Xiang Dai
email: xiang.dai@gipsa-lab.grenoble-inp.fr

Vahid Nateghi
email: vahid.nateghi@mail.polimi.it

Hassen Fourati
email: hassen.fourati@gipsa-lab.grenoble-inp.fr

Christophe Prieur
email: christophe.prieur@gipsa-lab.grenoble-inp.fr

Q-Learning-Based Noise Covariance Adaptation in Kalman Filter for MARG Sensors Attitude Estimation

Keywords: Extended Kalman filter, Q-learning, Attitude estimation, Reinforcement learning

The attitude estimation of a rigid body by magnetic, angular rate, and gravity (MARG) sensors is a research subject for a large variety of engineering applications. A standard solution for building up the observer is usually based on the Kalman filter and its different extensions for versatility and practical implementation. However, the performance of these observers has long suffered from the inaccurate process and measurement noise covariance matrices, which in turn entails tedious parameter turning procedures. To overcome the laborious noise covariance matrices regulation, we propose in this paper a Q-learning-based approach to autonomously adapt the values of process and measurement noise covariance matrices. The Qlearning method establishes a reinforcement learning mechanism that forces the noise covariance matrices pair with the least difference between predictions and measurements of output to be found in a predetermined candidate set of noise covariance matrices. The effectiveness of the Q-learning approach, applied to Extended Kalman filter-based attitude estimation, is validated through the Monte Carlo method that uses real flight data on an unmanned aerial vehicle.

I. INTRODUCTION

The determination of attitude and position are involved in navigation applications of any moving rigid bodies. The Kalman filter (KF) and especially its Extended version (EKF) for nonlinear dynamic models have been widely used for several years for this purpose [START_REF] Zmitri | BiLSTM network-based extended Kalman filter for magnetic field gradient aided indoor navigation[END_REF]- [START_REF] Bonnabel | Left-invariant extended Kalman filter and attitude estimation[END_REF]. A linearization step should be achieved for the nonlinear models of navigation at the current state estimate to approximate the KF equations. In such algorithms, it is well known that the model and measurement noise covariance matrices play essential roles, while it is challenging to design an optimal estimator in the absence of exact statistical knowledge about these matrices when using inertial and magnetic sensors, for example. The improper values of the noise covariance matrices in the filtering algorithm cause underestimation or overestimation of the uncertainty in model or sensor measurements, leading to degradation in attitude estimation performance, for example, usually represented by quaternions, rotation matrices, or Euler angles. Several approaches have been presented in the literature to overcome this problem of covariance matrix by using different strategies of adaptation of the measurement noise covariance matrix [START_REF] Odry | A novel fuzzy-adaptive extended kalman filter for real-time attitude estimation of mobile robots[END_REF]- [START_REF] Xiong | Adaptive iterated extended Kalman filter for relative spacecraft attitude and position estimation[END_REF] or process noise one only [START_REF] Wang | An adaptive Kalman filter estimating process noise covariance[END_REF]. An improvement is targeted if the adaptation is applied to the two noise covariance matrices. The main endeavor of this paper is to adapt the two noise covariance matrices simultaneously and in an autonomous way.

Recent advancements in Reinforcement Learning (RL) have made it appealing to be implemented to cope with uncertain environments. Specifically, this work is motivated by the strength of the Q-learning method [START_REF] Kim | Adaptive packet scheduling in IoT environment based on Q-learning[END_REF]- [START_REF] Xiong | Q-learning for noise covariance adaptation in extended Kalman filter[END_REF] in which an intelligent agent learns how to take action in an environment with uncertain parameters. To the best of our knowledge, the process and measurement noise covariance matrices adaptation for the EKF based on Q-learning has not been solved yet within the scope of attitude and related states estimation by MARG sensors.

In this paper, we first formulate the attitude estimation problem of a rigid body, in which the rotation is represented by quaternion and the state vector to be estimated is composed of quaternion and gyroscope bias. In the following, the dynamic and observation models are illustrated, and the traditional EKF for this purpose is also formulated. Next, we propose a Q-learning-based extended Kalman filter (QLEKF) approach, which consists of three parallel filters. The first filter, a traditional EKF with initial values of noise covariance matrices, is run for filtering performance comparison. The second filter, a learning EKF, is implemented to evaluate the estimation performance and search for appropriate noise covariance matrices. A reward is defined by comparing a predescribed index for the performance of the traditional EKF and the learning EKF, and the best couple of the process and measurement noise covariance matrices are selected. The third filter, the learned EKF, uses the noise covariance matrices returned by the learning EKF filter to provide the final estimated states. The estimator gradually adopts the most suitable noise covariance matrices selected by the Q-learning algorithm according to the cumulative reward.

The main contributions of the paper are twofold. First, the proposed algorithm successfully adapts the process and measurement noise covariance matrices for attitude and bias estimation using MARG sensors through the combination of Q-learning and EKF. Second, the superiority of the proposed algorithm over the traditional EKF in estimating attitude and gyroscope bias is validated through multiple Monte Carlo simulations based on real flight data.

The rest of the paper is organized as follows. Section II formulates the attitude representation and sensor models. Section III details the dynamic process and observation models, the traditional EKF, and the proposed QLEKF to estimate the rigid body attitude and gyroscope bias. Random Monte Carlo simulations that use real flight data are performed in Section IV. Conclusion and future research directions are given in Section V.

II. ATTITUDE AND GYRO BIAS MODELS FORMULATION FOR NAVIGATION

In this section, we first introduce quaternion to represent the attitude of rigid body and then formulate the sensor models. These materials are used later to establish the process/observation models and the estimation approaches.

A. Attitude representation with quaternion

In this paper, the attitude of the rigid body is represented by a quaternion-based formulation for its simplified algebra and universal application in 3D orientation. We first introduce the quaternion definition [START_REF] Trawny | Indirect Kalman filter for 3D attitude estimation[END_REF]:

q = q 1 i + q 2 j + q 3 k + q 4 , (1)
where q 4 is the scalar part, q 1 i + q 2 j + q 3 k is the vector part and i, j, k are hyperimaginary numbers.

The quaternion can also be written in a column vector, without loss of generality and for a concise formulation, the quaternions that appear in the rest of the paper are assumed with unit norm, that is: q = [q 1 q 2 q 3 q 4 ] T , ∥q∥ = 1.

(

) 2
Given a rigid body, let B denote its body frame and N denote the navigation (inertial) frame, then its position expressed in B (e.g. p b ∈ R 3 ) and in N (e.g. p n ∈ R 3 ) can be related by a rotation matrix as

p b = C b n (q b n )p n , (3)
where

C b n (q b n ) ∈ R 3×3
is the rotation matrix from N to B expressed in B using quaternion elements [START_REF] Kuipers | Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality[END_REF],

C b n q b n =   1 -2q 2 2 -2q 2 3
2 (q 1 q 2 + q 3 q 4 ) 2 (q 1 q 3 -q 2 q 4 ) 2 (q 1 q 2 -q 3 q 4 ) 1 -2q 2 1 -2q 2 3 2 (q 2 q 3 + q 1 q 4 ) 2 (q 1 q 3 + q 2 q 4 ) 2 (q 2 q 3 -q

1 q 4 ) 1 -2q 2 1 -2q 2 2   .
Without arising ambiguity, we denote q = q b n hereinafter in the paper. As the rigid body moves in 3D space, its associated quaternion time derivative can be formulated as [START_REF] Trawny | Indirect Kalman filter for 3D attitude estimation[END_REF]:

q = 1 2 Ω(ω)q, (4)
where ω = [ω x , ω y , ω z ] T ∈ R 3 is the true angular velocity of B w.r.t. N expressed in B, and

Ω(ω) = -⌊ω×⌋ ω -ω T 0 , ⌊ω×⌋ =   0 -ω z ω y ω z 0 -ω x -ω y ω x 0   .
Let T e = t k+1 -t k denote the sampling interval. To render (4) to be computationally efficient, we consider a discrete model under the assumption that the evolution of ω during T e is linear. In correspondence, the first order derivative of ω can be expressed as a constant:

ω = (ω k+1 -ω k )/T e ,
and higher order derivatives are accordingly zero.

Applying Taylor series expansion to q k+1 around time instant t k by substituting the first order derivative (4) and neglecting items of higher order derivatives yield the first order quaternion integration [START_REF] Wertz | Spacecraft Attitude Determination and Control[END_REF] as

q k+1 = q k + T e 2 Ω(ω k )q k . (5)

B. Sensor models

The MARG sensors considered in this paper are composed of a 3-axis gyroscope, a 3-axis magnetometer and a 3-axis accelerometer. These sensors measure respectively real angular velocity ω r ∈ R 3 , magnetic field m ∈ R 3 and acceleration a ∈ R 3 of the rigid body in B w.r.t. N . The simplified measurement equations are formulated as follows [START_REF] Fourati | A Nonlinear Filtering Approach for the Attitude and Dynamic Body Acceleration Estimation Based on Inertial and Magnetic Sensors: Bio-Logging Application[END_REF]:

     ω r = ω + b g + v g , a = C b n (q)g + v a , m = C b n (q)h + v m , (6)
where g ∈ R 3 is the gravity vector, h ∈ R 3 is the earth magnetic field, b g ∈ R 3 is the bias of gyroscope, and

v g ∈ R 3 , v a ∈ R 3 , v m ∈ R 3
are assumed to be uncorrelated Gaussian noises with zero mean and covariance matrices

Σ g = σ 2 g I 3 , Σ a = σ 2 a I 3 and Σ m = σ 2 m I 3 .
In this paper, we consider that the body linear acceleration expressed in N is zero since the rigid body is just rotating on itself and its center of mass is not moving. In addition, to be more focused on the attitude estimation, namely attitude of rigid body and gyroscope biases, accelerometer and magnetometer biases are omitted in the sensor models.

III. DYNAMIC PROCESS AND OBSERVATION MODELS AND LEARNING-BASED KALMAN FILTERING FOR NAVIGATION

In this section, we first build up the navigation dynamic model, based on which the traditional EKF is introduced to perform the attitude and bias estimation. In the continuation, the Q-learning method is proposed to recursively adapt the process and measurement noise covariance matrices in the EKF using a feedback from the uncertain environment.

A. Model design

The state vector consists of rotation quaternion and bias of gyroscope, and the state transition equation is formulated as

x k+1 = q k+1 b g k+1 = f (x k ) + w k = I 3 + 1 2 Ω(ω r k -b g k )T e 0 0 I 3 q k b g k + w q k w g k , (7)
where b g k is the gyroscope bias at time step k and modeled as standard random walk, and w q k and w g k form the process noise, assumed to be uncorrelated Gaussian with zero mean and covariance matrices Σ q w = σ 2 w,q I 3 and Σ g w = σ 2 w,g I 3 . As such, the process noise covariance matrix Q k can be expressed as

Q k = Σ q w 0 0 Σ g w . (8)
In what follows, we construct the observation model by grouping those of accelerometer and magnetometer as

y k = a k m k = g(x k ) + v k = C b n (q k ) 0 0 C b n (q k ) g h + v a k v m k , (9)
where v a k and v m k are the measurement noises of accelerometer and magnetometer, and are assumed uncorrelated with a zero mean covariance matrices Σ v a = σ 2 v,a I 3 and Σ v m = σ 2 v,m I 3 . Correspondingly, the measurement noise covariance matrix R k is expressed as

R k = Σ v a 0 0 Σ v m . (10)

B. The traditional extended Kalman filter

In this section, based on dynamic process and observation models presented before, first we introduce the EKF for state estimation, summarized in Alg. 1. We express the EKF in a higher level of abstraction as function format since it will be used to construct the QLEKF in the following subsection.

In Alg. 1, xk|k-1 is the a priori state estimate at step k given the knowledge of the process model prior to step k, A is the Jacobian matrix of partial derivatives of f w.r.t. x,

P k|k-1 = E[(x k -xk|k-1 )(x k -xk|k-1 ) T ]
is the a priori error covariance matrix estimate at step k given knowledge of the process model prior to step k, C is the Jacobian matrix of partial derivatives of g w.r.t. x, K k is the Kalman gain at step k (derived from conditional probability density function given that x and y are jointly Gaussian distributed), ỹk is the measurement innovation term at step k, xk|k is the a posteriori state estimate at step k given measurement y k ,

P k|k = E[(x k -xk|k )(x k -xk|k ) T ]
is the a posteriori error covariance matrix at step k given measurement y k .

Algorithm 1 Traditional Extended Kalman Filter

1: xk|k , P k|k , ỹk = EKF ( xk-1|k-1 , P k-1|k-1 , y k , Q k , R k ) 2: Input xk-1|k-1 , P k-1|k-1 , y k , Q k , R k 3: xk|k-1 = f ( xk-1|k-1 ) {time update of state estimate} 4: A = ∂f ∂x | xk-1|k-1 5: P k|k-1 = AP k-1|k-1 A T + Q k {time update of error covariance matrix} 6: C = ∂g ∂x | xk|k-1 7: K k = P k|k-1 C T (CP k|k-1 C T + R k ) -

C. Preliminaries on Q-learning approach

Q-learning is a method in reinforcement learning that maximizes the long-term reward in a multistate environment. That environment typically consists of discrete state-action pairs, each of which is assigned with a scalar, called Q-value.

In Q-learning, the agent learns to achieve a larger Q-value under uncertainty through a trial-and-error process by shifting among these state-action pairs. Suppose that the agent is at state s, and it needs to determine an action a to reach the next state s ′ . Commonly, there are various methods to determine how to choose the action [START_REF] Jiang | Path planning of a mobile robot in a free-space environment using Q-learning[END_REF] in Q-learning. In this paper, we adopt the ϵ-greedy algorithm [START_REF] Sutton | Reinforcement learning: An introduction[END_REF]: a standard algorithm in the RL domain where the agent chooses a random action with a probability of ϵ or pick the action that maximizes the Q-value with the probability of (1-ϵ). The value of ϵ defines how much the agent should rely on the exploration or exploitation; the greater the ϵ, the higher the probability to explore.

Each time after executing an action a, the agent receives a response from the environment, which is translated to a reward (R) showing how good the action is. Significantly, Q-learning at its core seeks to maximize the cumulative reward by performing the best action at each state [START_REF] Xiong | Q-learning for noise covariance adaptation in extended Kalman filter[END_REF]. The cumulative reward is stored as Q-value through the Q-learning update rule as [START_REF] Maoudj | Q-learning-based navigation for mobile robots in continuous and dynamic environments[END_REF] where Q(s, a) ∈ R is the Q-value for the action a in state s, R ∈ R is the reward gained by exeuting action a in state s, α is the learning rate, and γ is the discount factor.

Q(s, a) = Q(s, a) + α[R + γ max a Q(s ′ , a) -Q(s, a)],

D. Q-learning-based EKF for covariance matrices adaptation

In the QLEKF approach, the agent attempts to find appropriate values of process and measurement noise covariance matrices to improve the performance of the traditional EKF.

To implement the QLEKF, a states set S, composed of M candidates of process noise covariance matrices {Q

(1) k , Q (2) k , ..., Q (M ) k } and N candidates of measurement noise covariance matrices {R (1) k , R (2) k , ..., R (N )
k }, is first conceived to form a M × N grid. As such, element (i, j) in the grid, namely state (i, j), represents the couple of noise covariance matrices (Q

(i) k , R (j) k ).
In the continuation, an action set A i,j is formed with valid actions that can transit (i, j) to its adjacent states in the grid or keep it at (i, j). It is worth mentioning that the subset of valid actions at each element of the grid depends on the location of the agent comprising the corner area, the boundary area, and the central area. The last thing that needs to be defined is the reward. One can assume the reward is the difference of the innovation sequences between the EKF with the nominal (initial) process and measurement noise covariance matrices and the EKF with

Q (i) k and R (j)
k corresponding to the current state of the agent. The QLEKF comprises three EKFs as shown in Figure 1: the traditional EKF, which uses an initial value of covariance matrices; the learning EKF, which searches appropriate covariance matrices by the Q-learning algorithm; and the learned EKF, which outputs the result of estimation according to the covariance matrices found by the learning EKF. Step 20 ensures the identical initial conditions at each iteration for the traditional EKF and the learning EKF, which brings a fair and reliable reward accumulation in Step 14. In Alg. 2, superscripts t and l stand for the traditional and learning EKF, respectively. In this section, the effectiveness of the learned EKF in Alg. 2 is validated and compared with the traditional EKF using data from a real flight trajectory of an unmanned aerial vehicle.

Algorithm 2 Q-learning Extended Kalman Filter 1: Initialize xt 0|0 , xl 0|0 , P t 0|0 , P l 0|0 , s and ϵ 2: k ← 1, Q(s, a) ← 0, R ← 0 3: for each iteration do 4: Generate N from uniform distribution N ∼ U (0,
] = EKF ( xt k-1|k-1 , P t k-1|k-1 , y t k , Q k , R k ) 13: [ xl k|k , P l k|k , ỹl k ] = EKF ( xl k-1|k-1 , P l k-1|k-1 , y l k , Q (i) k , R (j)
k ) 14: R ← R + {[( ỹt k ) T ỹt k ] 0.5 -[( ỹl k ) T ỹl k ] 0.5 } 15: [ xk|k , P k|k , ỹk ] = EKF ( xk-1|k-1 , P k-1|k-1 , y k , Q (i) k , R (j)
k ) 16: k ← k + 1 17: end for 18: Q(s, a) = Q(s, a) + α[R + γ max a Q(s ′ , a) -Q(s, a)] 19: s ← s ′ , R ← 0 20: xl k|k ← xt k|k , P l k|k ← P t

A. Simulation setup

We use the ground truth data from the real flight trajectory of an unmanned aerial vehicle extracted from the experiments Euroc [START_REF] Burri | The EuRoC micro aerial vehicle datasets[END_REF] at http://robotics.ethz.ch/ ∼ asl-datasets/ ijrr euroc mav dataset/machine hall/MH 01 easy. From the ground truth data, we select the bias of gyroscope b g and quaternion. The latter is first transformed into unit quaternion and then substituted into (5) to solve out the true ω using matrix pseudo inverse.

For the numerical simulations, the sampling rate of the MARG sensors is set to 100Hz, the gravity and the earth magnetic field vectors are set to g = [0, 0, 9.81] m/s 2 , h = [0.23, 0.01, 0.41] Gauss. For the initialization of each Monte Carlo simulation, the quaternion is set as the first quaternion of the ground truth data1 , and the gyroscope bias and the error covariance matrix are set to b g 0 = [2.2, 2, 2] mrad/s, P 0 = 10I 7 .

In terms of the traditional EKF, we set σ w,q = 1 × 10 -3 , σ w,g = 0.01 rad/s, σ v,a = 0.01 m/s 2 , and σ v,m = 1 × * For a ground truth unit quaternion qtrue, the quaternion error of its unit estimate q is computed as ∥q -1 true ⊗ qq I ∥, where q I = [0 0 0 1] T is the identity quaternion.

k = Q k , R (3)
k = R k . The Q-learning search starts at the grid (Q

(1) k , R (1)
k ). For each Monte Carlo simulation, we run 200 iterations and 100 time steps for each iteration. The learning rate, discount factor and random action selection probability are fixed to α = 0.1, γ = 0.9 and ϵ = 0.1.

B. Results and analysis

Table I shows that after convergence of 50 Monte Carlo simulations, the learned EKF evidently outperforms the traditional EKF in estimating the rigid body attitude and the gyroscope bias, where the learned EKF averagely improves 39.0% of the mean of quaternion error norm and 50.8%, 36.0% and 35.6% of RMSE of gyroscope bias of x, y, and z axes compared to the traditional EKF. In Fig. 2345, we plot the evolution of quaternion error norm and gyroscope bias error, in which each point on the curve stands for the mean of 20 consecutive samplings of 50 Monte Carlo simulations after convergence, making 5 points collected during the period of 1 sec. As shown in Fig. 2, the 2 curves share similar tendency and fluctuations after convergence, while the quaternion error of the learned EKF is always distinctly lower than that of the traditional EKF in k } to search for values with better innovation term, thus leading to a better attitude estimate after convergence. Similar behaviors of error of gyroscope bias can be observed in Fig. 345as well, which again demonstrates the advantage of the learned EKF in the tuning process and measurement noise covariance matrices over the traditional EKF.

V. CONCLUSIONS

In this paper, we have first introduced a traditional EKF to estimate the attitude and gyroscope bias of a rigid body in rotation movement. To address the often-cumbersome tuning of process and measurement noise covariance matrices in the EKF, we have then introduced a Q-learning algorithm to enforce the filter to search for more accurate covariance matrices along the estimation course. This is realized by assigning a reward to covariance matrices that can produce better innovation terms than the traditional EKF, which encourages covariance matrices associated with better measurement estimation to be more likely selected by the reinforcement learning process.

Through Monte Carlo numerical simulations based on real flight data of an unmanned aerial vehicle, the proposed learned EKF on average has revealed an improvement of 39.0% in attitude estimation and at least 35.6% in gyroscope bias estimation compared to the traditional EKF after convergence.

Future work on the QLEKF can be undertaken by incorporating the position and linear velocity in the estimation, and combining vision data with an inertial measurement unit (IMU) for better navigation.

Fig. 1 :

 1 Fig. 1: Schematic diagram of QLEKF

k|k 21 :

 21 end for 22: return { xk|k } and {P k|k } IV. NUMERICAL SIMULATIONS WITH REAL DATA

10 - 3

 3 m/s 2 . The size of Q-learning grid is set to M = N = 5, of which {Q (i) k } and {R (j) k } are set as a geometric progression with ratio of 10 and Q (3)

Fig. 2 :

 2 Fig. 2: Trajectory of average quaternion error between traditional EKF and learned EKF after convergence in 50 Monte Carlo simulations

Fig. 3 :Fig. 4 :

 34 Fig. 3: Trajectory of average error of gyroscope bias on x axis between traditional EKF and learned EKF after convergence in 50 Monte Carlo simulations

Fig. 5 :

 5 Fig. 5: Trajectory of average error of gyroscope bias on z axis between traditional EKF and learned EKF after convergence in 50 Monte Carlo simulations

  1 {compute the Kalman gain} 8: ỹk = y k -g( xk|k-1 ) {compute the innovation term} 9: xk|k = xk|k-1 + K k ỹk {measurement update of state estimate} 10: P k|k = P k|k-1 -K k CP k|k-1 {measurement update of error covariance matrix} 11: Output xk|k , P k|k , ỹk

  1) 5: if N < ϵ then

	6:	select action a randomly
	7: else
	8:	a = arg max a Q(s, a)
	9: end if
	10: Execute action a and obtain state s ′
	11: for each time step in one iteration do
	12: [ xt k|k , P t k|k , ỹt k

TABLE I :

 I Average statistics of mean of quaternion error norm and Root Mean Square Error (RMSE) of gyroscope bias after convergence in 50 Monte Carlo simulations

		Mean of quaternion	RMSE of gyroscope bias (mrad/s)
		error* (×10 -3 )	x-axis	y-axis	z-axis
	Traditional EKF	1.419	9.944	4.449	6.078
	Learned EKF	0.866	4.893	2.846	3.912

It needs to be normalized as unit quaternion to keep all the quaternion along the simulation being unit quaternion.


domain: phys sde spi

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

-Allows to summarize all the contributions such as soil and vegetation contributions and to measure the net fluxes.

-Does not allow to measure separately and locally each contribution, requires a fast, ad expensive, gas analyzer, and requires some environmental conditions (air turbulence). Collected data processing is complex. ➢ Dynamic accumulation chambers:

-Allows measuring locally the effluxes with a slow air analyzer by all the time. Measurements data processing is relatively basic.

Overall measurement requires numerous chambers placement and measurements hardly allow to summarize all the contributions.

OBJECTIVES: Build cost-effective chambers adapted for each specific use.

Context & Objectives

Conclusion Long term installation chambers P-Gaz

➢ Fully automatized and piloted by an external or an internal data logger.

➢ Designed for an external gas analyzer and then operated serially. Or… ➢ Designed for an internal gas analyzer (small economic NDIR analyzers for carbon dioxide or water vapor can be embedded) along with an internal data logger allowing simultaneous uses without external pneumatic tubbing.

Zawilski, B. M. https://doi.org/10.5194/gi-11-163-2022, 2022. ➢ Independent stainless-steel collars for heavy, clayey soils use.

➢ Easy installation and uninstallation, easy chamber change for laboratory maintenance.

➢ Fully digital data transmission along with the diagnostic data.

➢ Vegetation anti-pinch grids.

➢ Double shielding (UV and IR). ➢ Soil GHG effluxes can be accurately monitored by dynamic accumulation chambers. Each uses require different solutions. Nowadays, possibilities derivate from omnipresent IOT technology allow to make an entirely automatized "bulletproof", cost-effective setups.

Fully autonomous portable chambers CoOxy

  Zawilski B. M. bartosz.zawilski@cnrs.fr Centre d'Etudes Spatiales de la BIOSphère 18 avenue Edouard Belin, 31400 Toulouse, FRANCE CHAMBERS' WORLD ➢ In the context of global climate warming, soil GHG effluxes are monitored. Several techniques are used such as eddy covariance or dynamic accumulation chambers.Each technique has its pro and cons and these techniques are complementary. ➢ Eddy covariance:

➢

  Designated for internal gas analyzers ➢ Preinstallable stainless-steel collars. ➢ Fully autonomous with rechargeable batteries (12h autonomy) ➢ Embedded air pressure, air temperature, air moisture, CO 2 , and O 2 monitoring ➢ Embedded GPS for precise measurements geolocalization. ➢ Embedded LCD. ➢ Embedded data logger with precis RTC. ➢ USB data transmission. Portable chambers for the external gas analyzer BPC ➢ Portable chambers for the external gas analyzer. ➢ Designated for external precise gas analyzer (FTIR Gasmet GT5000). ➢ Preinstallable stainless steel collars. ➢ Fully autonomous with rechargeable batteries (12h autonomy) ➢ Embedded air pressure, air temperature, and air moisture monitoring ➢ Embedded GPS for precise measurements geolocalization. ➢ Embedded LCD. ➢ Wireless real-time Bluetooth data transmission.

Acknowledgments

Instrumental developments were mainly funded by the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique (CNRS-INSU) through the ICOS and OSR SW observatories. I would also to acknowledge Aurore Brut, Tiphaine Tallec and Vincent Bustillo for their help and their expression of interest.


domain: sde.ie spi phys

text:
teaching and research institutions in France or abroad, or from public or private research centers.

ICOS mandatory measurements are achieved using self-calibrated heat flux plates HFP01SC.

Two questions arise:

-How to check correct soil heat flux plates functioning? -Subsequently, why the annual soil heat flux budget is not closed? OBJECTIVES: Check the soil heat flux plates functioning and complete the soil heat fluxes balance.

Context & Objectives

Soil Heat flux plates functioning

➢ To check correct SHFP functioning is not so evident and an annual integration may be of great help.

Systematic unbalances

➢ Systematic unbalance may be, in part, attributed to the advective fluxes.

-Evapotranspiration causes advective fluxes.

-Rainfall water infiltration causes surface cooling but also advective fluxes.

Localized unbalances

➢ Annual soil heat flux integration is not nil and geothermal energy does not explain this unbalance. ➢ Particularly important unbalance may be attributed to the soil or the sunshine inhomogeneities boundaries proximity.

Conclusion

➢ Soil Heat Flux Plates functioning con be checked by an annual integration. ➢ Important unbalance may be observed due to boundaries proximity of inhomogeneities and also due to the unmeasured advective fluxes.

  Zawilski B. M. bartosz.zawilski@cnrs.fr Centre d'Etudes Spatiales de la BIOSphère 18 avenue Edouard Belin, 31400 Toulouse, FRANCE SOIL'S HEAT FLUX WORLD ➢ In the context of global climate warming, soil heat flux is monitored.

  Annual integration should be close to zero as, by energy conservation, in the case of homogeneous soil with the same soil temperatures and moisture et the beginning and the end of the year, theoretically, the heat flux integration is equal to the geothermal energy flux integration. Heat propagate by radiation (concern only separation surfaces) by advection (concern only fluids) and by conduction. SHFP measure only conduction. Zawilski, B. M. https://doi.org/10.5194/gi-11-223-2022, 2022.

FR-

  Lam installation were mainly funded by the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique (CNRS-INSU) through the ICOS and OSR SW observatories. I would also to acknowledge Aurore Brut (FR-Lam PI) end Franck Granouillac (FR-Lam Tech).

Acknowledgments


Kerri M Bailey

Bruno L Giordano

Amanda L Kaas

Fraser W Smith
email: fraser.smith@uea.ac.uk

Decoding sounds depicting hand-object interactions in primary somatosensory cortex

Keywords: SI, SII, cortical feedback, multisensory, multi-voxel pattern analysis

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Introduction

Much traditional neuroscientific research has investigated the function of the primary sensory brain areas (e.g. visual, somatosensory, and auditory cortices) with respect to how sensory input is processed within its corresponding sensory modality (see [START_REF] Carandini | Do We Know What the Early Visual System Does?[END_REF][START_REF] Kriegeskorte | Deep Neural Networks: A New Framework for Modeling Biological Vision and Brain Information Processing[END_REF]). However, it is well known that primary sensory areas are subject to significant influences from other sensory modalities (for reviews, see [START_REF] Ghazanfar | Is neocortex essentially multisensory?[END_REF][START_REF] Driver | Multisensory Interplay Reveals Crossmodal Influences on "Sensory-Specific" Brain Regions, Neural Responses, and Judgments[END_REF]; see also [START_REF] Lemus | Do sensory cortices process more than one sensory modality during perceptual judgments?[END_REF][START_REF] Liang | Primary sensory cortices contain distinguishable spatial patterns of activity for each sense[END_REF].

Recent studies have used multi-voxel pattern analysis (MVPA) to show that primary sensory cortices can contain fine-grained information about stimuli that are not of their target modality. For example, Meyer et al. [START_REF] Meyer | Predicting visual stimuli on the basis of activity in auditory cortices[END_REF] showed that simply viewing a silent yet sound-implying video clip triggers discriminable activity in primary auditory cortex (A1) even in the absence of auditory stimulation (see also [START_REF] Vetter | Decoding sound and imagery content in early visual cortex[END_REF] for a complementary example from audition to V1). Recently we have shown that different visual images of familiar but not unfamiliar object categories could be discriminated in primary somatosensory cortex -SI, despite the absence of any tactile stimulation during the experiment [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]; see also [START_REF] Meyer | Seeing touch is correlated with content-specific activity in primary somatosensory cortex[END_REF]. Thus, there is compelling evidence that stimuli initially presented via one modality can trigger fine-grained activity in distal primary sensory areas for certain pairs of modalities. One possible explanation for these cross-modal effects is that prior experience of the co-occurrence of sensory stimulation across multiple modalities is responsible for such effects [START_REF] Meyer | Convergence and divergence in a neural architecture for recognition and memory[END_REF]Smith and Goodale 2015; see also [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]. At the anatomical level there are multiple routes by which information may be transmitted to primary sensory areas that originated from a distal modality: for instance via feedback from higher level multisensory areas (e.g. pSTS, posterior parietal or premotor cortex; see [START_REF] Ghazanfar | Is neocortex essentially multisensory?[END_REF][START_REF] Driver | Multisensory Interplay Reveals Crossmodal Influences on "Sensory-Specific" Brain Regions, Neural Responses, and Judgments[END_REF], or possibly even via direct connections between specific modalities e.g. from primary auditory to primary visual cortex (e.g. [START_REF] Falchier | Anatomical evidence of multimodal integration in primate striate cortex[END_REF][START_REF] Falchier | Projection from visual areas V2 and prostriata to caudal auditory cortex in the monkey[END_REF].

We note that no study to date has investigated whether fine-grained information about familiar sound categories can be discriminated in SIdespite the fact that anatomical studies in animals suggest direct connections between auditory and somatosensory areas [START_REF] Cappe | Heteromodal connections supporting multisensory integration at low levels of cortical processing in the monkey[END_REF][START_REF] Ghazanfar | Is neocortex essentially multisensory?[END_REF] and the demonstration of extensive ipsilateral connections in humans between primary auditory cortex and SI and SII [START_REF] Ro | A neural link between feeling and hearing[END_REF]). As such we would also expect fine-grained auditory responses to be present in early somatosensory areas. Recent work, in fact, has begun to explore whether somatosensory areas may be activated by and discriminate simpler auditory stimuli such as pure tones Decoding hand-object sounds in primary somatosensory cortex [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]). These authors have shown representations of auditory frequency in early somatosensory areas (pooled across likely SI and SII) that relate to perception. The authors propose that these representations of auditory information in somatosensory areas may be related to predictive processing of associated tactile features (see e.g. [START_REF] Friston | The free-energy principle: a rough guide to the brain?[END_REF][START_REF] Friston | Predictive coding under the free-energy principle[END_REF][START_REF] Clark | Whatever next? Predictive brains, situated agents, and the future of cognitive science[END_REF]. [START_REF] Zhou Y Di | Somatosensory cell response to an auditory cue in a haptic memory task[END_REF], moreover, have shown that neurons in SI respond to auditory cues when they are predictive of upcoming somatosensory stimulation while [START_REF] Lemus | Do sensory cortices process more than one sensory modality during perceptual judgments?[END_REF] showed auditory responses in SI and SII to acoustic flutter stimuli that could not, however, discriminate the stimulus identity presented. In addition, previous work has indicated the activation of somatosensory areas in audio-haptic matching tasks (postcentral gyrus: [START_REF] Kassuba | Multisensory interactions between auditory and haptic object recognition[END_REF], in listening to tool sounds [START_REF] Lewis | Distinct Cortical Pathways for Processing Tool versus Animal Sounds[END_REF]; likely SII; see also [START_REF] Lewis | Lefties Get It "Right" When Hearing Tool Sounds[END_REF]) and in particular subregions of SII (OP1 & OP4) while listening to various sound categories [START_REF] Beauchamp | Neural Substrates of Sound-Touch Synesthesia after a Thalamic Lesion[END_REF].

Building on these studies and our earlier work [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF], in the present experiment we set out to investigate whether primary somatosensory cortex (SI) would contain fine-grained information that discriminates sounds depicting familiar handobject interactions (e.g. bouncing a ball vs typing on a keyboard). We reasoned that such effects would occur in SI due to the prior experience of the co-occurrence of the haptic information that corresponds with hearing the sound of specific hand-object interaction categories ( e.g. bouncing a ball vs typing on a keyboardsee [START_REF] Meyer | Convergence and divergence in a neural architecture for recognition and memory[END_REF].

Based on previous univariate studies examining the responses observed to tools and animal sounds, we might also expect sounds depicting hand-actions to preferentially activate (see [START_REF] Lewis | Distinct Cortical Pathways for Processing Tool versus Animal Sounds[END_REF]) and possibly be discriminated within higher level somatosensory (likely SII) and also premotor areas (via the auditory dorsal stream: Rauschecker and Tian 2000; [START_REF] Bizley | The what, where and how of auditory-object perception[END_REF]. While premotor areas are not the focus of the present study, we note that mirroring accounts would also predict such sounds to be discriminated in premotor cortexmost likely in ventral premotor areas (see e.g. [START_REF] Gazzola | Empathy and the Somatotopic Auditory Mirror System in Humans[END_REF].

Thus in the present study, participants listened to sound clips of familiar hand-object interactions (e.g. bouncing a ball, typing on a keyboard), in addition to two control categories (animal vocalizationsfamiliar high level control; pure tonesunfamiliar low level control), in an event-related functional magnetic resonance imaging (fMRI) experiment. Based on our previous work [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF] and the co-occurrence account [START_REF] Meyer | Convergence and divergence in a neural architecture for recognition and memory[END_REF] we predicted that MVPA would show significant decoding of sound identity for hand-object interaction sounds in SI, particularly in independently localized tactile hand-Decoding hand-object sounds in primary somatosensory cortex sensitive voxels, but not for the two control categories. We further predicted decoding would be greater in SI for hand-object interaction sounds than for the two control categories. We repeated these analyses in a series of additional control regions -including secondary somatosensory cortex and premotor cortexwhere multiple accounts may predict reliable decoding for hand-object interaction sounds but possibly also for each additional sound categoryas these areas have both been implicated in the dorsal auditory 'how' pathway. In early auditory cortex we would expect reliable decoding of all sound categories (positive control), whereas in M1 (see [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]; see also [START_REF] Lewis | Distinct Cortical Pathways for Processing Tool versus Animal Sounds[END_REF] we did not expect to find any reliable decoding (negative control). We did not have a specific prediction regarding whether decoding would be present in V1 as previous studies finding such effects [START_REF] Vetter | Decoding sound and imagery content in early visual cortex[END_REF][START_REF] Gu | Cross-modal representations in early visual and auditory cortices revealed by multi-voxel pattern analysis[END_REF] have used rich natural soundscapes rather than particular object categories in isolation but we include this region for comparability to previous studies.

Methods

Participants

Self-reported right-handed healthy participants (N = 10; 3 male), with an age range of 18-25 years (M = 22.7, SD = 2.41), participated in this experiment. We based our sample size on prior work in this areainvestigating cross-sensory effects in early sensory areas with MVPA -that has all used a similar sample size of 10 or fewer [START_REF] Meyer | Seeing touch is correlated with content-specific activity in primary somatosensory cortex[END_REF][START_REF] Vetter | Decoding sound and imagery content in early visual cortex[END_REF][START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF][START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]; see also [START_REF] Wang | Population Receptive Field Characteristics in the between-and Within-Digit Dimensions of the Decoding hand-object sounds in primary somatosensory cortex Undominant Hand in the Primary Somatosensory Cortex[END_REF][START_REF] De Borst | fMRI-based Multivariate Pattern Analyses Reveal Imagery Modality and Imagery Content Speci fi c Representations in Primary Somatosensory , Motor and Auditory Cortices[END_REF]. No power analysis was conducted. All participants reported normal or corrected-to-normal vision, and normal hearing, and were deemed eligible after meeting MRI screening criteria, approved by the Scannexus MRI centre in Maastricht. Written consent was obtained in accordance with approval from the Research Ethics Committee of the School of Psychology at the University of East Anglia. Participants received €24 euros (equivalent to £20 sterling British pounds) for their time.

Stimuli & Design

Three different categories of auditory stimuli were used in a rapid event-related fMRI design; sounds depicting hand-object interactions, animal vocalizations, and pure tones. There were five different sub-categories within each of these categories, with two exemplars of each subcategory, thus resulting in 30 individual stimuli in total. The five hand-object interaction Decoding hand-object sounds in primary somatosensory cortex stimuli consisted of bouncing a basketball, knocking on a door, typing on a keyboard, crushing paper, and sawing wood. These stimuli were chosen for the reason that participants should have previously either directly experienced rich haptic interactions with such objects, or observed such interactions. Two control categories were also used. Firstly, animal vocalizations were used as familiar sounds not directly involving interactions with the hands. These consisted of birds chirping, a dog barking, a fly buzzing, a frog croaking, and a rooster crowing. An independent ratings experiment confirmed these sounds were matched to the hand-object interactions for familiarity (1-7 scale: M = 5.31 for both hand-object interactions and animal vocalizations; see Supp. Table 1) and a further similarity rating experiment with an independent group of participants confirmed that the exemplars within the familiar sound categories were also matched for within-category similarity (see Supp. Figure 1 and Supp.

Text). Sounds from these two categories were downloaded from SoundSnap.com, YouTube.com, and a sound database taken from [START_REF] Giordano | Hearing living symbols and nonliving icons: Category specificities in the cognitive processing of environmental sounds[END_REF]. The second control category were non-meaningful sounds, defined as pure tones. These consisted of pure tones of five different frequencies (400Hz, 800Hz, 1600Hz, 3200Hz, and 6400Hz;2000ms duration), created in MatLab. All sounds were stored in WAV format, and were cut to exactly 2000ms using Audacity 2.1.2, with sound filling the entire duration. Finally, all sounds were normalised to the root mean square level (RMS: [START_REF] Giordano | Abstract encoding of auditory objects in cortical activity patterns[END_REF]). More information regarding how these sounds were selected, including pilot experiments and ratings for the sounds, can be seen in Supp. Text and Supp. Table 1.

Each run began and ended with 12s silent blocks of fixation. After the initial 12s fixation, 60 individual stimuli were played, with each unique sound presented twice per run.

Stimuli were played in a pseudo-randomly allocated order at 2s duration with a 3s ISI (5s trial duration; no jitter). At random intervals, 15 null trials (duration 5s) were interspersed where no sound was played. This resulted in a total run time of 399s. We note that rapid event related designs are often used in perception research with relatively short trial lengths and hence ISIs (see e.g. Giordano et al 2021; see also [START_REF] Smith | Nonstimulated early visual areas carry information about surrounding context[END_REF]Petro et al 2013) as a way of maximizing the number of repetitions obtained. We used small trial lengths with more trials in order to have more data for training and testing the MVPA classifier, which is an important consideration (see e.g. Pereira et al 2009). After the main experiment, a somatosensory localiser was included to map the hand region in the somatosensory cortex (see [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]. Piezo-electric Stimulator pads (Dancer Design, UK) were placed against the participant's index finger, ring finger, and palm of each hand using Velcro (six pads total, three per hand; see Supp. Figure 8 for a visual example on one hand). Each Decoding hand-object sounds in primary somatosensory cortex pad contained a 6mm diameter disk centred in an 8 mm diameter static aperture. The disks stimulated both hands simultaneously with a 25Hz vibration in a direction normal to the surface of the disk and skin, at an amplitude within the range of ±0.5mm). Localiser runs consisted of 15 stimulation blocks and 15 baseline blocks (block design, 12s on, 12s off, 366s total run time). Note that for the first two participants, a slightly modified timing was employed (block design, 30s on, 30s off; 10 stimulation blocks, 9 baseline blocks).

Procedure

After signing informed consent, each participant was trained on the experimental procedure on a trial set of stimuli not included in the main experiment, before entering the scan room. Participants were instructed to fixate on a black and white central fixation cross presented against a grey background whilst listening carefully to the sounds, which were played at a self-reported comfortable volume (as in [START_REF] Kriegeskorte | Cortical Representation of Natural Complex Sounds: Effects of Acoustic Features and Auditory Object Category[END_REF][START_REF] Meyer | Predicting visual stimuli on the basis of activity in auditory cortices[END_REF][START_REF] Man | Sight and sound converge to form modalityinvariant representations in temporoparietal cortex[END_REF][START_REF] Man | Convergent and invariant object representations for sight, sound, and touch[END_REF]. Participants performed a one-back repetition counting task, and hence counted the number of times they heard any particular sound repeated twice in a row, for example, two sounds each of a dog barking (randomly allocated from 2 to 6 per run).

We chose this task as it was important that the task did not require an explicit motor action such as pressing a button, to prevent a possible confound in somatosensory cortex activity (see [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]. Thus, participants verbally stated the number of counted repetitions they heard at the end of each run, and they were explicitly asked to not make any movements in the scanner unless necessary. Overall, most participants completed either 8 or 9 runs (with the exception of one participant, who completed 7), thus, participants were exposed to approximately 32-36 repetitions per stimulus, and 16-18 repetitions per unique sound exemplar. After the main experiment, participants took part in the somatosensory mapping localiser. Participants were not informed about this part of the experiment until all main experimental runs had been completed. Each participant completed 1 (N = 2) or 2 (N = 8) somatosensory mapping runs, and kept their eyes fixated on a black and white central fixation cross presented against a grey background for the duration of each run. Participants were debriefed after completion of all scanning sessions.

MRI Data Acquisition

Structural and functional MRI data was collected using a high-field 3-Tesla MR scanner (Siemens Prisma, 64 channel head coil, Scannexus, Maastricht, The Netherlands).

High resolution T1 weighted anatomical images of the entire brain were obtained with a Decoding hand-object sounds in primary somatosensory cortex three-dimensional magnetization-prepared rapid-acquisition gradient echo (3D MPRAGE) sequence (192 volumes, 1mm isotropic). Blood-oxygen level dependent (BOLD) signals were recorded using a multiband echo-planar imaging (EPI) sequence: (400 volumes, TR = 1000ms; TE = 30ms; flip angle 77; 36 oblique slices, matrix 78 x 78; voxel size = 2.5mm 3 ; slice thickness 2.5mm; interslice gap 2.5mm; field of view 196; multiband factor 2). A short five volume posterior-anterior opposite phase encoding direction scan was acquired before the main functional scans, to allow for subsequent EPI distortion correction [START_REF] Jezzard | Correction for geometric distortion in echo planar images from B0 field variations[END_REF][START_REF] Fritz | Comparison of EPI distortion correction methods at 3T Decoding hand-object sounds in primary somatosensory cortex and 7T[END_REF]. Slices were positioned to cover somatosensory, auditory, visual, and frontal cortex. Sounds were presented via an in-ear hi-fi audio system (Sensimetrics, Woburn MA, USA), and the visual display was rear projected onto a screen behind the participant via an LCD projector. Finally, a miniature Piezo Tactile Stimulator (mini-PTS; developed by Dancer Design, UK) was used to deliver vibro-tactile stimulation to the hands, using the same fMRI sequence with a modified number of volumes (366s for the majority, slightly longer for the first two participants due to slightly different designsee

Stimuli & Design above).

MRI Data Pre-processing

Functional data for each main experimental run, in addition to somatosensory localiser runs, was pre-processed in Brain Voyager 20.4 (Brain Innovation, Maastricht, The Netherlands; [START_REF] Goebel | Analysis of functional image analysis contest (FIAC) data with Brainvoyager QX: From single-subject to cortically aligned group general linear model analysis and self-organizing group independent component analysis[END_REF], using defaults for slice scan time correction, 3D rigid body motion correction, and temporal filtering. Functional data were intra-session aligned to the pre-processed functional run closest to the anatomical scan of each participant. Distortion correction was applied using COPE 1.0 [START_REF] Fritz | Comparison of EPI distortion correction methods at 3T Decoding hand-object sounds in primary somatosensory cortex and 7T[END_REF], using the 5 volume scan acquired in the opposite phase encode direction (posterior to anterior) for each participant. Voxel displacement maps (VDM)'s were created for each participant, which were applied for EPI distortion correction to each run in turn. Functional data were then coregistered to the participant's ACPC anatomical scan. Note no Talairach transformations or spatial smoothing were applied, since such a transformation would remove valuable fine-grained pattern information from the data that may be useful for MVPA analysis [START_REF] Fischl | High-resolution intersubject averaging and a coordinate system for the cortical surface[END_REF][START_REF] Argall | Simplified intersubject averaging on the cortical surface using SUMA[END_REF][START_REF] Goebel | Analysis of functional image analysis contest (FIAC) data with Brainvoyager QX: From single-subject to cortically aligned group general linear model analysis and self-organizing group independent component analysis[END_REF][START_REF] Kriegeskorte | Cortical Representation of Natural Complex Sounds: Effects of Acoustic Features and Auditory Object Category[END_REF]. For the main MVPA analyses (described further below) we conducted a GLM analysis independently per run per participant, with a different predictor coding stimulus onset for each unique stimulus presentation (3 categories X 5 within-sub categories X 2 unique exemplars, each repeated twice = 60 predictors) convolved with a standard double gamma model of the haemodynamic Decoding hand-object sounds in primary somatosensory cortex response function (see [START_REF] Smith | Nonstimulated early visual areas carry information about surrounding context[END_REF][START_REF] Greening | Spatially generalizable representations of facial expressions: Decoding across partial face samples[END_REF]). The resulting betaweight estimates are the input to the pattern classification algorithm described below (see

Multi-Voxel Pattern Analysis).

The somatosensory mapping localiser data was analysed using a GLM approach, with one predictor defining stimulation onset convolved with the standard double gamma model of

Regions of Interest

Anatomical mask of SI

In order to accurately capture the potential contribution from each sub-region of SIi.e. area 3a, 3b, 1 or 2, hand-drawn masks of the PCG were created in each individual participant [START_REF] Meyer | Seeing touch is correlated with content-specific activity in primary somatosensory cortex[END_REF][START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]. This allowed us to go beyond the capabilities of the somatosensory localiser alone, by enabling inclusion of all the information potentially availablei.e. both tactile and proprioceptive -in SI for the pattern classification algorithms (see Smith and Goodale 2015 for further information).

Anatomical masks were created using MRIcron 6 [START_REF] Rorden | Improving Lesion-Symptom Mapping[END_REF]) using each participant's anatomical MRI scan in ACPC space. As in Meyer et al. [START_REF] Meyer | Seeing touch is correlated with content-specific activity in primary somatosensory cortex[END_REF]) and Smith and Goodale [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF], the latero-inferior border was taken to be the last axial slice where the corpus callosum was not visible. From anterior to posterior the masks were defined by the floors of the central and post-central sulci. Furthermore, masks did not extend to the medial wall in either hemisphere [START_REF] Meyer | Seeing touch is correlated with content-specific activity in primary somatosensory cortex[END_REF][START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]. This resulted in an average of 41 slices (total range 39 to 46) for each hemisphere per participant. The average voxel count was 1969 (SD = 229) for the right PCG, and 2106 (SD = 215) for the left PCG, which did not significantly differ from one another (see Figure 1 and Supp. Figures 2 &3).

SI Tactile Mask

We also created a sub-sampled version of the SI anatomical mask per participant which comprised the 100 most activated voxels in response to tactile stimulation of the hands from the tactile localizer scan (see above). The rationale for including this additional ROI is Decoding hand-object sounds in primary somatosensory cortex two-fold: first, it allows us to isolate whether any effects are present within tactile sensitive voxels in S1 as has been evident in our previous work (see [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]; see also Perez-Bellido et al 2018 for a comparable approach). Second, the analysis permits the use of a much small number of voxels (100 vs ~2000) allowing the influence of ROI size to be taken into account. An example of the somatosensory localizer activation is shown in Figure 1 (see Supp. Figure 4 for group activation). From this point onwards, this ROI will be referred to as SI -Tactile.

FIGURE 1 HERE

Additional Regions of Interest

In order to define a series of additional ROIs we used Freesurfer (version 6.0.0) together with the Glasser parcellation [START_REF] Glasser | A multimodal parcellation of human cerebral cortex[END_REF]). The atlas annotation files were converted to fsaverage coordinates [START_REF] Fischl | High-resolution intersubject averaging and a coordinate system for the cortical surface[END_REF]) and from there mapped to each individual participant's cortical reconstruction via spherical averaging (see [START_REF] Kietzmann | Recurrence is required to capture the representational dynamics of the human visual system[END_REF]. We defined each region, independently per hemisphere, according to the detailed specification given in Glasser et al. [START_REF] Glasser | A multimodal parcellation of human cerebral cortex[END_REF]): Early Auditory Cortex (Areas M, P & L Belt, A1 and RI), Pre-Motor cortex (Areas 6a, 6d, 6r, 6v, FEF, PEF and area 55b), Primary Motor Cortex (Area 4), Secondary Somatosensory Cortex (Areas OP1-4; see Eickhoff, Amunts, et al. 2006;[START_REF] Eickhoff | The human parietal operculum. I. Cytoarchitectonic mapping of subdivisions[END_REF][START_REF] Keysers | Somatosensation in social perception[END_REF] and Primary Visual Cortex (Area V1). Finally, we used the co-registration procedure in Brain Voyager to align the native space anatomy from Free Surfer with that of the functional data in ACPC space. In Figure 1 we show each of these regions in surface space for a representative participantand in Supp. Figure 3 these regions are displayed for each individual participant (see Supp. Table 2 for mean volume for each additional ROI).

Multi-Voxel Pattern Analysis

For the multi-voxel pattern analysis (MVPA; e.g. Haynes 2015), we trained a linear support vector machine (SVM) to learn the mapping between the spatial patterns of brain activation generated in response to each of the five different sounds within a particular sound category ( for example: for hand-object interactions, the classifier was trained on a five way discrimination between each relevant sub-category: typing on a keyboard, knocking on a Decoding hand-object sounds in primary somatosensory cortex door, crushing paper and so on; [START_REF] Smith | Nonstimulated early visual areas carry information about surrounding context[END_REF][START_REF] Vetter | Decoding sound and imagery content in early visual cortex[END_REF][START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF][START_REF] Greening | Spatially generalizable representations of facial expressions: Decoding across partial face samples[END_REF]. The classifier was trained and tested on independent data, using a leave one run out cross-validation procedure [START_REF] Smith | Nonstimulated early visual areas carry information about surrounding context[END_REF][START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]. The input to the classifier was always single trial brain activity patterns (beta weights) from a particular ROI while the independent test data consisted of an average activity pattern taken across the repetitions of specific exemplar in the left out run (e.g. the single trial beta weights of the four presentations of 'bouncing a ball' in the left out run were averaged). We have used this approach successfully in previous studies, as averaging effectively increases the signal to noise of the patterns [START_REF] Smith | Nonstimulated early visual areas carry information about surrounding context[END_REF][START_REF] Vetter | Decoding sound and imagery content in early visual cortex[END_REF][START_REF] Muckli | Contextual Feedback to Superficial Layers of V1[END_REF]. For similar approaches applied to EEG and MEG data, see Smith and Smith [START_REF] Smith | Decoding the dynamic representation of facial expressions of emotion in explicit and incidental tasks[END_REF]) and Grootswagers, Wardle, and Carlson [START_REF] Grootswagers | Decoding Dynamic Brain Patterns from Evoked Responses: A Tutorial on Multivariate Pattern Analysis Applied to Time Series Neuroimaging Data[END_REF] respectively.

Finally, we used the LIBSVM toolbox [START_REF] Chang | LIBSVM: a library for support vector machines[END_REF] to implement the linear SVM algorithm, using default parameters (C = 1). LIBSVM uses the one vs one method for multiclass classification [START_REF] Chang | LIBSVM: a library for support vector machines[END_REF]. The activity pattern estimates (beta weights) within each voxel in the training data was normalised within a range of -1 to 1, prior to input to the SVM [START_REF] Smith | Nonstimulated early visual areas carry information about surrounding context[END_REF][START_REF] Chang | LIBSVM: a library for support vector machines[END_REF][START_REF] Vetter | Decoding sound and imagery content in early visual cortex[END_REF][START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF][START_REF] Greening | Spatially generalizable representations of facial expressions: Decoding across partial face samples[END_REF][START_REF] Knights | Hand-Selective Visual Regions Represent How to Grasp 3D Tools : Brain Decoding during Real Actions[END_REF]. The test data were also normalised using the same parameters as in the training set, in order to optimise classification performance. To test whether group level decoding accuracy was significantly above chance, we performed non-parametric Wilcoxon signed-rank tests using exact method on all MVPA analyses, against the computed empirical chance level [START_REF] Formisano | Who" is saying "what"? Brainbased decoding of human voice and speech[END_REF][START_REF] Greening | Spatially generalizable representations of facial expressions: Decoding across partial face samples[END_REF], with all significance values reported two-tailed. We used a permutation approachrandomly permuting the mapping between each condition and each label, independently per run, to calculate the empirical chance level for each participant and each decoding analysis separately (we note here that the average empirical chance level across all participants, regions and analyses was 0.202, with a standard deviation of .0061, which is very close to the theoretical chance level of 0.20). We implemented control for multiple comparisons by using the False Discovery Rate (q < .05) method [START_REF] Benjamini | The control of the false discovery rate in multiple testing under dependency[END_REF]. Effect sizes are reported for the Wilcoxon tests using the Z/sqrt(N) formula [START_REF] Rosenthal | Meta-analytic procedures for social research[END_REF]. In each region where decoding accuracy was significant for any category, we conducted follow-up tests between each sound category again with Wilcoxon signed rank tests (two tailed, FDR corrected for multiple comparisons across all regions showing significant decoding effects; see [START_REF] Knights | Hand-Selective Visual Regions Represent How to Grasp 3D Tools : Brain Decoding during Real Actions[END_REF] Decoding hand-object sounds in primary somatosensory cortex

Univariate Deconvolution Analysis

In order to examine whether there were univariate differences between sound categories in each ROI we performed a deconvolution analysis (see [START_REF] Smith | Nonstimulated early visual areas carry information about surrounding context[END_REF][START_REF] Petro | Contributions of cortical feedback to sensory processing in primary visual cortex[END_REF]. In this analysis, there were 20 predictors (each TR=1s here) to cover the full extent of the HRF response for each stimulus presented in a given condition (so 60 predictors in total, plus confounds for each experimental run). We then used an ANOVA approach to ask whether the average beta weight across time points 5-8s, corresponding to the peak of the HRF, were significantly different across sound categories, hemisphere and ROI.

Erosion Analysis

We also performed a subsequent decoding analysis where we eroded the closest voxels between neighbouring (EAC and SII) and relatively near (SI and PMC) ROIs that displayed significant effects in a systematic manner in order to demonstrate that the decoding effects found in nearby areas are not trivially due to partial volume effects or other spatial artifacts [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]. Our approach (see [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]) involved computing the Euclidean distance between each voxel's position in each relevant ROI pair (in ACPC space) and then removing those voxels deemed closest in several discrete steps (1-7mm; see Supp. Figure 6). We show FDR-corrected decoding accuracy as a function of distance to the nearest voxel in the neighbouring ROI (see Figure 3). We also plotted the univariate signal as a function of distance to the nearest voxel (see Supp. Figure 7).

Results

Bilateral anatomical masks of the lateral postcentral gyri (SI) were manually defined in each participant (see Figure 1 & Methods) whilst a subject-specific cortical parcellation was used to define a set of additional regions of interest (see Methods). We computed crossvalidated decoding performance of sound identity for each sound category independently (hand-object interactions; animal vocalizations, and pure tones control) in each ROI, and report FDR-corrected effects on decoding accuracy below.

Decoding hand-object sounds in primary somatosensory cortex

Primary Somatosensory Cortex

As expected, significantly above-chance decoding was found for hand-object interaction sounds in left SI (Med = 30.56%; p = .0195; d =.73), right SI (Med = 23.65%; p = .0273; d = .69) and pooled SI (Med = 28.75%; p = .0098; d = .79); signed rank, two-tailed test, versus subject-specific empirical chance level, FDR corrected (see Figure 2A).

Crucially, the same analyses for our two control categories of familiar animal vocalizations and unfamiliar pure tones did not show any significant decoding above chance in right, left, or pooled SI (all p's > .432). When pooled across hemispheres, SI showed reliably greater decoding for hand-object interactions than pure tones (p = .0156, d = .75; FDR corrected, signed rank, two-tailed test). No other differences between sound categories in any subregion were significant (all p's > .0527). The confusion matrices underlying the classification performance can be seen in Supp. Figure 4. Thus, SI carries content-specific information for the hand-object interaction sounds which convey haptic properties with the hands, regardless of hemisphere.

FIGURE 2 HERE

We sought to corroborate the above finding when selecting the top 100 most active voxels in each sub-region of SI from the independent somatosensory localiser (SI -Tactile; see Methods) as an independent means of selecting a subset of sensitive voxels in the present task (see Smith and Goodale 2015; see also [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]). These analyses revealed significant decoding for hand-object interactions only in left SI (Med = 29.44%; p = .009, d = .79); signed rank, two-tailed test, versus subject-specific empirical chance level, FDR corrected (see Figure 2B). Critically, decoding accuracies for hand-object interactions in left SI were significantly higher than for pure tones (Hands vs Tones: p = .006, d = .82) while the predicted difference between hand-object interactions and animal vocalizations was not significant after FDR correction (Hands vs Animal Vocalizations: p = .0195, d =.55). In agreement with the previous analyses using the entire SI, no other sound categories were decoded above chance (all p's ≥ .232). These results show the classifier could reliably decode only hand-object interaction sounds above chance when constrained to the hand-sensitive voxels in left SI, with accuracies that were significantly higher than the pure tone control sounds. Thus sounds depicting hand-object interactions were reliably discriminated when Decoding hand-object sounds in primary somatosensory cortex restricting the MVPA analysis to voxels with high responses to tactile stimulation of the right, but not left, hand.

Additional Regions of Interest

Using a recently published cortical surface based parcellation atlas [START_REF] Glasser | A multimodal parcellation of human cerebral cortex[END_REF] we defined several additional control regions that we expected to be important in the present task (see Figure 1 & Methods; see also [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF].

Early Auditory Cortex.

As would be expected, decoding in early auditory cortex (EAC) was robustly significant for all sound categories (all Meds ≥ 68%, all p's ≤ .002, all d's >= .884; signed rank, two-tailed test, versus subject-specific empirical chance level, FDR corrected: see Figure 2C). In each sub-region of EAC decoding accuracy was significantly better for pure tones than hand object interactions (all p's ≤ .0059, all d's ≥ .82), whilst pure tones were also decoded better than animal vocalizations Left and Right EAC (both p's ≤ .0078, both d's ≥ .81). Furthermore, decoding was greater for animal vocalizations than hand-object interactions in both Left and Right EAC (both p's ≤ .0117, both d's ≥ .77). Thus in EAC, all sound categories were highly discriminated with the specific pattern of decoding suggesting the opposite to that in SI, with better decoding of pure tones, followed by animal vocalizations, then hand-object interaction sounds.

Secondary Somatosensory Cortex.

Decoding in SII was robustly significant for all sound categories in each hemisphere (all Meds ≥ 47.80%, all p's ≤ .0039, all d's ≥ .85; signed rank two-tailed test versus subjectspecific empirical chance level, FDR corrected; see Figure 2C). In Left SII, decoding accuracy was significantly better for pure tones than for hand-object interactions (p = .004, d = .85) whilst the difference between pure tones and animal vocalizations was not significant (p = .080, d = .56). In Right SII, decoding was significantly higher for animal vocalizations than hand-object interactions (p = .004, d = .85), and for pure tones than for hand-object interactions (p = .002, d = .89) but again there was no significant difference between animal vocalizations and pure tones (p = .078, d = .58). When pooling across hemispheres, higher decoding for animal vocalizations than hand-object interactions (p = .002, d = .89) and for pure tones than hand-object interaction (p = .004, d = .84) was found. Thus in SII better Decoding hand-object sounds in primary somatosensory cortex decoding was found for both pure tones and animal vocalizations than for hand-object interactions.

Pre-Motor Cortex.

In pre-motor cortex (PMC), significantly above chance decoding was found for handobject interactions in right PMC (Med = 27.5%; p = .002, d = .89), left PMC (Med = 29.31%, p = .0039, d = .85) and pooled PMC (Med = 31.25%, p = .0098, d = .79), signed rank twotailed test versus subject-specific empirical chance level, FDR corrected (see Figure 2D). In addition, significant decoding of animal vocalizations was found in Left (Med = 28.80; p = .0273, d = .69), Right (Med = 33.1; p = .004, d = .85) and Pooled PMC (Med = 32.2; p = .002, d = .89), and of pure tones again in Right (Med = 30.54; p = .004, d = .86) and Pooled PMC (Med = 28.89; p = .002, d = .79). There were no significant differences in decoding accuracy after FDR correction in any ROI (all p's > .107, all d's ≤ .51). Thus PMC contains information about multiple types of sound category in each hemisphere.

Primary Motor Cortex.

Decoding accuracies in primary motor cortex (M1) revealed no reliable above-chance decoding after FDR correction (all p's > 0.13, all d's ≤ .50; signed rank two-tailed test versus subject-specific empirical chance level, FDR corrected; see Figure 2E).

Primary Visual Cortex.

Decoding accuracies in primary visual cortex (V1) revealed no significant above chance decoding after FDR correction (all p's ≥ .037, all d's ≤ .66; signed rank two-tailed test versus subject-specific empirical chance level, FDR corrected; see Figure 2F).

Erosion Analysis

As some regions showing significant decoding are either directly neighbouring to one another (EAC and SII) or relatively close at specific locations (SI and PMC) and showed similar decoding effects, we performed a control analysis (Figure 3) where we eroded a portion of the voxels (in 1mm steps from 1-7 mm, see Methods & Supp. Fig 5) from each ROI to minimize the contribution of partial volume effects or other spatial artifacts to the effects observed (see [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]). These analyses reveal that decoding Decoding hand-object sounds in primary somatosensory cortex remained significant even when the closest 3mm voxels were discarded in both Left SI and Left PMC for hand-object interaction sounds (two tailed signed rank tests against subjectspecific empirically determined chance levels, FDR corrected -see Figure 3A). In addition, significant effects were present in each region of EAC and SII for each sound category at all eroded voxel levels (two tailed signed rank tests against per participant empirically determined chance levels, FDR corrected, see Figure 3B). Thus the key effects observed in somatosensory brain areas to sound stimuli are unlikely to be due to partial volume or spillover effects from neighbouring or nearby regions that also display significant effects in the present experiment.

Univariate Analysis

Finally, we examined the univariate responses to each stimulus category in each ROI (Figure 4: deconvolution analysis). As expected, strong responses were evident in EAC but also in SII. However, the signal was much weaker in SI, M1, PMC and V1. A three-way ANOVA (Sound Category, Hemisphere and Region) revealed a significant three-way interaction (F20, 180 = 4.60, p < .001), as such separate 2-way ANOVAS were run in each region separately. There were no reliable main effects or interactions in SI, V1, M1 (all p's > .179) or in PMC (all p's > .053). However in EAC there was a significant interaction between Sound Category and Hemisphere: F2.79, 25.15 = 7.25, p = .001. In each sub-region of EAC however, both animal vocalizations and hand-object interactions produced stronger activity than pure tones (all corrected p's ≤ .0167) but there was no difference between the two former categories (both p's ≥ .639). In contrast, in SII only the effect of Sound Category was significant (F1.60, 14.40 = 9.73, p =.003), with higher amplitude for animal vocalizations than either hand-object interactions or pure tones (corrected p's ≤ .016) but no significant difference between the latter two (corrected p = .099). Thus there is preferential activation of EAC for familiar sound categories (hand object interactions and animal vocalizations) versus pure tones, whereas in SII preferential activation is observed only for the animal vocalizations versus each other category. In SI however, there is no evidence of significant univariate differences between sound categories (we note that the same is true for the tactilesensitive voxel subsetall p's ≥ .33).

Decoding hand-object sounds in primary somatosensory cortex

Discussion

In the present study we show that hearing sounds depicting familiar hand-object interactions elicit significantly different patterns of activity in primary somatosensory cortex (SI), despite the complete absence of external tactile stimulation. Such decoding was not found for two control categories of familiar animal vocalizations, and unfamiliar pure tones, in any analysis involving SI. Moreover, decoding accuracies were significantly higher for hand-object interaction sounds compared to pure tones when restricted to the independently localized hand-sensitive voxels of the left SI (or when pooling across hemispheres using the entire SI). We further show that SIIa higher order somatosensory regionshows reliable decoding for all sound categories presented. Control analyses demonstrated that these effects in SI and SII were not driven by proximity to nearby regions also displaying significant effects (PMC and EAC respectively). Thus, fine-grained information about different sound categories is present within both primary (SIhand-object interactions) and higher somatosensory brain areas (SII -hand-object interactions, animal vocalizations and pure tones).

Representation of Sound Categories in Somatosensory Cortices

The present findings are in broad agreement with previous work showing auditory responses in early somatosensory areas [START_REF] Zhou Y Di | Somatosensory cell response to an auditory cue in a haptic memory task[END_REF][START_REF] Beauchamp | Neural Substrates of Sound-Touch Synesthesia after a Thalamic Lesion[END_REF][START_REF] Lemus | Do sensory cortices process more than one sensory modality during perceptual judgments?[END_REF][START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]. In particular, the current study partially replicates Pérez-Bellido et al. [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]) by showing reliable discrimination of pure tone stimuli in SII, even after eroding voxels close to the border with early auditory areas to control the possible influence of partial volume effects. The current study extends this previous work by showing that A) SII further discriminates different exemplars within specific high level sound categories (hand-object interactions and animal vocalizations) and that B) SI contains representations that discriminate particular high level sound categories (hand-object interactions) but not others (animal vocalizations and pure tones) and may manifest a degree of functional specialization for specific sound categories (Left SI -tactile sensitive voxels and also in Pooled SI entire region for hand-object interaction sounds vs pure tones).

Interestingly, when analyses were split by hemisphere and by different putative areas (specifically SI) in [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF], effects were only found when voxels responsive to auditory stimulation in an independent localizer were used to define the regions. Defining the regions using voxels responsive to tactile stimulation did not Decoding hand-object sounds in primary somatosensory cortex lead to any reliable effects for their pure tone stimuli in putative SI. In contrast, in the present experiment we show that selecting voxels responsive to tactile stimulation of the hand produced robust discrimination in Left SI for sounds depicting hand-object interactions but not others (animal vocalizations or pure tones). Thus, it might be the case that early somatosensory regions contain information about multiple types of sound category but that the method used to select voxels for input to the analysis is critical in determining the effects that are found. This may be particularly the case given that somatosensory cortices are involved in more than just sensory processing of touchbeing also implicated in processing of emotional states for instance [START_REF] Adolphs | Neural systems for recognizing emotion[END_REF][START_REF] Keysers | Somatosensation in social perception[END_REF]).

The findings observed in SII (and also premotor cortexsee below) of reliable decoding for all sound categories suggest the involvement of the dorsal auditory stream [START_REF] Rauschecker | Mechanisms and streams for processing of "what" and "where" in auditory cortex[END_REF][START_REF] Bizley | The what, where and how of auditory-object perception[END_REF]. This pathway -originating in posterior auditory regions and linking to IPL and then premotor areas -is thought to be involved in linking sounds to the actions that have produced them and as such in sensorimotor integration and control [START_REF] Rauschecker | Ventral and dorsal streams in the evolution of speech and language[END_REF]. Importantly neurons responsive to tactile stimulation are present in posterior auditory cortex (e.g. [START_REF] Fu | Auditory cortical neurons respond to somatosensory stimulation[END_REF]; see also [START_REF] Rauschecker | Maps and streams in the auditory cortex: Nonhuman primates illuminate human speech processing[END_REF] and these may contribute towards the effects we observe in SII (see [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF].

Triggering cross-modal content-specific information in SI from audition

The present study agrees with a set of studies that show fine-grained representation of distal sensory categories even in the earliest regions of supposedly unimodal primary sensory areas, across multiple sensory domains [START_REF] Meyer | Predicting visual stimuli on the basis of activity in auditory cortices[END_REF][START_REF] Vetter | Decoding sound and imagery content in early visual cortex[END_REF]Smith and Goodale 2015; see also [START_REF] Pérez-Bellido | Auditory Frequency Representations in Human Somatosensory Cortex[END_REF]. Our results significantly extend this previous body of work by demonstrating, for the first time, that a similar effect is present across the domains of audition and touch for particular familiar sound categories. It is important to note, furthermore, that the pattern of decoding performance was different in SI and in auditory cortex, with better decoding of pure tones than hand-object interactions in auditory cortex whereas SI showed some evidence for better decoding of hand-object interactions than pure tones in particular analyses (Left SI tactile sensitive voxels, SI entire region pooled across hemispheres). As such we suggest that the present results in SI are unlikely to reflect passive relay of low-level acoustic features from auditory cortex via the auditory dorsal stream [START_REF] Rauschecker | Mechanisms and streams for processing of "what" and "where" in auditory cortex[END_REF][START_REF] Bizley | The what, where and how of auditory-object perception[END_REF].

Decoding hand-object sounds in primary somatosensory cortex

The current results expand on our earlier study that showed simply viewing images of familiar graspable objects led to reliable decoding in SI [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]; see also [START_REF] Meyer | Seeing touch is correlated with content-specific activity in primary somatosensory cortex[END_REF]. Thus either viewing images or hearing sounds of particular objectsi.e. those related to hand-object interactions-triggers fine-grained representations of those objects in SI. What might be the function of this cross-sensory information being present in SI? If Predictive Processing is assumed to be the general computational function of the brain [START_REF] Friston | The free-energy principle: a rough guide to the brain?[END_REF][START_REF] Friston | Predictive coding under the free-energy principle[END_REF][START_REF] Clark | Whatever next? Predictive brains, situated agents, and the future of cognitive science[END_REF], then it may be the case that either seeing a familiar graspable object, or hearing the sounds depicting a familiar hand-object interaction, leads to fine-grained activation of associated tactile/haptic features in SI that is useful for future interaction with the specific object (see Pérez-Bellido et al. 2018 for a related explanation; see also [START_REF] Jacobs | Can multisensory training aid visual learning? A computational investigation[END_REF]. The strength of this effect would be expected to be determined by the magnitude of co-occurrence of sensory stimulation across audition and touch for particular object categories [START_REF] Meyer | Convergence and divergence in a neural architecture for recognition and memory[END_REF]; see also [START_REF] Jacobs | Can multisensory training aid visual learning? A computational investigation[END_REF].

How does auditory stimulation lead to content-specific information being present in SI? There are several possible anatomical routes through which this could be accomplished (see e.g. [START_REF] Driver | Multisensory Interplay Reveals Crossmodal Influences on "Sensory-Specific" Brain Regions, Neural Responses, and Judgments[END_REF]. First, auditory information may first arrive at high level multisensory convergence zones, such as pSTS, posterior parietal cortex or ventral premotor areas, before such areas then send feedback to SI (see [START_REF] Driver | Multisensory Interplay Reveals Crossmodal Influences on "Sensory-Specific" Brain Regions, Neural Responses, and Judgments[END_REF][START_REF] Meyer | Convergence and divergence in a neural architecture for recognition and memory[END_REF]; see also [START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF]. Another possible high-level convergence site is the fusiform gyrus, since Kassuba et al. [START_REF] Kassuba | Multisensory interactions between auditory and haptic object recognition[END_REF] found semantically coherent auditory and haptic object features activated this area. Second, auditory information may be directly projected to SI, without passing through such higher multisensory regions. Such direct connections have been found in animal models between certain sensory pairings: e.g. from primary auditory to primary visual cortex (e.g. [START_REF] Falchier | Anatomical evidence of multimodal integration in primate striate cortex[END_REF][START_REF] Falchier | Projection from visual areas V2 and prostriata to caudal auditory cortex in the monkey[END_REF] and between primary auditory and somatosensory cortex [START_REF] Budinger | Multisensory processing via early cortical stages: connections of the primary auditory cortical field with other sensory systems[END_REF]; see also [START_REF] Cappe | Heteromodal connections supporting multisensory integration at low levels of cortical processing in the monkey[END_REF]. However it has been proposed that such direct connections are relatively sparse as opposed to the amount of feedback arriving from higher multisensory areas [START_REF] Driver | Multisensory Interplay Reveals Crossmodal Influences on "Sensory-Specific" Brain Regions, Neural Responses, and Judgments[END_REF]. Finally a third possibility is the involvement of lower tier multisensory regions [START_REF] Driver | Multisensory Interplay Reveals Crossmodal Influences on "Sensory-Specific" Brain Regions, Neural Responses, and Judgments[END_REF] that are anatomically located next to primary sensory areas: for instance auditory regions located close to SII may be bimodal responding to both auditory and tactile information (see e.g. [START_REF] Wallace | A revised view of sensory cortical parcellation[END_REF][START_REF] Cappe | Heteromodal connections supporting multisensory integration at low levels of cortical processing in the monkey[END_REF]. Our current results clearly highlight robust information about all sound categories in both SII and also in premotor cortices (Rightall categories; Lefthand object interactions and animal Decoding hand-object sounds in primary somatosensory cortex vocalizations)and as such these regions may be involved in transmitting information back to SI about specific sound categories. However, this would not explain why decoding in Left SI (hand sensitive voxels) is higher for hand-object interactions than pure tonesthe opposite of the pattern observed in SII, while no differences between categories were observed in premotor areas. Thus, the specific route by which such information is transmitted to SI is something that will need to be addressed in future research.

The role of prior audio-haptic experience

In the present study we only ever found reliable decoding of hand-object interactions in SI regardless of whether the analysis used the entire SI anatomical mask or a small subset of tactile sensitive voxels. Critically, when limited to hand sensitive voxels in Left SI was there a reliable difference between hand-object interactions and our low-level pure tone control stimuli. This difference was also apparent when pooling across hemispheres using the SI anatomical mask. Thus, we demonstrate a degree of functional specialization for handobject interactions in some SI analyses: particularly in the Left SI hand sensitive voxels.

However, it is important to highlight that we did not find any evidence of significantly greater decoding for hand-object interaction sounds than our high-level control of animal vocalizations. As such, it is possible that similar effects may be present in SI for familiar sound categories in general, especially when one considers the multifaceted role of SI in both somatosensation but also higher-level socio-emotional processing [START_REF] Keysers | Somatosensation in social perception[END_REF].

Future studies should set out to explicitly dissociate the influence of these features on crossmodal activity in early somatosensory regions.

Decoding Sound Categories in (Pre-) Motor Regions

In Left PMC we found reliable decoding of both familiar categories whereas in the Right and Pooled PMC we found reliable decoding of all sound categories. We did not find any differences between sound categories in any PMC sub-region. Thus, premotor cortex contains information about all sound categories presented, across the two hemispheres.

Finding reliable decoding for multiple sound categories in PMC is consistent with multiple theoretical accounts: first, the relatively non-specific pattern of decoding implicates the auditory dorsal stream [START_REF] Rauschecker | Mechanisms and streams for processing of "what" and "where" in auditory cortex[END_REF][START_REF] Bizley | The what, where and how of auditory-object perception[END_REF] which terminates in premotor areas and would be expected to contain information about all types of sound presented. While PMC is also known to play a large role in processing action related Decoding hand-object sounds in primary somatosensory cortex information through a potential mirroring mechanism [START_REF] Gallese | Action recognition in the premotor cortex[END_REF][START_REF] Gazzola | Empathy and the Somatotopic Auditory Mirror System in Humans[END_REF], this account would predict greater decoding for sounds strongly implying an association action (e.g. hand-object interaction & animal vocalizations) which we did not find in the current data (although Left PMC only showed decoding for both familiar object categories but not pure toneswhich may be partially in agreement with this view). Finally, the absence of decoding in primary motor areas (M1) is broadly consistent with past work in this area [START_REF] Lewis | Distinct Cortical Pathways for Processing Tool versus Animal Sounds[END_REF][START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF].

Conclusion

We have shown that the identity of familiar hand-object interaction sounds can be discriminated in SI, in the absence of any concurrent tactile stimulation. Our work provides converging evidence that activity in supposedly modality-specific primary sensory areas can be shaped in fine-grained manner by relevant contextual information originating in different sensory modalities [START_REF] Meyer | Predicting visual stimuli on the basis of activity in auditory cortices[END_REF][START_REF] Meyer | Seeing touch is correlated with content-specific activity in primary somatosensory cortex[END_REF][START_REF] Vetter | Decoding sound and imagery content in early visual cortex[END_REF][START_REF] Smith | Decoding visual object categories in early somatosensory cortex[END_REF].

Such an effect implies the potential for fine-grained multisensory interactions even in the earliest regions of sensory cortex.

Decoding hand-object sounds in primary somatosensory cortex

  the haemodynamic response function. The t-values were defined from the somatosensory localiser by taking the contrast of stimulation vs baseline in each participant. This allowed us to define the 100 voxels showing the strongest tactile response to hand stimulation in each individual's hand-drawn anatomical mask (see Regions of Interest below) of the post central gyrus (see Smith and Goodale 2015; Perez-Bellido et al 2018; for comparable analyses).

Figure 1 :

 1 Figure 1: Hand drawn anatomical mask of the SI ROI (Green) in a representative participant shown on an inflated cortical reconstruction of each hemisphere and in both medial and lateral views. Additional ROIs defined from the Glasser parcellation are also shown overlaid. The underlying activation shows the stimulation vs baseline contrast from the somatosensory hand localizer for the same participant (t > 3, p = .002, uncorrected). Warm colours signify stimulation > baseline and cool colours stimulation < baseline.

Figure 3 :Figure 4 :

 34 Figure 3: Erosion Analysis. (A) Decoding of sound identity in PMC and SI for each sound category and each ROI (split by hemisphere), as a function of the level of voxel erosion employed to eliminate the contribution of nearby voxels (1-7mm). (B) As in A except for EAC and SII. * = significant after FDR correction.