Jérôme Tribollet
email: tribollet@unistra.fr

Dominique Muller

Stephane Roques

Jeremy Bartringer

Thomas Fix

Shallow implanted SiC spin qubits used for sensing an internal spin bath and external YIG spins

Shallow implanted SiC spin qubits used for sensing an

internal spin bath and external YIG spins.

Introduction

It is well known that silicon vacancies (VSi) color centers in silicon carbide (SiC), created far in the bulk by electron 1,2 or proton 3 irradiation, or during growth, 4 are highly quantum coherent electron spin qubits, even at room temperature. Recently, methodologies for single 4H-SiC silicon vacancies spin qubit ODMR (optically detected magnetic resonance) spectroscopy were demonstrated, for both single V1 silicon vacancies 5 and single V2 silicon vacancies, 6 further demonstrating the potential of those SiC spin qubits. The potential of those silicon vacancies color centers spin qubits in 4H-SiC for developping a relevant spin-photon interface was also recently underlined, 5 suggesting the possibility of a futur large scale quantum network, interfacing those spins qubits with photons travelling in optical fibers.

While many things have been demonstrated on bulk Vsi spin qubits, the study of shallow color centers spin qubits in SiC remains to be done. Beyond the fundamental interest, this study is also highly technologically relevant because many proposed spin based SiC quantum devices, like quantum sensors, 4,7 quantum processors 8 and single quantum photon source, 9 require quantum coherent shallow color centers spin qubits, located below the SiC surface, between few nm 4,7 and hundreds of nm, 8,9 depending on the targeted application, as illustrated on Fig. 1. In this field of shallow spin qubits in semiconductors, it is also well known from previous studies performed for example with shallow NV-centers in diamond, 10 that various kinds of additionnal noise and thus additional decoherence exist for color centers spins located nearby the surface of the semiconductor. It is thus reasonable to assume that the same occurs in the SiC semiconductor. SiC has however the advantage over diamond of a more mature SiC semiconductor technology for nanoelectronics and nanophotonics, which could be also an advantage for quantum technologies. [7][8][9] While arrays of shallow VSi color centers have already been created with success by low energy ion implantation in SiC through a mask 11 or using a focused ion beam, 12 almost nothing is known about their intrinsic quantum spin coherence and more broadly about their spin dynamics, near surfaces or interfaces. Only Ramsey and Rabi experiments, performed on shallow silicon vacancies spin ensembles created by ions implantation in SiC, and using an on chip copper wire to bring microwave to the spins, have been performed 13 to date. Very short decay times of the Ramsey and Rabi oscillation were observed, 13 in the range of hundreds of nanoseconds. However, it is well known that the Ramsey decay reflects inhomogeneous broadening, and that the Rabi oscillation damping time also contains many effects, including inhomogeneities of the applied microwave field (important in studies using microwave chip), inhomogeneities of the magnetic parameters of the spin hamiltonian (like distribution of g factor or of the zero field splitting), as well as dipolar couplings when measurements on spin ensembles are performed. 14,15 Thus, nothing about the intrinsic T2 spin coherence time, as usually obtained by Hahn spin echo decay, 2,7,[START_REF] Schweiger | Principles of pulse electron paramagnetic resonance[END_REF] and about T1, the spin lattice relaxation time, as usually obtained by inversion recovery, 2,7,[START_REF] Schweiger | Principles of pulse electron paramagnetic resonance[END_REF] can be extracted from those kind of Ramsey and Rabi measurements on spin ensembles.

With in mind the idea of developping hybrid paramagnetic-ferromagnetic SiC based quantum processors or sensors, as recently proposed, 4,7,8 here we first demonstrate a new methodology for creating shallow VSi spin qubits located at a controlled nanoscale distance below the SiC surface by low energy ion implantation through a sacrificial SiO 2 layer, and then, we demonstrate by various magnetic resonance methods, that our shallow silicon vacancies spin qubits are 1/ coupled to an electronic spin bath, 2/ can be also coupled to the stray magnetic field of a nearby YIG ferrimagnetic thin film, and 3/, that despite the interaction with the spin bath, they remain quantum coherent, even at room temperature, which is quite promising for the development of quantum sensors and processors based on shallow Vsi spin qubits in 4H-SiC.

Experiments and Results

Ion implantation technology is particularly well suited to create shallow silicon vacancies in SiC at a controlled nanoscale depth. This is due to the fact that controlling the ions energy allows the control of the average depth <z> of the ions positions in the solid, [START_REF] Ziegler | Nuclear Instruments and Methods in Physics Research section B Beam interaction with Materials and Atoms[END_REF] and also the position of the Figure 1: Drawings showing silicon vacancies spin qubits (blue dots) in SiC in dipolar interaction with the stray field of a YIG nanostructure (in red), and a/, also in dipolar couplings between themselves (blue dots) and eventually also with nuclear spins I = 1 2 (yellow dots), like 29 Si or 13 C, or other electron spins (white squarres), for Quantum Information processing/storage/communication (note that here V2 qubits are few hundreds of nm below SiC surface), and b/, also in dipolar couplings with external paramagnetic molecules (green stars) for external spins Quantum Sensing (note that here V2 qubits are few nm below SiC surface). V2a, V2b, V2c and V2j are assumed to be shallow V2 type silicon vacancies spins qubits in 4H-SiC, with the c axis along x. Boz is the static external magnetic field applied, B1y(t) is the microwave magnetic field applied, with a frequency around 9.5 GHz (X band). ODMR of shallow V2 spins in those quantum devices require excitation of the photoluminescence (exciting laser light with wave vector kex), and detection of the photoluminescence (photoluminescence with wave vector kpl). See also cited references. 4,7,8 vacancies defects created by this implantation. This was for example demonstrated for the creation of arrays of silicon vacancies color centers at <z>= 42 nm, with a longitudinal straggling of 35 nm, using 30 keV C + ions implantation in SiC. 11 While this might be an interesting approach for fabricating a SiC quantum processor using Vsi silicon vacancies spin qubits, this is still a too large distance from the surface for quantum sensing based on spin-spin dipolar couplings. A more recent study investigated the possibility to bring silicon vacancies spin qubits exactly at the surface of SiC using ion implantation in SiC followed by controlled reactive ion etching of SiC. 13 This study confirmed the feasability of creating very shallow silicon vacancies near the surface, but no information about their intrinsic quantum spin coherence properties, depurated from inhomogeneous effects and ensemble effects, could be obtained, such that we cannot conclude whether this approach is detrimental or not to their usefull intrinsic quantum spin coherence properties. 2b) and photoluminescence (see Suppl. Info.).

We then started our magnetic resonance study by demonstrating fiber based ODMR detection of this ensemble of shallow V2 color centers spin qubits at X band, as it is shown on Fig. 3a. This X band ODMR spectrum observed at T=130K under optical pumping and when the magnetic field was applied parallel to the C axis of 4H-SiC, revealed a 50 G splitting between the two lateral EPR transitions associated to the spin S = 3 2 of the V2 silicon vacancies in 4H-SiC. We then performed optical pumping assisted direct detected pulsed electron-electron double resonance experiments at X band (OP-DD-PELDOR) to search for some electron spin bath in interaction with our shallow V2 spin qubits. This OP-DD-PELDOR spectrum, obtained following our previsously demonstrated methodology, 4 is shown on Fig. 3b. Two minima or dip in the spin echo amplitude are observed on the spectrum of Fig. 3b. The main dip at around 9.296 GHZ corresponds to the shallow V2 spins used as spin probes for external spins quantum sensing (V2 EPR transition (+3/2 <-> +1/2) also observed at 3291.6 G on Fig. 3a). The smaller dip at around 9.227 GHZ corresponds to external spins located in the near local environment of the shallow V2 spin probes. It is well known that in 4H-SiC many paramagnetic centers, including carbon related defetcs, exhibit a central EPR line corresponding to a g factor equal or close to g = 2.0028, corresponding here, to the dip at around 9.227 GHz for an applied field fixed at 3291.6 G. The OP-DD-PELDOR spectrum of Fig. 3b thus demonstrates that the microwave drive at the microwave pump frequency of this electronic spin bath at 9.227 GHz reduces the spin coherence and thus the spin echo amplitude of the nearby shallow V2 spin probes observed at the probe microwave frequency of 9.296 GHz.

The precise nature of this electronic spin bath is not clear, but what is clear is that this driven decoherence can be easily suppressed if one avoids to pump with microwave this spin bath. However, this electronic spin bath can also have a passive detrimental effect on the spin coherence of the nearby V2 spins to which it is dipolar coupled, through their thermal fluctuations. However, as we will show it in the next section, it is possible, to some extent, to freeze this spin bath at low temperature such that their impact on the decoherence of the nearby shallow V2 spins could be reduced.

To investigate the passive action of this electron spin bath present nearby the shallow V2 spins, we thus performed Hahn spin echo decay experiments at several temperatures, searching for a spin bath cooling effect visible on the V2 spin coherence time T 2 extracted from such an experiment. The Fig. 4 shows three Hahn spin echo decay curves measured at 297K (RT), 130K and 28K respectivelly, as well as their fit by a stretched exponential, with a characteristic decay time T 2, Hahn and a stretching exponant n Hahn . Such a stretched exponential decay was already observed in the case of NV centers in diamond in interaction with a nearby electronic spin bath. [START_REF] De Lange | [END_REF] Theory also predicts a stretched exponential decay of the Hahn spin echo due to such kind of electronic spin bath, [START_REF] De Lange | [END_REF] whether continuous optical pumping was used or pulsed optical pumping), for example at around 130K, was much longer than the T 2, Hahn (130 K) = 84 µ s, as shown on Fig. 5c and5d. This confirmed that spin lattice relaxation do not participate to the main decoherence process which affects the shallow V2 spins, as expected from the known 2 very long spin lattice relaxation times T 1, dark , which were previously measured for bulk V2 spins.

While cooling the V2 spins and their nearby electron spin bath allows to slightly improve their spin coherence time, it is well known 10 that dynamical decoupling pulsed EPR methods can allow a large increase of the spin coherence time of spin qubits by filtering a large part of the magnetic noise from their environment to which they are submitted, even at a rather high temperature. Thus, we performed a dynamical decoupling study at T = 100 K of the effect of Carr-Purcell-Meiboom-Gill (CPMG) type 10 microwave pulse sequences applied to those shallow V2 spins on their spin coherence time, T 2, cpmg (Fig. 5a and5b). As shown on Fig. 5a performed at X band and RT versus the angle of the applied magnetic field with respect to the <111> axis of YIG, that the FMR rotational pattern was well simulated assuming Bsat=1700 G for the YIG thin film (Fig. 6). Then, we put the two samples in close contact and then looked for a signature of their dipolar magnetic interaction through the dipolar stray field produced by the YIG igure 6: left/ Several Ferromagnetic resonance spectrum (FMR), obtained at X band and RT and at various magnetic field orientation, of a YIG thin film on GGG substrate, which was used in this study. The angle indicated is the one between the applied magnetic field and the <111> direction of YIG, which is also the normal of the sample. An angle of 90 degree corresponds here to the case when B0 and the normal of the YIG film are parallel. right/ Extracted FMR rotational pattern (magnetic resonance field versus angle, dashed dot blue line), as well as its numerical simulation (red dot line) without any free parameter (Bsat= 1700 G and g=2.00 fixed). thin film on the nearby V2 spins. The Fig. 7 shows two V2 spin echo field sweep spectrum recorded in this experimental situation but with two different orientations of the static magnetic field applied with respect to the normal of the two solid samples in contact, as shown on the drawings of Fig. 7.

Note that the normal of the two samples corresponds both to the c axis for 4H-SiC and to <111> for YIG. The detailed analysis of those two V2 spin echo field sweep spectrum (see Suppl. Info.)

shows that in the two orthogonal configuration tested, the paramagnetic resonance lines of the V2 spins are shifted, and that those shift are of opposite sign.

The quantitative analysis of those shift of few Gauss (See Suppl. Info.), by means of standard magnetostatic calculations, suggests that magnetic disks in this 210 nm thick YIG film, having an average diameter close to 60 µ m, can well reproduce the dipolar stray magnetic field sensed by the V2 spins in SiC, which is responsible of their magnetic resonance shift. An open question remains however, which is the interpretation of such magnetic disks of 60 µ m in diameter in a YIG film considered in the fully saturated regime of its magnetization, where no static magnetic domains are expected. We suggest here that the magnetic dipolar couplings between V2 spins and nearby YIG spins combined with the intense resonant microwave drive of V2 spins used in those experiments, can produce some drive of one or few ferrimagnetic spin wave resonance mode of the YIG film. In this picture, the ferrimagnetic magnon coherence length would probably be involved in this experiment. We note that previous studies of spin wave propagation in YIG have shown that the YIG magnon coherence length can reach 31 µ m in YIG (100 nm)/Pt waveguide structures, 20 despite the enhanced damping due to metal Pt. As here we use a YIG film (210 nm) on GGG substrate, with an expected lower spin wave damping, it seems reasonable to assume

Discussion

Let us now discuss the relevance of the shallow implanted V2 spin qubits we successfully fabricated here in the context of planed quantum sensing and quantum computing applications. In our previous theoretial work on the SiC-YIG OD-PELDOR quantum sensor, 7 capable of sensing at nanoscale the electron spin labels of a nearby large target protein or the spin qubits of a nearby large paramagnetic molecular nanocrystal (Fig. 1b), we underlined the need of having a shallow V2 spin probe with a sufficiently long spin coherence time. More precisely, in ODPELDOR, the maximum distance that can be measured between target and probe spins is determined by the maximum dipolar evolution time, such that 20 µ s are necessary to measure a distance of 10 nm, and 60 µ s are necessary for measuring a distance of 15 nm. As the nano-object of interest for SiC-YIG ODPELDOR sensing at nanoscale will have a diameter of 10 nm or more, one immediatly concludes that a shallow V2 spin qubit, located within the first 5 nm below the SiC surface and having a spin coherence time of at least 60 µ s is required. As a long T1 of the dark spins (spin labels or remote qubits) is also necessary, 7 which almost always implies cooling the whole sample at or below 100K, having T 2 (T = 100 K) = 60 µ s for the V2 shallow spin probe is what we need in practice.

Here, we have demonstrated that our shallow silicon vacancies V2 spin qubits are dipolar coupled to an electronic spin bath, which seems localized near the SiC surface considering our first OP-PELDOR and CPMG Dynamical Decoupling (DD) experiments. This spin bath limits the shallow V2 spin coherence time to around T 2 = 84 µs at 130K, without DD, which is however sufficient to perform the planned nanoscale resolution OD-PELDOR experiments applied to structural biology.

We also showed that T 2 can reach around 100 µs at 28K without DD, which offers some further improvement. Extending T 2 up to 220 µs at 100K by CPMG DD has also been demonstrated here, also suggesting that further improvements by DD are possible, even at 100K. It must be also noted that surface passivation or surface capping has not been tested here, and this could also allow futur improvements by eliminating or diluting the surface electronic spin bath which limits T 2 without CPMG DD. It must be also underlined that here we performed spin ensemble measurements, such that T 2 = 84 µs at 130K has to be considered as an average value, and future single shallow V2 spin experiments may reveal some distribution of T 2 values depending on the local surface spin bath concentration experienced by those shallow single V2.

Finally, let us discuss our results in the context of quantum computing with V2 spin qubits introduced by ion implantation in a SiC quantum device. Even simply considering single qubit quantum gates, generally performed using short resonant microwave pulses (a typical Pi pulse in a 3D microwave cavity last 30 ns), one would need at least T 2 ≥ 300 µs to go beyong the T 2 T gate 1 Q ≥ 10 4 threshold previously established for fault tolerant quantum computing. [START_REF] Divincenzo | [END_REF] T 2 = 100 µs at 28K without DD is thus not sufficient for fault tolerant quantum computing with this kind of shallow V2 spins. Extending T 2 up to 220 µs at 100K by CPMG DD has been demonstrated here for our shallow V2 spin qubits, but it is still limited by either surface phonon or by the instantaneous diffusion related to the too high local concentration of such shallow V2 spin qubits created by ion implantation. However, assuming one wishes to perform quantum simulations on a diluted cluster of dipolar coupled V2 spins (or a mixture of V2 and V1 silicon vacancies spin qubits), created by ion implantation at low dose and submitted to the strong dipolar magnetic field gradient produced by a nearby YIG nanostripe, located at an optimal distance of x opt = 150 nm from V2 spin qubits 7,8 (see Fig. 1), then in that case, we see we do not need anymore the very shallow V2 spin qubits used for OD-PELDOR quantum sensing. One just needs here V2 spins located between 100 nm and 200 nm below the SiC surface for quantum computing. In that case, the V2 spins should become strongly isolated from the intrinsic surface noise of SiC, which is detrimental to their T 2 , and also from the noise related to thermal fluctuations of the nearby ferrimagnetic YiG nanostripe. 7,8 If one assumes that at such a large distance from the surface of SiC, the V2 spins have spin coherence properties similar to those previously measured for bulk V2 spins, 2 then one expect to extend the T 2 of such nearly bulk V2 spin qubits up to T 2 , cpmg = 45 m s at 17K using a 10 5 CPMG DD pulse sequence, as it was previously demonstrated at lower magnetic field. 2 It was also deduced by extrapolation that using a 10 7 CPMG DD pulse sequence, one could reach T 2 , cpmg = 300 ms at 17K. 2 Now, considering two V2 electron spins in the V2 cluster separated by a distance of 10 nm, one would need typically a dipolar evolution time of around 20 µ s, as already discussed above in the ODPELDOR quantum sensing context, to perform a two qubit quantum gate, such that one would need T 2 ≥ 200 ms to go beyong the T 2 T gate 2 Q ≥ 10 4 threshold requiered for fault tolerant quantum computing with such a diluted cluster of V2 spins. Thus, using a ion implanted cluster of nearly bulk V2 spins located few hundreds of nanometers below the SiC surface, using intensive dynamical decoupling microwave pulse sequences below 17 K, using the strong magnetic field gradient produced by a nearby YiG ferrimagnetic nanostripe (between 0.1 G/nm and 0.5 G/nm), 7,8 and using resonant selective optical and microwave manipulations 6 of the various V2 spin qubits, it seems feasible to perform fault tolerant quantum computing at X band (10 GHz) using an hybrid SiC-YIG quantum device, such as the one shown on Fig. 1a. Adding one or few V1 silicon vacancies (or few other SiC color centers more appropriate for quantum communication) to this V2 cluster of spin qubits would also offer interesting possibilities for an optical fiber based spin-photon interface 5 compatible with the proposed experimental approach, 7 and which could be usefull for extending the scalability of such an intermediate-scale fault-tolerant hybrid SiC-YIG quantum computing approach. 7,8 As a last remark, we note that diluted non-zero nuclear spins in the SiC device, like those of 29 Si or 13 C, present from growth or introduced by ion implantation nearby the cluster of V2 spin qubits, could also be used as a quantum ressource, 5 both for long term storage of quantum states, and for extending the scalability of such an intermediate-scale fault-tolerant hybrid SiC-YIG quantum computer without using the spin-photon interface.

Conclusion

In conclusion, here we have demonstrated i/ a new methodology for creating shallow VSi spin qubits located at nanoscale distance below the SiC surface by low energy ion implantation through a sacrificial SiO 2 layer, ii/ that those shallow Vsi spin qubits are dipolar coupled to an electronic spin bath, probably localized near or at the surface, analysing Hahn echo decay, dynamical decoupling (DD), and OP-PELDOR experiments, iii/ that their coherence time increase with cooling the spin bath (from 55µs at 297K, to 84µs at 130K, and to 107µs at 28K), and that it can be further extended to 220µs at 100K by DD. At temperatures below 130K, with or without DD, the spin coherence time of those shallow V2 spin probes is thus clearly sufficient for OD-PELDOR quantum sensing applications. Finally, iv/ we demonstrated the shift of the shallow V2 spin qubits magnetic resonance induced by the stray field of a nearby YIG film. This demonstrates external YIG spins sensing by V2 spins in SiC. This work thus constitutes a promising step towards the development of the recently proposed SiC-YIG hybrid quantum devices, for both nanoscale ODPELDOR quantum sensing and for spin based fault tolerant quantum computing technologies, which have both the advantage that they could be fiber integrated to a state of art commercially available pulsed EPR spectrometer, offering a wide access to those intermediate scale quantum technologies.

Supplementary Information

Details on the fabrication of shallow silicon vacancies.

First, we start with a high purity and semi-insulating commercial 4H-SiC wafer. Due to growth, this substrate already contains many bulk defects, including the silicon vacancies defects we are interested in here. As it is well known that those silicon vacancies spin qubits color centers can be removed by a high temperature annealing typically above 800 • C, we started by a long 1100 • C thermal annealing under argon gaz of this wafer. As it is shown on Fig. 2a, a cw EPR (electron paramagnetic resonance) study of this annealing process, called the Reset process, was performed at room temperature under optical pumping. It is clearly seen on Fig. 2a that after 8 days of such an annealing, the photo-EPR signal of V2 type silicon vacancies at X band (around 9.7 GHz) was no more detected. Using other reference pieces of this wafer, and using profilometry and ellipsometry experiments (not shown), we determined the oxidation rate of 4H-SiC by thermal oxidation under pure Oxygen at 1100 • C, as well as the chemical etching rate of the resulting SiO 2 layer by a diluted solution of HF. In our experimental conditions, we found an etching rate close to 63 nm per minute, thus of roughly 1 nm per second. Of course, slower or faster etching rates of SiO 2 on SiC could be designed, depending on the HF solution concentration. Controlling the 4H-SiC oxidation rate and the SiO2 chemical etching rate, we fabricated a 74 nm oxide layer on our Reset and oxidized 4H-SiC wafer, which was then used as a sacrificial layer for the subsequent ion implantation process. SRIM simulation indicated that for such a system, SiO 2 (74 nm)/4H-SiC(infinite), C + ions having an energy of around 23 keV would produce a maximum of silicon vacancies near the SiO 2 /4H-SiC interface. Thus, 23 keV C + ions were implanted through this 74 nm oxide layer at a dose of 2 10 13 cm -2 . The SiO2 was then removed from the implanted 4H-SiC sample by a full HF etching, producing a nearly half gaussian distribution of silicon vacancies below the SiC surface, with a maximum at the surface and a half width of around 25 nm, according to SRIM simulations (see further). Finally, as we wanted to activate a large enough ensemble of those shallow silicon vacancies created by ion implantation, we then performed a post implantation annealing of 90 minutes at 700 • C under argon gas, in order to optimize the amount of shallow silicon vacancies of V2 type in this implanted 4H-SiC sample. Still using CW photo-EPR, we clearly observed the re-appearance of the silicon vacancies in our 4H-SiC sample as a result of this ion implantation process (see Fig. 2b), as requiered for a full pulsed EPR study of their quantum spin coherence properties. Fig. 8 shows the result of a SRIM numerical simulation of the ion implantation process in 4H-SiC through a sacrificial SiO2 layer, used here to create shallow V2 spins. The Fig. 9 compares the V2 infrared photoluminescence spectrum of the 8 days annealed 4H-SiC reference sample and the one of the fully processed and ion implanted 4H-SiC sample studied here in details.

All the magnetic resonance experiments presented here were performed on a commercial ELEXYS E580 pulsed EPR spectrometer from BRUKER operating at X band (9.3 -9.7 GHz). This pulsed EPR spectrometer was interfaced by means of an optical fiber to a standard external photolminescence setup, allowing both laser light excitation at 785 nm and photoluminescence collection and detection, following previously published methodologies for fiber based OP-pulsed EPR, OP-PELDOR and ODMR. 4,7 Details on the analysis of CPMG DD experiments on the shallow V2 spins.

Following the previously described method used for shallow NV centers in diamond, 10 we extracted T 2, cpmg from a stretched exponential fit ( expt T 2, cpmg α ) of the echo decay under CPMG sequence. As shown on Fig. 5a, under application of CPMG dynamical decoupling pulse sequence involving N pulses Pi pulses, with N pulses = 1 , 2 , 3 , 6 , 10, we clearly observed an increase of the T 2, cpmg spin coherence time of the shallow V2 spins (respectively, T 2, cpmg in µ s and α were found to be: (89,1.86), (111,1.79), (136,2.06), (197,1.99), (224,2.28)). To further investigate the nature of the noise filtering effect of this CPMG pulse sequence on the electronic spin bath nearby the shallow V2 spins, we plotted on Fig. 5b, T 2, cpmg as a function of N pulses , the number of Pi pulses in the CPMG sequence. We observed a saturation effect with respect to N pulses , starting at a low value of N pulses . This effect was previously observed for isolated shallow NV centers in diamond. 10 In this previous study on isolated shallow NV centers, the data were fitted by a func-

tion of the type T 2, cpmg N pulses , N sat , k , T 2, 1p = T 2, 1p N k sat + N k pulses -N k sat e - N pulses N sat
. For shallow NV centers in diamond located 20 nm below the surface, the fit reported gave the parameter k = 0.53, close to the k = 2/3 expected for a simple lorentzian spin bath, 10 while for very shallow NV centers in diamond (2 or 3 nm below the surface), the fit reported gave the parameter k in the range [0.30 , 0.48]. 10 Concerning the parameter N sat found for shallow NV centers in diamond, it was found in the range [13 , 200], 10 depending on the depth and surface properties of the diamond surface. Here, the fit of our CPMG results at T=100K on shallow V2 spins in 4H-SiC provided the parameters: N sat = 17.38, k = 0.44 +/-0.1, T 2, 1p = 73360 n s, and thus an optimal shallow V2 spin coherence time in SiC with our CPMG noise filtering sequence of T 2, cpmg ∞ = 258 µ s, which can be reached with a good approximation using N pulses ≥≥ N sat = 17.

The value k = 0.44 +/-0.1 that we found is close to the values observed for isolated shallow NV centers. This is somehow expected here because we performed CPMG experiments on V2 spins ensemble, distributed according to SRIM after C+ ion implantation, mainly between 0 nm and 25 nm below the SiC surface. This value of k = 0.44 +/-0.1 is however closer to the values found for very shallow NV centers in diamond 10 which were more exposed to the surface noise, which was considered as a 2D surface spin bath with a correlation time at room temperature of around τ c (RT ) = 11 µ s. As here, our V2 spin distribution is expected to be roughly a half gaussian with maximum at the SiC surface, this seems reasonable. This similarity in the k factor value also suggests that in our case the surface noise is also due to an electronic spin bath, as already suggested by our PELDOR experiments (Fig. 3b) and Hahn echo decay experiments versus temperature (Fig. 4).

Note that our CPMG experiments were performed at a fixed delay τ = 7 µ s between the Pi pulses, corresponding to a CPMG filter function centered at around f 0 = 1 2 τ = 71 kHz. With N pulses = 10 , the spectral bandwidth of this CPMG filter is of around 7 kHz. Here we found a rapid saturation of T 2, cpmg with the number of Pi pulses. This is also somehow expected because by cooling our 4H-SiC sample at T=100K, the spin bath is also cooled and thus its correlation time becomes longer, typically on the order of the spin lattice relaxation time of the spin specy that constitute the surface spin bath at this temperature. Assuming that at 100K, the surface spin bath has a correlation time 1 + (ω τ c ) 2 (∆ being the spin qubit -spin bath coupling in this model), 10 then we see that our CPMG filter at f 0 = 1 2 τ = 71 kHz with N=10 removes a large part of this noise. As the CPMG filter becomes narrower and narrower when the number of Pi pulses increase, this could explains why T 2, cpmg saturates rapidly with the number of Pi pulses applied in our experimental conditions.

τ c (100 K) = 1 m s (thus f noise cuto f f = 1 τ c = 1
The remaining question is what is the fundamental decoherence process which remains in our CPMG experiments at T=100K and which is responsible for the ultimate value T 2, cpmg ∞ = 258 µ s.

Here we suggest two possibilities. Either, like for shallow NV centers in diamond, 10 another noise contribution has to be considered which is related to surface phonon in SiC and which would have a spectral density of noise with a frequency cutoff located at a much higher frequency, like around 10 MHz as it was found for shallow NV centers in diamond. 10 Our CPMG noise filter at f 0 = 1 2 τ = 71 kHz with N=10 could thus not remove efficiently this high frequency noise, which would explain T 2, cpmg ∞ = 258 µ s. The other possibility, is possible in our study but which was not possible in the previous study of shallow NV centers, is that T 2, cpmg ∞ = 258 µ s is in fact limited by the instantaneous diffusion decoherence process [START_REF] Schweiger | Principles of pulse electron paramagnetic resonance[END_REF] which exist when spin ensemble are studied and which can not be removed by CPMG dynamical decoupling methods. Thus, the ultimate spin coherence time in our sample for the shallow V2 spins would be T 2, cpmg ∞ = T ID = 258 µ s. To decide between those two possible explanations of T 2, cpmg ∞ = 258 µ s, one needs to perform a set of similar CPMG noise spectroscopy experiments with various CPMG filter at various filter frequencies, with various bandwidth, eventually at various temperature, and on various samples with various doses of C+ ions implanted below the SiC surface. This is beyond the scope of this study and this is let for a future work. Detailed analysis of the two shift of opposite sign observed on the V2 magnetic resonance lines when placing a YIG thin film into contact with our implanted SiC sample.

The first field direction applied was perpendicular to the normal of the two solid samples, SiC and YIG (Fig. 7 top spectrum), and the second one was parallel to this normal (Fig. 7 bottom spectrum). 25 Gauss, centered around the field resonance value corresponding to g = 2.0028 at the fixed mi-crowave frequency used. For a magnetic field applied parallel to the c axis of 4H-SiC, one expects, without YIG, two V2 EPR lines splittted by 50 Gauss, centered around the field resonance value corresponding to g = 2.0028 at the fixed microwave frequency used. We clearly observe on the Fig. 7 top spectrum two V2 EPR lines splittted by 25 Gauss as expected in this configuration, but not centered around a field resonance value corresponding to g = 2.0028 at the fixed microwave frequency used, but at a higher magnetic field value, corresponding to a shift of around + 2.5 G.

This shift of the two EPR lines towards higher magnetic field values can be explained if one considers that a dipolar stray magnetic field produced by the YIG magnetic film is sensed by the shallow V2 spins and that it has the same direction as the one of the externally applied magnetic field, but is of opposite sens. This is qualitatively what one expects in this first experimental configuration, as schematically explained by the drawing nearby the Fig. 7 top spectrum. We also clearly observe on the Fig. 7 bottom spectrum two V2 EPR lines splittted by 50 Gauss as expected in this second configuration, but not centered around a field resonance value corresponding to g = 2.0028 at the fixed microwave frequency used, but at a lower magnetic field value, corresponding to a shift of around -4.4 G. This shift of the two EPR lines towards lower magnetic field values can be explained again, if one considers that a dipolar stray magnetic field produced by the YIG magnetic film is sensed by the shallow V2 spins and that it has the same direction as the one of the externally applied magnetic field (along the c axis of SiC, which is also the <111> axis of YIG) and also the same sens. This is qualitatively what one expects in this second experimental configuration, as schematically explained by the drawing nearby the Fig. 7 bottom spectrum.

One question remains which concerns the microscopic origin of this dipolar stray magnetic field sensed by the V2 spins in SiC, located below the YIG thin film, which is related to the quantitative analysis of the observed shift in the V2 magnetic resonance position. Indeed, for a uniformly magnetized thin film, with static magnetic domains of infinite dimension, one would expect no dipolar stray magnetic field which could be sensed by the V2 spins in SiC located nearby the YIG film. However, if one makes the hypothesis that we have a typical magnetic length of 60 µ m involved in this experiment (see text for discussion of its origin), then standard magnetostatic cal-culations (not shown) allow to explain those two shift of opposite sens, simply assuming magnetic squares (or disk) exist into the YIG thin film, with the dimension of one edge of the square being a edge = 60 µ m, assuming a film thickness of 210 n m, and assuming a saturation magnetization of this YIG film of B sat = 1700 G, as confirmed by our YIG film FMR experiments (Fig. 6). More precisely, the calculations show that one expect a dipolar stray magnetic field induced shift of around +2.5 G for the case where V2 spins are located anywhere within the first 6 µ m below the SiC surface and at the vertical of the center of the magnetic square considered, and when the magnetic field was applied perpendicular to the normal of the two solid samples. Calculations also show that one expects a dipolar stray magnetic field induced shift of -5 G for the case were V2 spins are located anywhere within the first 6 µ m below the SiC surface and at the vertical of the center of the magnetic square considered, and when the magnetic field was applied parallel to the normal of the two solid samples. The magnetostatic calculations are thus in good quantitative agreement with the experimentally observed shift.

Contributions

JT proposed the study, performed magnetic resonance experiments and analysed them, DM and YLG designed and performed ion implantation of SiC, SR performed the SiC oxydation, SiO2 chemical etching, various SiC processing and profilometry, TF performed various ellipsometry and AFM measurements, JB performed various micro-Photoluminescence measurements. All authors contributed to the manuscript.

(nm)

Figure 9: Infrared micro-photoluminescence spectrum of the 8 days annealed 4H-SiC reference sample (in blue) and the one of the fully processed and ion implanted 4H-SiC sample studied here in details (in red). Spectrum obtained on a micro-Raman spectrometer at RT (300K), objective *100, NA=0.9, Plaser= 90mW at 532 nm, Tinteg= 60sec.

Figure 3 :→

 3 Figure 3: a/ ODMR spectrum of shallow V2 spins of the fully processed ion implanted 4H-SiC sample at T=130K, X band, Plaser= 40 mW at 785 nm, Pi pulse train and continuous optical pumping used; b/ OP-DD-PELDOR spectrum of shallow V2 spins of the fully processed ion implanted 4H-SiC sample at 130K, Plaser= 40 mW at 785 nm.

Figure 4 :

 4 Figure4: Three Hahn echo decay curves of the shallow V2 spins of the fully processed ion implanted 4H-SiC sample recorded at various temperature and at X band (f=9.3 GHz), with B0 parallel to c axis of 4h-SiC, with Plaser= 45 mW at 785 nm, echo recorded on the low field EPR line of V2 spins, using two steps phase cycling; from top to bottom: T= 297 K, 130 K, 28 K.

T 2 ,Figure 5 :

 25 Figure5: a/ CPMG dynamical decoupling echo decay curves at T= 100 K of the shallow V2 spins of the fully processed ion implanted 4H-SiC sample recorded for Npulses= 1,2,3,6,10, at X band (f=9.3 GHz), with B0 set at an angle of 20 degree with respect to the c axis of 4H-SiC, which is the normal of the sample; Plaser= 43 mW at 785 nm; 7 µ s delay between successive Pi pulse used in the CPMG sequence; echo recorded on the low field EPR line of V2 spins, using two steps phase cycling; b/ Spin coherence time under CPMG DD, T 2, cpmg , as extracted from a stretched exponential fit of the CPMG echo decay curves shown on a/, and presented as a function of the number of Pi pulses in the CPMG DD sequence. T 2, cpmg is noted here T dse because it is due to spectral diffusion induced by an electronic spin bath near the V2 spins. c/ and d/ Spin lattice relaxation time, respectively noted T 1, bright and T 1, dark , depending whether continuous optical pumping was used or pulsed optical pumping; we found c/ T 1, bright (130 K) = 814 µ s and d/ T 1, dark (130 K) = 4.8 m s, with Plaser = 40 mW at 785 nm, echo recorded on the low field EPR line of V2 spins at B0= 3291.6 G, f=9.297 MHz.

Figure 7 :

 7 Figure7: Two V2 spin echo field sweep spectrum recorded at RT, with f=9352 MHz, on the fully processed ion implanted 4H-SiC sample put into contact with a 210 nm thick YIG film on GGG substrate. Two different orientation of the static magnetic field applied with respect to the normal of the two solid samples in contact are presented. The normal of the two samples corresponds both to the c axis for 4H-SiC and to <111> for YIG. Top/ The field direction applied was perpendicular to the normal of the two solid samples and Bottom/ the applied field was parallel to the normal of the two solid samples. The two spectrum reveal shifts of few Gauss of the expected V2 magnetic resonance positions, which are found in opposite sens for those two configuration.

a 2 )

 2 ferrimagnetic magnon coherence length in our sample on the order of 60 µ m. The detailed investigation of this question is beyond the scope of this paper. What is clear however, is that the observed shifts of opposite signs in the two configurations tested can not be explained by the standard spin hamiltonian of V2 spins (H = g µ B → and are thus due to the presence of the nearby YIG film, introducing an additional dipolar coupling hamiltonian between V2 spins and nearby YIG spins. Those experiments thus constitute a demonstration of external YIG spins sensing by means of V2 spins in 4H-SiC, through dipolar magnetic couplings.

  kHz), with an associated spectral density of noise of the form S (ω) = ∆ 2 π τ c

For a magnetic field

  applied perpendicular to the c axis of 4H-SiC, without YIG and just considering the well known spin hamiltonian H = g µ B →

  unit vector along the C axis of 4H-SiC, g = 2.0028 and D = 35 MHz, one expects two V2 EPR lines splittted by

Figure 8 :

 8 Figure 8: SRIM simulation of the ion implantation process of 23 keV C+ ions through a 74.5 nm SiO2 sacrificial layer present on top of the 4H-SiC substrate pre-processed (see text).

  SiO 2 , the energy of the C + ions being chosen, with the help of SRIM simulation (see Suppl. Info.), such that the maximum of silicon vacancies produced occurs near the SiO 2 /SiC interface. As a result, after a simple full HF chemical etching of the oxide layer, we obtain a nearly half gaussian distribution of silicon vacancies below the SiC surface, whose creation can be revealed by CW photo-EPR (see Fig.

	EPR signal (a.u.)	-0.3 -0.2 -0.1 0 0.1	a/	5/ 4/ 3/ 1/ 2/		SiC annealing time
		-0.4
				3430	3440	3450	3460	3470	3480	3490
							B0(G)
	EPR signal (a.u.)	3290 -0.4 -0.2 0 0.2 0.4 b/	3300	3310 C+ implanted SiC	3320	3330	3340	3350
							B0(G)
	new fabrication method (see Suppl. Info. for details) starts by a high temperature annealing of
	the HPSI 4H-SiC substrate at 1100 • C to remove growth induced silicon vacancies (see Fig.2a),
	and then basically consist in implanting low energy C + ions in SiC but through a thin sacrificial
	thermal oxide layer of

Figure

2

: a/ Optical Pumping assisted CW EPR study at RT of the effect of annealing time at 1100 degree C under Argon, on V2 spins in bulk 4H SiC and on other intrinsic defects: 1/ as received bulk 4H-SiC not annealed, 2/ 30 minutes annealed, 3/ 14 h annealed, 4/ 4 days annealed, 5/ 8 days annealed. Laser at 785 nm, P=32 mW; B0 parallel to c axis of 4H-SiC, MD5 cavity, microwave frequency f=9.7 GHz. b/ again CW EPR under OP: comparison between 8 days annealed 4H-SiC sample and the full processesed 4H-SiC sample ion implanted (see text); Laser at 785 nm, P=44 mW; RT, B0 parallel to c axis of 4H-SiC, MS3 cavity, f=9.3 GHz.

Here we investigated a new methodology for creating very shallow Vsi spin qubits in SiC and we performed a detailed investigation of their intrinsic spin quantum coherence properties. The

3280 3290 3300 3310 3320 3330 3340 3350 3360 B0 (G) 0 5 10 ODMR signal (a.u.) 10 7 9.16 9.18 9.2 9.22 9.24 9.26 9.28 9.3 9.32 9.34 pump frequency (GHz) 2 4 6 8 10 DD OP PELDOR signal (a.u.) 10 7 b/ a/ T=130K, f=9.297GHz T=130K, f=9.297GHz

  , under application of CPMG dynamical decoupling pulse sequence involving N pulses Pi pulses, with N pulses = 1 , 2 , 3 , 6 , 10, we clearly observed an increase of the T 2, cpmg spin coherence time of the shallow V2 spins and a rapid saturation of T 2, cpmg with the number of Pi pulses used in the CPMG DD sequence. The detailed analysis of those CPMG DD results (see Suppl. Info.), interpreted in the light of previous results obtained on shallow NV centers,10 suggests that at 100K, our CPMG filter removes a large part of the low frequency noise due to an electron spin bath sensed by the shallow V2 spins, localized near or at

the SiC surface. The saturation value of T 2, cpmg to 258 µ s, extracted from this analysis, reveals another decoherence source not removed by our CPMG filter. We suggest that it is either a high frequency noise (related to some surface phonon in SiC) or an instantaneous diffusion decoherence process

[START_REF] Schweiger | Principles of pulse electron paramagnetic resonance[END_REF]

related to the local concentration of shallow V2 created near the SiC surface. Further CPMG DD studies, performed with various CPMG filters and various SiC samples implanted at various doses are necessary to determine the precise origine of this T 2, cpmg limit.

Finally, as we are interested to build hybrid paramagnetic-ferromagnetic SiC based quantum devices,

4,7,8

particularly hybrid SiC-YiG quantum devices,

4,7

here we present our first experiments in this direction, demonstrating the magnetic interaction between V2 spins in SiC and a nearby ferrimagnetic thin YIG film. In practice we used our 4H-SiC sample with shallow V2 spins and we used a commercial thin film of YIG (insulating ferrimagnetic oxide: Y 3 Fe 5 O 12 , film thickness: 210 nm, normal direction to sample plane: <111>) of high quality, grown by liquid phase epitaxy (LPE) on a GGG substrate. We first checked by Ferromagnetic Resonance (FMR) Experiments

Acknowledgments

The authors thanks Yann Le Gall for his contribution to the ion implantation in this study. The authors thanks the University of Strasbourg and CNRS for the reccurent research fundings.

Competing financial interests

The authors declare that they have no competing financial interests.


Frederic Alexandre
email: frederic.alexandre@loria.fr

Cortical basis of communication: local computation, coordination, attention

Keywords: Computational neurosciences, Communication, Visual attention, Coordination, Model of the cortex

Human communication emerges from cortical processing, known to be implemented on a regular repetitive neuronal substratum. The supposed genericity of cortical processing has elicited a series of modeling works in computational neuroscience that underline the information flows driven by the cortical circuitry. In the minimalist framework underlying the current theories for the embodiment of cognition, such a generic cortical processing is exploited for the coordination of poles of representation, as it is reported in this paper for the case of visual attention. Interestingly, this case emphasize how abstract internal referents are built to conform to memory requirements. This paper proposes that these referents are the basis for communication in humans, which is firstly a coordination and an attentional procedure with regard to their congeners.

Introduction

The cerebral cortex is known to be composed of millions of similar elementary circuits, repeated throughout its surface, the cortical columns [START_REF] Burnod | An adaptive neural network : the cerebral cortex[END_REF][START_REF] Mountcastle | chapter An Organizing Principle for Cerebral Function: The Unit Model and the Distributed System[END_REF][START_REF] Ballard | Cortical connections and parallel processing: Structure and function[END_REF]. A fascinating challenge with the study and modeling of the cortex is to understand how the wide spectrum of functions generated by this ultimate structure in the evolution process can emerge from this repetitive paving. The corresponding approach of modeling in Computational Neuroscience is to consider the cortical column as the adequate level of computation [START_REF] Alexandre | The Cortical Column : A New Processing Unit for Multilayered Networks[END_REF] and to define its functioning and learning rules in such a way that whatever the cortical area or processing pathway we consider, only the nature of the inputs and the size and connectivity scheme of the considered cortical regions will specify its resulting activity.

Three kinds of data from Neuroscience are requested to guide modelers in this domain. At the microscopic level, it is fundamental to be informed about the inner structure of the cortical column, seen as a circuit of a hundred of neurons, including its inputs, outputs and dynamics. At the mesoscopic level, the organization of a network of automata, proposed as models of cortical columns, must be consistent with current knowledge about the main information flows in the brain. Columns must be gathered in cortical areas; cortical areas must be interconnected with a precise connectivity scheme; the cortical processing is also frequently dependent on extra-cortical information flows (including perceptive input and motor output) that have to be defined at this level. At the macroscopic level, behavioral studies are also necessary to figure out what kind of information is processed and how it is manipulated, stored and exploited to interact with the outer world.

Other non bio-inspired theories in machine intelligence are perhaps more intuitionist. They rely on a logic, sequential and structural approach and have a tendency to build symbolic and abstract representations of information (models of the world), whereas the distributed, local, numerical and asynchronous approach in Computational Neuroscience is rather slanted toward the emergence of properties and toward the intensive use of interactions with the real world to build the minimal necessary internal representations. Experiments from psychophysics and other developmental issues are therefore necessary not to follow our misleading intuition.

In this paper, my goal is to explain that current studies modeling cortical processing with distributed simple local computations can be directly used to emulate complex behaviors related to communication. I will report several studies that have been carried out to define the local functioning of a cortical automaton (section 2). Elementary behavioral functions using such local computations will then be presented in section 3. I will refer to them as coordination functions since they allow for the linkage of representational poles in the cortex. Section 4 will report recent developments of a more ambitious study about mechanisms of selective attention. One of the goals of that study is to show that elaborated functions like attention, central in the cognition and often presented as related to consciousness [START_REF] Taylor | Neural networks for consciousness[END_REF], can emerge from the distributed asynchronous computations of local automata and can avoid many representational hypotheses difficult to implement and justify. Similarly, the claim of this paper is that communication capabilities can also emerge from the same distributed asynchronous computations. In section 5, I will argue that an artificial system, endowed with a distributed substratum of computation inspired with the local mechanisms of cortical circuitry presented here, could be able to exhibit some fundamental communication capabilities as observed in evolved living being. Section 6 will conclude on the amount of work that remains to be done to obtain more elaborated communication channels like observed in spoken language.

Principles of local distributed computation

The local circuitry in the cortex has been studied for a long time. Many studies have laid emphasis on the cortical column, seen as the elementary computing block of the cortex [START_REF] Burnod | An adaptive neural network : the cerebral cortex[END_REF][START_REF] Mountcastle | chapter An Organizing Principle for Cerebral Function: The Unit Model and the Distributed System[END_REF][START_REF] Ballard | Cortical connections and parallel processing: Structure and function[END_REF][START_REF] Grossberg | A laminar cortical model for 3d perception of slanted and curved surfaces and of 2d images: development, attention and bistability[END_REF][START_REF] Korner | A model of computation in neocortical architecture[END_REF]. The cortical column is perpendicular to the surface of the cortex and goes through the six layers of the cortex. A very basic and functional description of these layers can be proposed as follows: Layer 4 receives extra-cortical (thalamic) and feedforward cortical input; layers 1, 2 and 3 are cortico-cortical connections; and layers 5 and 6 send feedback in the cortex and projections outside the cortex. Apart from the granular layer 4, all these projections are performed by pyramidal excitatory neurons and other excitatory and inhibitory interneurons achieve the internal logic of the automaton, coupling and uncoupling these layers. The interplay between these information flows is the basis of neural field approaches developed by many authors [START_REF] Wilson | Excitatory and inhibitory interactions in localized populations of model neurons[END_REF][START_REF] Taylor | Neural bubble dynamics in two dimensions[END_REF][START_REF] Amari | Dynamic of pattern formation in lateral-inhibition type neural fields[END_REF][START_REF] Rougier | Dynamic neural field with local inhibition[END_REF]. Others have proposed a cortical automaton including several inputs and outputs and internal learning and functioning rules [START_REF] Grossberg | A laminar cortical model for 3d perception of slanted and curved surfaces and of 2d images: development, attention and bistability[END_REF][START_REF] Alexandre | The Cortical Column : A New Processing Unit for Multilayered Networks[END_REF][START_REF] Korner | A model of computation in neocortical architecture[END_REF].

From an evolutionary perspective, the cortex can be seen as a new evolved loop, added to more primitive perception-action loops [START_REF] Ballard | Cortical connections and parallel processing: Structure and function[END_REF]. In this view, the cortex offers a substratum characterized by modal maps where specific information can be displayed, by associative areas where subtle intermodal dependencies can be expressed and by an original relaxation dynamics [START_REF] Doya | What are the computations of the cerebellum, the basal ganglia and the cerebral cortex?[END_REF]. These powerful properties are obtained from the layered organization of the cortex. They can be described through four principles of information processing, as described in the next subsections and summarized in Table 1.

Thalamic input and feedforward

Thalamic and cortical feedforward integration is certainly the most classical principle of cortical functioning. Cortical columns in sensory areas are known to be selective to specific stimuli and to perform filtering on the incoming perceptive information, from thalamus to primary sensory areas or from primary to secondary sensory areas. Kohonen has popularized this operation with the self-organizing map principle [START_REF] Kohonen | Self-Organization and Associative Memory[END_REF]. It combines adaptive feedforward links conveying thalamic inputs and learning relevant filters with static lateral inhibition implementing a competition between filters. More precise and developmental details have been introduced by Miikkulainen [START_REF] Miikkulainen | Self-organization, plasticity, and low-level visual phenomena in a laterally connected map model of the primary visual cortex[END_REF] and Taylor has proposed a dynamic and distributed version of such a processing, where bubbles of activity are generated and maintained from an initial stimulation [START_REF] Taylor | Neural bubble dynamics in two dimensions[END_REF].

The learning rule proposed by Kohonen highlights the main principles of plasticity related to the thalamic feedforward information flow. The cortex plays a role of reduction of dimensionality from the huge set of possible thalamic inputs to a reduced set of prototypes selected to represent the statistical distribution of the inputs. Prototypical learning (quantization) selects the best representatives. Lateral inhibition ensures their sparseness. The bidimensional nature of the cortex allows for the emergence of a topography where close units are selective to close stimuli [START_REF] Kohonen | Self-Organization and Associative Memory[END_REF].

Lateral propagation of information within an area

Apart from stereotyped bell-shaped (eg with DOG: difference of Gaussians) pattern of connection allowing for competition within population of close columns (and evoked in the previous subsection), lateral connectivity within cortical areas plays an important role in temporal information processing in the cortex [START_REF] Jancke | Imaging cortical correlates of illusion in early visual cortex[END_REF][START_REF] Bringuier | Horizontal propagation of visual activity in the synaptic integration field of area 17 neurons[END_REF]. Events and stimuli in the world have an important temporal dimension and representing only static stimuli is not sufficient. Spatio-temporal self-organization mechanisms have been proposed, which exploit lateral excitatory connectivity in cortical areas [START_REF] Wiemer | The time-organized map algorithm: Extending the self-organizing map to spatiotemporal signals[END_REF]. The principle can be illustrated with the image of drops of water falling on a liquid surface: consider a sequence of events, each event stimulating a cortical unit. For event n, the stimulation of a cortical unit will generate a lateral wave of excitation within the map. This wave will collide with the waves emitted by the cortical units excited by events n-1 and n+1. Cortical units situated at the collision loci of the waves will be able to learn the corresponding co-excitation and consequently the sequence of activation within the map. A bayesian mechanism has been proposed [START_REF] Koechlin | Bayesian inference in populations of cortical neurons: a model of motion integration and segmentation in area mt[END_REF] for the learning of such sequences. It also enables anticipation, with the pre-activation of the next event in the sequence. Its principle relies on a Hebbian learning between the thalamic or feedforward activation of the unit representative of an event and the cortical activation of the unit representative of the preceding event in the sequence.

This mechanism of lateral propagation of excitation is described here as encoding sequences of events but it could have a more general usefulness. This processing principle of the cortex is not yet fully mastered but seems to be a fundamental property to be better understood. For example, the cerebellum shares some structural properties with the cortex (tilled with similar micro-circuits) but does not have such a lateral connectivity [START_REF] Doya | What are the computations of the cerebellum, the basal ganglia and the cerebral cortex?[END_REF]. Its appearance in the cortex could have endowed it with dynamic relaxation properties, allowing for propagation of waves on its surface for the search of solutions to multiple constraints expression [START_REF] Burnod | An adaptive neural network : the cerebral cortex[END_REF].

Cortico-cortical connections

Connections between cortical areas have been studied for two general cases of activity: multi-modal integration and feedback projections. In both cases, the problem is to interconnect two cortical maps representing information of different kinds, either to create a mixed representation of both (multi-modality) or to enable one map to be controled or monitored by the activity of the other (feedback).

A large amount of work has studied multi-modality as well as feedback, most of which is somewhat consistent as far as functioning and learning rules are concerned. The general idea is to advocate for the implementation of a gating effect between maps. Differently from afferent connections having an integrative effect onto cortical units, such cortico-cortical connections will rather have a multiplicative influence onto existing activity in the map: a strong signal will enhance the activity whereas a weak signal will inhibit it. Such a logic has been frequently implemented in sigma-pi units [START_REF] Alexandre | Neurobiological Inspiration for the Architecture and Functioning of Cooperating Neural Networks[END_REF][START_REF] Fix | A computational model of spatial memory anticipation during visual search[END_REF] for which Hebbian learning rules can be easily derived.

Sub-cortical output and feedback

Competition and association between cortical columns yield a pattern of activation in cortical maps that has to be transformed into actions or decisions in the outer world or into a feedback influence onto lower maps. This is the role of deeper layers 5 and 6 of the cortex, particularly in the motor and premotor cortex. Layers 5 and 6 also establish feedback links between hierarchical sensory areas.

In summary

We have presented here some principles of information processing generally considered as responsible for cortical organization and involving the laminar architecture of the cortex. This functional view defines a basic automaton of computation, the cortical column, considered as the crossroad of several information flows in the cortex. Local specialization and coupling and uncoupling in the automaton enhance functional circuits. We now illustrate how elementary behavioral functions exploit these mechanisms.

Coordination

Many models of the cerebral cortex have been illustrated by applications devoted to the discrimination of perceptive stimuli (e.g. visual recognition) and to the orientation of actuators in space (e.g. target reaching). These two kinds of tasks illustrate a fundamental property of the cortex, structured into two pathways [START_REF] Goodale | The objects of action and perception[END_REF]. The parietal axis (where pathway) which associates perceptive and body poles of the cortex. And the temporal axis (what pathway) which associates the perceptive and the limbic poles of the cortex, the latter being known to be the locus of multi-modal episodic memory [START_REF] Squire | Memory and the hippocampus: a synthesis from findings with rats, monkeys, and humans[END_REF] (pathway toward the hippocampus).

Identification and location

Identification and location might appear as rather different tasks. Particularly, imagining that they emerge from the same local logic of computation and that only the nature of the data and the structure of the network specify the task can appear as a rather difficult exercise. Effectively, even if many models are consistent with the general principles mentioned above, their detailed implementation generally makes identification and location models incompatible. This is not acceptable in the framework of the unified theory of cortical processing that this paper tries to promote. I first explain here why the tasks are not so different as they could appear at first sight and then propose a framework of interpretation that could correct some excesses which in my opinion are often made in classical models.

As mentioned by Norman [START_REF] Norman | Two visual systems and two theories of perception[END_REF] and by Goodale and Humphrey [START_REF] Goodale | The objects of action and perception[END_REF], it is important to underline that identification and location tasks have been designed by researchers from different origin and with different goals. Identification is a classical task in statistics and artificial intelligence (e.g. classification, recognition tasks) and the general goal of such a task is to activate only one output unit (the class number) for each possible perceptive input. Location rather refers to geometrical and behavioral aspects and the goal is here to compute, within a population of neurons, transformations from one reference frame to another. Moreover in this latter case, the underlying task is more ecological and compatible with Gibsonian theories [START_REF] Gibson | The Ecological Approach to Visual Perception[END_REF], known to be difficultly compatible with symbolic artificial intelligence promoted by the former domain.

Are these theories and principled approaches only a distorting mirror which hides the similarity of the tasks? The first argument for a positive answer comes from a description of the tasks in terms of information flows. First of all, it must be reminded that parietal and temporal axis can be seen as providing an association between different poles of representation in the cortex. In a more dynamical view, it can be said that they coordinate poles of representation. Basically, the parietal axis performs a coordination between perceptive (visual, auditory) and body representation, whereas the temporal axis performs a coordination between perceptive stimuli and the inner representations that they trigger in the limbic system (attractive vs repellent; love vs hate; etc.). In both cases, learning the coordination corresponds to extract hints that are discriminant in the association between the poles into consideration. Later, this learning can be used to activate a population of neurons to orient the body toward a target or to activate few neurons representative of a class to be recognized, but in both cases, the same kind of distributed network establishing relations between poles of representation is exploited (cf Table 2). This unified view of coordination between poles of representation promotes the principle of purposive perception [START_REF] Goodale | The objects of action and perception[END_REF]: the axes of processing depend on the purpose of the poles to be associated and consequently determine the hints to be extracted in the intermediate representations.

Ballard and colleagues [START_REF] Ballard | Deictic codes for the embodiment of cognition[END_REF] have illustrated such a dual view in a task of identification or location of stimuli. From high-dimensional feature vectors extracted from the image of objects, they first explain how a neuronal distribution of activity can be memorized in internal representations. Then, they underline the similarity of identification and location tasks: Identification corresponds to build a neuronal activation from the current foveal view, to compare it with a large number of memorized internal representations and to select the one best matching the current view. Location corresponds to activate only one internal representation (the object we wish to locate in the scene), to find the place in the visual field with the closest neuronal activation and to return its location. In both cases, the resources are the same but they are transformed by the way they are used.

The situatedness of cognition

The most synthetic way to reconcile identification and location is to remember that the phenomenon we are interested in here, the human cognition, emerges from the interactions of the body with the world. As evoked above, the body can orient toward objects to better perceive and analyze them. The analysis is performed on the basis of physical measurements and more or less elaborated emotional reactions of the body generated by the stimuli. This will elicit other orientation activities of the body (approach and grasping or avoidance). This elementary behavior is made possible by the capacity to coordinate the perceptive representation of the outer world (including the perception of the body itself) with the answer that it generates either in the physical body reference frame (parietal axis) or in the more emotional reference frame linked to the limbic system (temporal axis). In both cases, this capacity of coordination is acquired from experience and interaction with the world. In this perspective, the cortex is seen as a multi-modal device, learning the self-organization of the various frames of representation sent to it by the outer (perception, proprioception) and the inner (emotion, rhythms) world, and also the self-organization of the associative substratum linking the poles of representation. Menard and his colleagues have shown that a self-organization process can also act on such multi-modal information. This process displays information in such a way that it builds in associative areas an intermediate representation between the poles [START_REF] Ménard | Multi-map self-organization for sensorimotor learning: a cortical approach[END_REF].

In the elementary tasks mentioned here (identification and location), only two pathways are considered but the same explanation apply to other more complicated behaviors. Particularly, the frontal lobe of the cortex is known to stand for the motor pole of representation [START_REF] Fuster | The Prefrontal Cortex : Anatomy, Physiology, and Neuropsychology of the Frontal Lobe[END_REF]. Thanks to its links with the basal ganglia and the posterior part of the cortex, the prefrontal cortex associates the consequences of motor action with sensory information from the inner and outer world, self-organized in the posterior part of the cortex as mentioned above, and combines this information with goal oriented rewards computed in the basal ganglia to decide the temporal organization of behavior which best satisfies the constraints. This aspect is out of the scope of this paper and will be only evoked in the concluding part. Nevertheless, it is worth mentioning that the present approach also claims that units in the prefrontal cortex obey the same rules of local computation and global organization in poles of representation, as in the posterior cortex.

Moreover, the theory of the situatedness of cognition gives other principles about information representation which are of high interest to understand which relations and coordinations are learned in the cortex. Opposite to intellectualist symbolic approaches and their abstract, complex and hierarchical representations, the situatedness of cognition proposes to minimize representational contents [START_REF] O'regan | A sensorimotor account of vision and visual consciousness[END_REF] and privileges simple strategies, more directly coupling perception and action [START_REF] Brooks | Intelligence without representatio[END_REF] and more efficient to react quickly in the changing environment.

A key aspect of this theory of intelligence is the Gibsonian notion of affordance [START_REF] Gibson | The Ecological Approach to Visual Perception[END_REF]: perception is not a passive process and, depending on the current task, objects are discriminated as possible tools that could be used to act in the environment. Whereas a scene full of details can be memorized in very different and costly ways, a task-dependent description is a very economical way that implies minimal storage requirements. Hence, remembering becomes a constructive process.

Ballard and his colleagues [START_REF] Ballard | Deictic codes for the embodiment of cognition[END_REF] have done a decisive step to operationalize this concept. From the idea that the orientation of the body is important for cognition, they propose that eye movements, performed at an average rate of one third of a second, are the right level of description of the computational interface between neuronal and behavioral processes: the embodiment level. They propose to consider eye fixation as a deictic pointer (with the same meaning and usefulness as in computer science) that binds variables extracted from the environment. In this framework, the meaning of the pointer corresponds to task-relevant components of the object being fixated. It must be underlined how, as in computer science, the pointer mechanism is clever and economical: the pointer can be manipulated internally for complex operations. For the same operation to be performed on different objects, it is not necessary to store all the details in memory but just to change the referent of the pointer. Also, with such a deictic strategy, the organism can keep track of relevant targets in the environment by only storing the movement of the eye necessary to foveate it. We do not memorize details of the object but we know which eye movement to perform to get them: The world itself is considered as an external memory.

All these principles can possibly be applied to coordination tasks (identi-fication and location) but are not necessary for modelers working at the level of only one processing pathway: it is still possible for them to be influenced by a more symbolic approach and to build a fully detailed representation of information; the system is generally effective and only its biological plausibility can be discussed. The same cannot be said about more complex tasks, where several processing pathways and poles of representation are implicated. My opinion is that such systems are difficult to build and master with a too rich representation of information just because this approach is not sustainable, as it is demonstrated at this level of complexity. In the next section, I present some experiments, based on the embodiment of cognition, which successfully implement complex tasks with a minimal representation.

Attention

We now consider more complex tasks, involving several frames of representation and, in the framework of the above theory, several pointers to index the world. In this section, among the variety of body orienting movements, real and virtual eye movements only are considered: fixation and attention, seen as mechanical and neural deictic devices.

Concerning fixation, Ballard and colleagues [START_REF] Ballard | Deictic codes for the embodiment of cognition[END_REF] have deeply studied an experimental procedure, in which a subject has at his disposal a set of colored blocks to copy a model onto a workspace. Behavioral studies reveal the strategy generally chosen by subjects, faithful to the minimal internal memory principle and described by a set of eye movements. One typical iteration of the block copying task can be described as follows: the eye goes to the model to acquire the color of the next block to be copied (identification), goes to the set of blocks to find one with the same color (location), the hand picks up the foveated block while the eye goes back to the model to acquire the position of the considered block; the hand with the block moves toward the workspace and drops the block at the place where, meanwhile, the eye has indicated the similar place as in the model. It can be remarked that this multiple fixation strategy draws minimally on internal memory by binding objects to variables, at the cost of a longer execution time. This behavioral study is directly linked to several computational models, related to computer vision and reinforcement learning but, as far as I know, not to connectionist approaches. I now present a connectionist model that we are currently building, based on such a unified theory of cortical processing. This model aims at implementing covert and overt visual attention, as a way to internally and externally manage eye movements and their related deictic properties.

Local functioning rules

The model is composed of a set of two dimensional discrete neural fields, which are direct extensions of the model proposed by Amari [START_REF] Amari | Dynamic of pattern formation in lateral-inhibition type neural fields[END_REF], in 2D and with a discrete implementation of topological maps. Each of the maps corresponds to a cortical area, composed of units corresponding to cortical automata, as presented above. As described below and sketched in Figure 1, a set of maps is implemented to represent two information flows, the Where and the What pathways, receiving external information from a visual input (retina) and able to internally focus on a target and to produce camera movements to center a desired target in the middle of the retina (fovea).

As a consequence, at the level of the cortical automaton, several kinds of input and output have to be specified. The feedforward flow between areas and the lateral flow within areas are integrated with weighted summations. Cortico-cortical connections between areas are implemented by a multiplicative rule (weighted sum of the product of activity of afferent neurons). The weighting functions are chosen as a Gaussian for the lateral flows and as a difference of Gaussians for the feedforward flows. They are constant for the cortico-cortical connections. At the moment, these weights are fixed from biological data [START_REF] Miikkulainen | Self-organization, plasticity, and low-level visual phenomena in a laterally connected map model of the primary visual cortex[END_REF]; current work aims at defining learning rules to adapt them.

Emerging properties

From these local uniform functioning rules, several interesting properties emerge from a structured network, depending only on the connectivity.

Saliency: The feedforward weights can be chosen in such a way that, in a topological map receiving an external visual input, each unit responds best to a stimulus in a given receptive field and with a given orientation or color. This allows to implement Feature maps (cf. Figure 1) acting as topological filters on these features. These elementary feature maps converge onto the Saliency map which displays a multimodal representation. In all these maps, the Gaussians are narrow and several stimuli can be represented. Gaussians are larger in the Focus map that receives information from the Saliency map. As a consequence, a stronger competition takes place in the Focus map and only one blob of activity can survive. This competition can be biased by feedback information from one map in the What axis (Feature processing axis in Figure 1) which can specify one feature of the desired target (eg: a red pattern or orientation on the left). Conversely, the Focus map can bias the What axis in order to display the identity of the pattern that win the competition in the Focus map (eg: red pattern oriented on the left).

Inhibition of return: If the goal of the task is to successively focus onto each pattern with specified features, a mechanism is desired to prevent the system from going several times to the same place. This mechanism is known as the inhibition of return [START_REF] Posner | Components of visual orienting[END_REF] and is implemented with a couple of maps called Working memory in Figure 1 and described in [START_REF] Vitay | A distributed model of spatial visual attention[END_REF]. One map in the Working memory receives topological (one to one) excitations from the Focus and the Saliency maps and sends reciprocal excitatory topological connections to another similar map that helps to maintain excitation: both external inputs are necessary to create excitation but only one (from the Saliency map) is sufficient to maintain it. This cumulative mechanism creates a dynamical memory of the locations that have been explored. When the focus of attention has to change ('switch' order in the covert mode), this memory will inhibit the Focus map and force it to look for another location.

Anticipation: A camera movement completly modifies the visual reference frame and all that have been built in the working memory could be lost. To avoid this perturbating phenomenon, a Memory anticipation map is built (cf. Figure 1). It is computed as a convolution product of the Working memory and the Focus map. Just before a movement is triggered, the Focus map gives the information of the next location that will be attended. Thanks to the multiplicative effect of the Memory anticipation map, the activity of the Working memory is translated by the movement vector represented in the Focus map. When the camera movement is performed, this prediction of the future state of the working memory meets the feedforward activity sent by the Saliency map and the representation remains valid and stable.

Integrated behavior

The properties evoked above are only a functional interpretation of the collective behavior of few interconnected maps of cortically-inpired automata. This level of interpretation can also be used to relate the whole system to such a complex behavior as visual attention.

Covert attention does not imply eye movements and allows for parallel feature search and sequential conjunction search (involving several features) with inhibition of return. Treisman and Gelade [START_REF] Treisman | A feature-integration theory of attention[END_REF] explain this property in their Feature Integration Theory where a global feedforward processing is only possible inside one feature map and an iterative sequential process including feedback operates in the conjunctive cases.

An initial model [START_REF] Vitay | A distributed model of spatial visual attention[END_REF] including the Focus and Working memory maps is able to perform covert attention and displays similar properties [START_REF] Fix | From physiological principles to computational models of the cortex[END_REF]: if the desired target is encoded only in a feature map, it can directly bias the competition in the Focus map; else a selection corresponding to only one feature dimension is made, must be compared to the desired target and eliminated (thanks to the inhibition of return) or selected (hence a search time proportional to the number of targets).

We have recently extended the system (adding the Memory anticipation map) to allow for eye movements (overt attention). This is consistent with the premotor theory of attention [START_REF] Rizzolati | Reorienting attention accross the horizontal and vertical meridians[END_REF] that considers that covert and overt attentions share several neuronal structures. As eye movements perturbate the frames of representation, there is a need to anticipate the consequences of eye movements to update the working memory [START_REF] Fix | A top-down attentional system scanning multiple targets with saccades[END_REF], as illustrated in Figure 2. Here the goal is to center the retina on a blue target. In the figure, the red square corresponds to the retina and contains a blue target at the bottom. This target is selected by the focus map; in the Anticipation map, it is anticipated that the target will be in the middle of the retina and the Working memory will be translated accordingly, as the movement is performed.

In this system, the visual search can be also much more complex; it is for example possible to sequentially focus on all patterns with the same characteristics, the search for one pattern being itself a conjunctive search. In this case, for example, the goal would be to focus on all blue bars with a Pi/4 orientation. First, the covert attention will successively make more salient several Blue or Pi/4 patterns until one with both characteristics in found (else, the Switch neuron eliminates a bad candidate with inhibition of return and ask for the next candidate). When a matching candidate is found, over attention can apply and ask for a real camera movement to translate this pattern in the middle of the retina. Just before the movement, the Memory anticipation mechanism will anticipate the modification in the frame of representation and modify the Working memory accordingly. Here too, it must be underlined that this functional interpretation emerges from distributed asynchronous computations of cortically inspired maps of units.

This mechanism can also be interpreted in the framework of the situatedness of cognition. In the "feature axis" corresponding to the temporal axis, a kind of saliency map uses a filtering process to choose targets from intrinsic characteristics of perceived objects or because they are "desired" (the goal of the task). Then, on this basis, in the "spatial axis" standing for the parietal axis, only the locations of stimuli, that can be considered as pointers toward objects in the real world, are manipulated. Particularly, a gating mechanism using sigma-pi units combines the activity of a focus map indicating the next target to focus on with the activity of the working memory to anticipate what should be the state of the working memory after the eye movement (cf. figure 1 and refer to [START_REF] Fix | A computational model of spatial memory anticipation during visual search[END_REF] for details). After this internal process of pointer manipulation, when the eye movement is performed, it is possible to relate this information about location to the real objects in the world and to their characteristics.

Figure 2 illustrates the model running in a simplified environment, where the behavior of the system can be finely observed. Current work complexifies the input filters to apply the system to natural images. Concerning the size of the current model, it should be underlined that it consists of eighteen maps, fifteen thousands units and over six millions connections, which illustrates the fact that fully distributed asynchronous computations can be mastered until that level, provided that a solid theoretical framework ensures the consistency of the whole.

Communication

In the preceding sections, I have presented the principles of a theory of intelligence based on the situatedness of cognition, together with several behavioral and biological related facts. I have shown the interests of such a framework for tasks related to visual scene exploration with or without eye movements. The main goal of this paper is to argue that this framework is also fundamental to endow artificial beings with efficient and bio-inspired communication skills.

It was indicated above that the orientations of any parts of the body can be used as deictic pointers toward the real world and that this principle is used by the human being to keep track of relevant "objects" (with a broad meaning) in the world. Firstly, since all humans use that strategy, consciously or unconsciously observing the orientation of the body parts of other humans can be useful to be informed about their intentionality: This is a first way to communicate. Secondly, the spoken language can be integrated to that framework if we go beyond the visual modality put to the fore for the moment. From the multi-modal integration principles evoked at the beginning of this paper, it can be understood that an "object" that is evoked, observed or manipulated can be associated with an articulated sound. Similarly to pointers to the outer world, this sound can also be considered as a pointer to the object it used to be associated with.

Concerning non-verbal communication, referents can be achieved by pointing with the hand, the head, the eyes, etc. and the listener is able to bind the real object to those deictic pointers (e.g.: do it where I am fixating). Concerning spoken communication, deictic pointers are useful to interpret indexicals (e.g.: this is mine). In both cases, we find again that principle to represent information from hints toward the outer world as it is needed rather than to build complete and complex internal representations of the world.

All this phenomenological description particularly matches with what we know about the role of mirror neurons in communication [START_REF] Rizzolatti | The mirror neuron system and its function in humans[END_REF]. Besides, they are ideally located at the crossroads of multimodal sensory information and action representation in the cortex. They are also characterized by a generic spectrum of responses, independent from the agent and the sensory modality and, as part of the cortex, share the same structuration in cortical columns with the other parts of the cortex.

Perspectives

The preceding section is itself a prospective part because a lot of work remains to be done to operationalize such concepts. Nevertheless, it seems to me that the way forward is rather clear to proceed in the domain. The main prerequisite is to be able to operate several (artificial and/or real) agents creating, observing and manipulating such deictic pointers in a real world.

It must be also underlined that I mainly developed here the first level of the theory, based on deictic strategies at a third of a second or so, concerning orientations of parts of the body or uttered words. A lot remains to be done to consider behaviors with longer constants of time, requiring manipulations and combinations of elementary pointers. Similarly to computer science, it is possible to imagine creating pointers of pointers and preserving the genericity of the computations. Two cerebral mechanisms must be evoked in that perspective. Firstly, the perirhinal cortex and the hippocampic system are reputed to store high level abstract representations [START_REF] Squire | Memory and the hippocampus: a synthesis from findings with rats, monkeys, and humans[END_REF]. Secondly, the prefrontal-striatal-thalamic-cortical loops own a variety of time constants that allow for the organization of behavior in time respecting several kinds of constraints [START_REF] Fuster | The Prefrontal Cortex : Anatomy, Physiology, and Neuropsychology of the Frontal Lobe[END_REF]. At the moment, I have described separated elements of behavior. Such mechanisms are necessary to integrate them in behaviors with longer constant of time while preserving their reactivity and flexibility. First, this is necessary to develop longer term dynamical memory (to have the illusion of a stable world in the visual case; to remember the general meaning of the sentence while uttering a word). Second, this is necessary to give a stronger meaningful structure to the behavior (intelligent exploration of the world in the visual case; syntactic rules in language). My claim is that such powerful processes could emerge from these mechanisms and that these mechanisms could be implemented with the same local computational logic as the one described in this paper.

Finally, concerning both aspects, they should be developed in parallel to solid knowledge concerning the underlying cerebral circuitry. Here also, there exists a number of evidence, evoked above, relating most aspects to posterior and prefrontal cortex, hippocampus and basal ganglia. Modeling experiments could also bring new predictions to be confronted to the biological and behavioral reality. Caption for Figure 1: General structure of a model of visual overt and covert attention: feature and spatial processing are respectively performed in models of temporal and parietal cortical axes. Features are extracted in the Feature maps and combined in the Saliency map. The Focus map selects only one pattern because it is salient or because it is desired thanks to the monitoring of the Feature processing axis, encoding Target and Perceived features. The Working memory maps memorize the patterns that have been explored (inhibition of return) and the Memory anticipation map anticipates eye movements and update the Working memory. In the covert mode, the Switch mechanism inhibits the Focus map to put the focus on the next selected target. In the overt mode, a camera movement is performed if the target corresponds to the perceived feature. In accordance with a unified theory of cortical processing, all these apparently different processing are in fact produced by maps of cortically inspired units driven by identical functioning rules.

Caption for Figure 2: Screenshot of the model. This is an implementation with maps and units of the functional circuit presented in Figure 1. Left part: The perceived world is in the red square which can be moved (overt attention) or can be internally explored (switch: covert attention). Observed (bottom row) and desired (middle row) hints of color (Blue; Green) and orientation (Pi/4; 3Pi/4). Upper row: Move or Switch order. Right part: implementation in maps of cortically-inspired units of anticipation, working memory and inhibition of return for the appropriate analysis of the scene. The perceptual map stands for the Saliency map; the Premotor map stands for the Focus map. The Working memory is composed of wm and thalwm maps. The four upper left maps related to inhibition correspond to the Switch mechanism, not described here. Refer to the text and to [START_REF] Fix | A computational model of spatial memory anticipation during visual search[END_REF][START_REF] Fix | A top-down attentional system scanning multiple targets with saccades[END_REF][START_REF] Fix | From physiological principles to computational models of the cortex[END_REF] for details.

Caption for Table 1 :

 for1 Fundamental principles of information processing are applied to various information flows in the laminar organization of the cortex.

	Task	Identification	Location
	Associative cortex	Temporal	Parietal
	Linking sensory pole with	Limbic pole	Body pole
	Extracts hints related to Emotional value Position in space

Table 2 :

 2