in sensory substitution[END_REF]. In particular, the vertical integration model involves the idea that, at the perceptual level, performance and experience with the device will depend on each person's abilities. Secondly, if the use of sensory substitution devices is both perceptual and cognitive, then this leaves room for perceptual strategies that will differ depending on people's specificities and cognitive style. In other words, performance and experience with the device will then be done with different weights attributed to each of the sensory modalities. These weights will depend on people's individual capacities, perceptual preferences, and cognitive styles. Note that these weights might subsequently vary depending on expertise, mastery of the device, and type of task. For example, a musician might be able to perform auditory analyses that non-musicians would not, consequently giving more weight to auditory processes, and possibly having a predominant auditory experience when using the device.

In order to start and behaviourally investigate the vertical integration hypothesis, we conducted an experiment with the visual-to-auditory conversion device The vOICe [START_REF] Meijer | An experimental system for auditory image representations[END_REF], which translates visual images into soundscapes. Before and after training, participants were tested to see whether auditory stimuli would spontaneously evoke visual images (Pesnot-Lerousseau, Arnold, & Auvray, personal communication). This stoop-like paradigm [START_REF] Stroop | Studies of interference in serial verbal reactions[END_REF] consisted in a sound recognition task combined with a simultaneous presentation of visual distractors. The sounds corresponded to the auditory conversion of visual lines with The vOICe. Visual distractors, presented simultaneously, could have either the same orientation as the sound or a different one. In addition, we measured participants' auditory abilities and performance with the device to see if they correlate. Our results revealed a stroop-like effect only after training, suggesting that people visualize auditory stimuli. In addition, participants' performance during training for localisation and recognition tasks as well as their associated phenomenologies depended on their auditory abilities.

Overall, these results suggest that the plasticity at stake in sensory substitution is complex, and based on a multisensory architecture involving both visual and auditory processes. They are in line with the vertical integration thesis model (Arnold et al., 2017).

These results are also in line with the complementary metamodal/ supramodal view of sensory substitution processing [START_REF] Cecchetti | Are supramodality and cross-modal plasticity the yin and yang of brain development? From blindness to rehabilitation[END_REF][START_REF] Heimler | Origins of task-specific sensoryindependent organization in the visual and auditory brain: neuroscience evidence, open questions and clinical implications[END_REF][START_REF] Proulx | Multisensory perceptual learning and sensory substitution[END_REF][START_REF] Proulx | Other ways of seeing: From behavior to neural mechanisms in the online "visual" control of action with sensory substitution[END_REF] which proposes that the functional plasticity at stake occurs at higher levels, involving supramodal representations of shapes with a spatial integration of visual and auditory stimuli.

More generally, these results highlight that sensory plasticity in humans is a complex phenomenon which depends both on the kind of processes that are involved and on individual specificities. Several questions remain open and are currently under scientific investigation in our lab, in particular the question of whether the interference appears at the visual or at a supramodal level, as well as the influence of visual imagery in the processes.

III. Sensory substitution and learning

An important feature in mastering sensory substitution devices is how easy they are to use and how much training they require on the users' part. For instance, with the TVSS, extensive training is required. Most users are able to explore their environment, approximate objects' positions, and describe their raw shape within a couple of hours. The training period required to reach a more complete level of performance is estimated at around 8 hours with visual-to-tactile devices [START_REF] Kaczmarek | Pattern identification and perceived stimulus quality as a function of stimulation current on a fingertip-scanned electrotactile display[END_REF] and 10 to 15 with visual-to-auditory devices (Auvray et al., 2007-a), and an even a longer time to perform fine-grained tasks, such as recognizing body postures (Striem-Amit & Amedi, 2014) with visual-to-auditory devices.

It is thus crucial to investigate users' learning abilities, to identify the most efficient learning methods and those that are adapted to different users' profile. Another crucial characteristic of learning lies in the ability to generalize, that is, the ability to extend the acquired perceptual abilities to new bodily locations, new stimuli, and new perceptual conditions.

Regarding bodily locations, one important claim of Bach-y-Rita is that, once trained, users of visual-to-tactile sensory substitution devices no longer feel the stimulation on their skin, where it occurs, but they directly attribute the stimulation as resulting from an external object, i.e. located at a distance (Bach-y-Rita & Kercel, 2003). Bach-y-Rita then asserted that, consequent to this externalization process, the tactile stimulator array can be moved from one body surface to another, without loss in spatial localization abilities or other perceptual capacity. This claim, although recurrent, was only based on few users' verbal reports. In order to investigate it with objective methods, participants in our study were trained to recognize tactile letters on one body part (belly, thigh, or shin) and their performance were tested preand post-training on all three body surfaces. Our results revealed that participants' performance (both in terms of accuracy and reaction times) improved, and this improvement was similar for surfaces represented in adjacent (e.g., belly and thigh) and in non-adjacent (e.g., belly and shin) areas of the somatosensory cortex [START_REF] Arnold | Perceptual learning: Tactile letter recognition transfers across body surfaces[END_REF].

This result provides behavioural support for the claim that training in sensory substitution results in a relative independence from the stimulated body surface. These results have implications for the use of sensory substitution devices and vibrotactile systems by visually impaired people. First, they suggest that training on one body surface is beneficial to the entire body. As a consequence, users do not need to undergo an extensive training on all body surfaces. This study also provides better understanding of the learning process, which is a crucial feature for efficient use of tactile devices. It reveals that transfer of learning to other body surfaces occurs within a relatively short time frame (i.e., less than 90 min).

In a subsequent study, we investigated the extent to which learning transfers to novel perceptual conditions and to novel stimuli (Arnold, & Auvray, 2018). The learning protocol consisted in alternating repeated and new lists of tactile alphanumerical stimuli. Our results showed a transfer of learning to novel orientations. In addition, they showed that the ability to generalize to new symbols depend on the number of stimuli in the list and on feature variability. Our results are in line with the reverse hierarchy theory (RHT) of perceptual learning (Ahissar & Hochstein, 2004). According to this theory, the degree of specificity depends on the difficulty of the perceptual task and on the level of cortical processing that is required to perform the task. For a difficult task involving low-level cortical processes, perceptual learning is specific to the characteristics of the task and it does not generalize to new characteristics. On the other hand, for an easier task, involving higher-level processing, perceptual learning is less specific to the low-level characteristics of the task or of the stimuli. This study has applied implications for the design of learning protocols for sensory substitution. In particular, the results suggest that short training sessions with high variability and diversity will facilitate generalization and will allow for a more optimal use of the device in real-life conditions. It should be added that beyond the nature and variability of the stimuli sample, the instructions given to users during training also has an influence on generalization abilities. For instance, in a study by Striem-Amit et al. (2012-a), the participants were requested to describe the entire detailed shape of the image provided by the visual-to-auditory conversion device The vOICe before identifying it. The results showed wide generalization in this condition, in line with reverse hierarchy theory of perceptual learning.

Finally, during learning, there are important individual differences to take into account. For instance, it was found that people with good auditory abilities (Pesnot-Lerousseau et al., personal communication), good musical abilities [START_REF] Haigh | How well do you see what you hear? The acuity of visual-to-auditory sensory substitution[END_REF], or high visuo-spatial abilities [START_REF] Hanneton | Intermodal recoding of a video game: Learning to process signals for motion perception in a pure auditory environment[END_REF] although see [START_REF] Brown | Seeing with sound? Exploring different characteristics of a visual-to-auditory sensory substitution device[END_REF] have better performance when using visual-to-auditory substitution devices. Differences also occur as a function of visual experience. In particular, regarding navigation tasks, two reference frames are used: an egocentric reference frame, based on body coordinates and characterized by a serial aspect, and an allocentric reference frame based on cardinal coordinates. The allocentric reference frame is characterized by a high level of flexibility and it allows reorganization of itineraries such as taking shortcuts or finding alternative routes. The construction of an allocentric reference frame is facilitated by vision as this sensory modality gives access to a simultaneous multiple perception of distant spatial elements. Consequently, sighted, early-blind, and late blind people differ in the adopted reference frame (e.g., see [START_REF] Noordzij | The influence of visual experience on the ability to form spatial mental models based on route and survey descriptions[END_REF][START_REF] Pasqualotto | Visual experience facilitates allocentric spatial representation[END_REF][START_REF] Rieser | Sensitivity to perspective structure while walking without vision[END_REF]. In general, sighted and late-blind participants prefer to adopt an allocentric reference frame, whereas congenitally blind participants prefer to adopt an egocentric one (see [START_REF] Gallay | Navigation assistance for blind pedestrians: Guidelines for the design of devices and implications for spatial cognition[END_REF][START_REF] Pasqualotto | The role of visual experience for the neural basis of spatial cognition[END_REF]Schinazi et al., 2016, for reviews). Differences also occur in the way people plan and perform an itinerary, for which blind and sighted people use different heuristics and procedures [START_REF] Brunet | Strategies and needs of blind pedestrians during urban navigation[END_REF]. In addition, blind participants have been shown to be better than sighted participants at obstacle avoidance when using a sensory substitution device (Kolarik et al., 2016). These results suggest that performance with the device relies on users' individual sensory abilities and that learning protocols will benefit from taking them into account.

IV. Improving the design of sensory substitution devices

One crucial question when designing sensory substitution devices is how best to code visual dimensions into tactile or auditory dimensions. Each category of devices raises questions and in particular, visual-to-auditory conversion devices raise the issue of matching the sensory dimensions of the signal and visual-to-tactile conversion devices raise the question of the reference frame according to which information has to be encoded. Thus, with visual-to-auditory devices, several dimensions of the visual information (most of the time horizontal and vertical dimensions, depth, brightness, and sometimes colour) are coded using several auditory dimensions (most of the time pitch, time scanning, inter-aural differences, loudness, and timber). The question arises as to how to determine the pairings between auditory and visual dimensions. The four main visual-to-auditory devices (e.g., the vOICe, Meijer, 1992; The PSVA, [START_REF] Capelle | A real-time experimental prototype for enhancement of vision rehabilitation using auditory substitution[END_REF]Vibe, Hanneton, Auvray, & Durette, 2010;the EyeMusic, Abboud et al., 2014) have been designed by using the correspondence between direction of pitch and direction of movement (higher-higher; lower-lower). However, no one tested whether this correspondence, which was intuitive for the designers and welldocumented in audiovisual contexts for sighted individuals (see [START_REF] Parise | Audiovisual crossmodal correspondences and sound symbolism: A study using the implicit association test[END_REF][START_REF] Spence | Crossmodal correspondences: A tutorial review[END_REF], was also relevant for blind people.

In order to investigate the relevance of the pitch-elevation correspondence for blind persons, we tested the audio-tactile analogue of this correspondence [START_REF] Deroy | Differentiated audio-tactile correspondences in sighted and blind individuals[END_REF]). An implicit association test was used, in which auditory and tactile stimuli were presented sequentially and associated to different response buttons. Our results crucially showed that the pitch-elevation correspondence exists in sighted people but is absent in both early and late blind people. This results calls for a rethinking of the codes used in sensory substitution and one of our research axes is to investigate more systematically the possible crossmodal correspondences between audition, vision, and touch focusing on the dimensions of the signals that are relevant for sensory substitution. We also investigate the ways in which these correspondences are combined together, as they are, so far, only investigated in isolation.

With visual-to-tactile devices, it is important to take into account the reference frame in which the information is encoded. Indeed, tactile stimulation received on the body surface can be interpreted from a body location (i.e. self-centred perspective) or from an external location (i.e. decentred perspective, e.g., see [START_REF] Sekiyama | Importance of head axes in perception of cutaneous patterns drawn on vertical body surfaces[END_REF][START_REF] Arnold | A unity of the self or a multiplicity of locations? How the graphesthesia task sheds light on the role of spatial perspectives in bodily self-consciousness[END_REF], for a review). These different perspectives can correspond to a mental localization of the tactile stimulation either on the body or on the external space (see figure 2). In order to investigate spatial reference frames, we used a graphesthesia task, consisting of recognizing ambiguous symbols (the letters b, d, p, and q) drawn on the body surface by means of a tactile matrix. The participants' response allows determining the adopted perspective. Take the example of the lowercase letter "b" (from an external perspective) drawn on the participants' stomach. Recognizing the letter "b" requires the participant to take a decentred perspective (i.e., decentred from the participant's position and centred on that of the experimenter).

Recognizing letter "d" requires taking a trunk-self-centred perspective, as if the letter were to be projected forward and "seen" from the participant's position. Recognizing the letter "q" requires taking a head-self-centred perspective, as if the head was bending forward to "see" the letter "q" on the stomach. In addition to investigating the perspectives that are naturally adopted, the graphesthesia task, by alternating imposed self-centred and decentred reference frames, allows investigating the flexibility in changing perspectives.

Figure 2 (figure from [START_REF] Arnold | A unity of the self or a multiplicity of locations? How the graphesthesia task sheds light on the role of spatial perspectives in bodily self-consciousness[END_REF]. Illustration of the different spatial perspectives that can be adopted in the graphesthesia task, with the example of the tactile letter "b" drawn by the experimenter.

Firstly, our studies showed that there is an important individual variability, with 50% of the sighted participants preferring to perceive space from a trunk-centred perspective, 29% from a head-centred perspective and 21% from a decentred perspective [START_REF] Arnold | A unity of the self or a multiplicity of locations? How the graphesthesia task sheds light on the role of spatial perspectives in bodily self-consciousness[END_REF]. This reference frame appeared to be natural and cannot be reduced to a mere cognitive choice [START_REF] Arnold | Taking someone else's spatial perspective: Natural stance or effortful decentring?[END_REF]. Secondly, our studies revealed the influence of vision on the reference frames that were adopted with i) blind people adopting less frequently the decentred perspectives; ii) the (temporary or permanent) lack of vision favouring the head-self-centred perspective, and iii) early-blind people having more difficulties than sighted in switching reference frames (Job et al., personal communication).

Additional studies allowed showing variability as a function of where the stimuli were located on the body surface: more specifically, the head-centred perspective is easier to adopt for surfaces that can be easily looked at with real head movements (Arnold & Auvray, 2017).

Similarly, the adopted perspective varied for stimuli presented on the hand, with differences as a function of the orientation of the hand and differences between hand and palm [START_REF] O'brien | Cognition overrides orientation dependence in tactile viewpoint selection[END_REF]. This suggests that the codings for visual-to-tactile sensory substitution devices might benefit from taking into account the location of the tactile matrix as well as inter-individual differences. We are currently using this paradigm to investigate the mechanisms of distal attribution with visual-to-tactile sensory substitution devices (see O'Brien & Auvray, 2014, for a review on distal attribution). In particular, our aim is to investigate how, with the help of training, users might transition from sensing the tactile stimuli on their body to perceiving the object as being located in front of them, in the 3-D space.

Questions are frequently raised concerning the location of the camera used to explore the scene. For instance, according to sensorimotor theories of perception, the use of a headmounted camera shares more sensorimotor resemblance with vision than the use of a handheld camera and thereby might favour better performance (e.g., O'Regan, 2011). We investigated participants' performance in a localization task with a visual-to-auditory device when the target's position was computed either from the participants' hand of from their head [START_REF] Hanneton | Reaching three-dimensional targets with an audio-motor device[END_REF]. Our results revealed that performance in hand mode was similar to that in head mode, and that improvements were slower in head mode. Additional analyses revealed that performance was less linked to the natural aspect related to sensor location than to the spatial coincidence between the sensor and the body part performing the motor task and to the latter's degrees of freedom. It should be added that different results might be obtained as a function of visual experience. Indeed, sighted and late blind persons might find it easier to explore a scene with the sensors located on the head than early blind persons.

Finally, in sensory substitution, two main trends are possible: either developing generalist devices aiming at compensating for a maximum of lost visual functions, or, conversely, targeting specific perceptual functions (localization, recognition, navigation) that can be impaired in blind people. One hypothesis we raised is that one of the reasons of the under-use of sensory substitution devices lies on the unrealistic promises of a generalist device that would restore the entirety of a deficient sensory modality. By contrast, blind persons more easily use technical devices devoted to a specific function (such as auditory or tactile navigation devices or software to navigate the internet, [START_REF] Deroy | Reading the world through sensory substitution devices[END_REF]. This hypothesis remains to be experimentally tested and is the topic of future studies.

V. General discussion

Although sensory substitution seems a promising technology to compensate visual impairments, as of today, the developed devices are barely used by visually impaired individuals, either because the tools' design is not optimal, or because their use involves too many constraints and cognitive effort. At the applied level, the studies developed in our lab help in the design of sensory substitution devices. Firstly, the learning protocols will benefit from taking into account specific and generalized conditions of learning in order to favour the transfer of learning to novel stimuli and novel perceptual conditions. Secondly, taking into account individual differences, as suggested by the vertical integration hypothesis, will allow optimal appropriation of these devices. For example, we could identify different perceptual strategies associated to different phenomenologies, with some people having more of a visual use of the device and other people having more of an auditory or tactile use. Then the learning protocols could be customized as a function of the different types of use (see also [START_REF] Elli | Is there a future for sensory substitution outside academic laboratories[END_REF]. For people having more auditory experiences, learning could be oriented toward favouring the auditory processes. This can be done by learning to better discriminate auditory intensities and frequencies. For people having more visual experiences, learning could favour tasks requiring visuo-spatial imagery, or tasks designed to better apprehend depth, to learn how to form global images of the objects. Third, the choice of the conversion codes for visual-to-auditory devices will benefit from the identification of the crossmodal correspondences existing in the different target populations. Finally, the design of the devices can be improved by taking into account the reference frames adopted by people (trunkcentred, head-centred, or decentred), for instance by implementing flexible options.

Regarding the conceptual aspects, our studies help making advances in the understanding of the processes involved when using a sensory substitution device. Our results with visual-toauditory devices show that experience takes roots both on the visual and the auditory sensory modalities. Our results with tactile devices show that performance depends on both the task and individual abilities. This suggests that there is room for processes that are more cognitive, and thus more subject to individual variability. These results are in line with the vertical integration hypothesis, according to which sensory substitution devices are vertically integrated on pre-existing capacities that involve cognitive and perceptual processes.

VI. References

Abboud, S., Hanassy, S., Levy-Tzedek, S., [START_REF] Maidenbaum | The "EyeCane", a new electronic travel aid for the blind: Technology, behavior & swift learning[END_REF]. EyeMusic: Introducing a "visual" colorful experience for the blind using auditory sensory substitution. Restorative Neurology and Neuroscience, 32, 247-257. Ahissar, M., & Hochstein, S. (2004). The reverse hierarchy theory of visual perceptual learning. Trends in Cognitive Science, 8, 457-464. Amedi, A., Hofstetter, S., Maidenbaum, S., & Heimler, B. (2017). Task selectivity as a comprehensive principle for brain organization. Trends in Cognitive Sciences, 21, 307-310. Arno, P., De Volder, A. G., Vanlierde, A., Wanet-Defalque, M. C., Streel, E., Robert, A., et al. (2001). Occipital activation by pattern recognition in the early blind using auditory substitution for vision. Neuroimage, 13, 632-645. Arnold, G., & Auvray, M. (2018). Tactile recognition of visual stimuli: Specificity versus generalization of perceptual learning. Vision Research,152,[40][41][42][43][44][45][46][47][48][49][50]

Figure 1 (

 1 Figure 1 (figure from Arnold, Pesnot-Lerousseau, & Auvray, 2017). Three alternative views on the processes involved in sensory substitution, with their specificities at the behavioural, neural, and phenomenological levels. Illustrative examples are given into brackets.