Time scale separation of information processing between sensory and associative regions

Stimulus perception is assumed to involve the (fast) detection of sensory inputs and their (slower) integration. The capacity of the brain to quickly adapt, at all times, to unexpected stimuli suggests that the interplay between the slow and fast processes happens at short timescales. We hypothesised that, even during resting-state, the flow of information across the brain regions should evolve quickly, but not homogeneously in time. Here we used high temporal-resolution Magnetoencephalography (MEG) signals to estimate the persistence of the information in functional links across the brain. We show that shortand long-lasting retention of the information, entailing different speeds in the update rate, naturally split the brain into two anatomically distinct subnetworks. The “fast updating network” (FUN) is localized in the regions that typically belong to the dorsal and ventral streams during perceptive tasks, while the “slow updating network” (SUN) hinges classically associative areas. Finally, we show that only a subset of the brain regions, which we name the multi-storage core (MSC), belongs to both subnetworks. The MSC is hypothesized to play a role in the communication between the (otherwise) segregated subnetworks.

Introduction channels with intrinsic operational times, resulting in a spatio-temporally nested activity (21,22) . In this scenario, the temporal unfolding of pairwise interactions might not be homogeneous throughout the brain network. In fact, some tasks might require quick interactions that are constantly reupdated, while other functions might instead require integration of more information, and consequently a longer time to unfold. In this line of thinking, it has been shown in the Macaque that areas that are hierarchically lower in information processing interact at higher velocities as compared to associative areas (which integrate information) (23) . Such differences in the integration process should reflect in the duration of effective interactions between areas. In this paper, we hypothesize that, if this is the case, then classifying the edges upon retention of information should naturally lead to topographic clustering separating low (retaining information only shortly) and high (retaining information longer -as to integrate it) hierarchical structures. Traditionally, time-resolved analyses have been performed using EEG. However, EEG is difficult to analyze and interpret because the electric fields are distorted and filtered between their sources and the recording sites. Hence, to test our hypothesis we have used source-reconstructed magnetoencephalographic (MEG) data from a cohort of 58 healthy subjects. MEG records the (weak) magnetic fields induced by post-synaptic electric activity. Given that the magnetic field is (almost) undistorted by the skull and meningeal sheets, MEG allows for an optimal trade-off between spatial and temporal resolution (24,25) . The temporal unfolding of the interactions between region signals was estimated based on the pairwise co-activations. This procedure defines a characteristic time series for each edge of the brain network (26) . The Auto Mutual Information (AMI) is used to estimate the time up to which the functional information is retained within each edge. Finally, we further hypothesized that specific regions should mediate the integration of groups of edges operating at different processing speeds. To test this, we built a multiplex network where each layer is filled by either fast or slow decaying edges, so as to pinpoint the set or regions that are relevant to both and, likely, mediate the temporal integration of the whole brain.

Functional connections store information differently
Using source-reconstructed magnetoencephalographic (MEG) data from a cohort of 58 healthy young subjects, we analyzed the temporal unfold of the pairwise correlations between the MEG source signals reconstructed in any couple of brain regions. Namely, for each functional edge in the brain network we extracted a time series which keeps track of the co-fluctuations of the MEG signals at the extremal nodes ( Fig.1.A) (See Materials and Methods) . Information theoretic tools were used in order to estimate the decay in time of the functional information within each edge. In particular, the Auto Mutual Information (AMI) was used to measure the amount of statistical dependence between any co-activation time series and its time-delayed copy (Mackay, 1995).
Repeating this operation for several delays, a profile of functional information decay was drawn for each edge of the brain network ( Fig.1.B). For short time delays, the high value of the AMI indicates little information loss. The AMI drops as we increase the time delay, suggesting a loss of functional information. A more rapid decay indicates faster information loss and, consequently, smaller information storage capability. The Functional Information Decay (FID) matrix in Figure 1.C shows the characteristic decay time for each couple of brain regions, indicating the average information storage capability within specific functional connections. From our analysis on the temporal properties of the network interactions, an organized spatial structure emerges, with heterogeneous basins each with a characteristic duration of information storage. This may entail different update rates across the brain network, in line with our working hypothesis that information buffering is not homogeneous.

Functional information storage discerns two brain subnetworks
The distribution of the decay times of the functional information reflects a different capability of storing information across the brain network ( Fig.2.A). Considering the edges populating the left and right tails of the distribution separately, we find two topographically segregated subnetworks characterized by short and long storage of the functional information, respectively. We expect that the different rates of information loss in the two subnetworks entail a different speed in the information re-updating. In the light of this interpretation, we refer to them as the fast-updating network (FUN) The multi-storage core defines brain regions hinging communication across subnetworks Following from the above results, we built a multiplex network, with the FUN and the SUN as the two layers (Fig3). Using the multiplex participation coefficient (MPC) we characterized each node based upon its connections within the FUN and the SUN layers. We discover the presence of specialized nodes (with low MPC), whose edges project selectively into a single layer (FUN or SUN). Furthermore, there exist nodes sharing their edges equally with both SUN and FUN layers. We define the latter group as the multi-storage core (MSC). Notice that the above definitions of SUN and FUN, as well as that of the MSC, depend on the choice of a threshold density (i.e., the number of edges) (see Fig.2 The MSC (Fig.4A) is hypothesized to play a role in the communication between the (otherwise) segregated subnetworks and, hence, to be able to integrate both fast and slow timescales. Intriguingly, the MSC naturally clusters around areas that are concerned with high-level processing of auditory stimuli, and speech in particular.
Regions involved in the MSC are reported in Table 1.

Discussion
In this paper, we set out to test the hypothesis that the information retained in the link between any two regions has a characteristic lifetime. To test this hypothesis, we estimated the decay of the mutual information of each edge co-activation signal. Based on this measure, we discover two complementary subnetworks. These networks appear to be robust across individuals (Fig.S2). We then proceeded to estimate whether some regions are simultaneously relevant in both (fast and slow) networks. To do so, we conceptualized the two different temporal networks as two layers of a multiplex network and estimated a nodal metric of concurrent participation to multiple layers, namely the multiplex participation coefficient (MPC) (27,28) . The distribution of the information decays naturally splits the functional network into two spatially segregated subnetworks: one with short storage capability, that we called fast updating network (FUN), and one with greater storage capability, that we named slow updating network (SUN) (Fig2.B-C). The FUN encompasses occipito-parietal and latero-frontal areas, while the SUN spans prefrontal areas and the temporal poles. Multiple models (29) and experimental evidence (30) show that the processing of external stimuli involves (bottom-up) perception and abstraction, as well as (top-down) interpretation according to expectations (priors), embodied in the internal brain state. In turn, such expectations are constantly updated according to new incoming environmental stimuli (31) .
Previous functional imaging data show that, on the one hand, the prefrontal cortex and areas related to memory storage are involved in top-down processing (30) , perhaps by facilitating the entrainment of incoming stimuli into already-existing neuronal ensembles (29) . On the other hand, parietal regions contribute to the bottom-up processing of visual tasks (30) . Our findings suggest that the division that arises from the timescale separation distinguishes regions involved in bottom-up perception, that are related to a faster timescale, as they need to quickly update external stimuli (FUN), and regions typically involved in top-down processing, operating more slowly (SUN), to allow for higher order integration of information. It has then been posited that communication that answers to different evolutive requirements is underpinned by frequency-specific channels. For example, Bastos et al. reported, in the visual cortical areas of two macaque monkeys, that feedforward influences operate in the gamma and theta band, while feedback influences operate in the beta band (32) . In humans, a recent paper applying phase transfer entropy to MEG data shows that two distinct, frequency-specific directed flows exist in resting-state, with an alpha-band forward flow, and a front-to-back flow in the theta band (33) . The two separated flows show some overlap with the FUN and the SUN networks, with the alpha flow partly overlapping the FUN, and the theta flow partly overlapping the SUN. While current evidence does not allow inference about such spatial relationships, one could speculate that the specific frequencies of oscillations might subserve the different velocities at which information needs to be processed across large-scale networks.
The FUN and SUN subnetworks are topographically distinct, as shown in Fig. 2.
Fast-updating edges are often incident upon occipital regions, although not uniformly.
In fact, it appears that the cunei and the occipital gyri are specifically involved in the FUN network. These regions roughly correspond to Brodmann areas 17, 18 and 19, and are known to be hierarchically related to the extraction of abstract shapes from the visual input. The cuneus directly receives inputs from the retina, that are subsequently processed up to the superior occipital gyrus, in the visual associative cortex, which is responsible of the perception of the properties of objects and plays a role, for instance, in face and object recognition (34,35) . The occipital regions are connected bilaterally to the inferior parietal gyrus (e.g.. the angular and supramarginal gyri as well as the inferior parietal lobe), the posterior temporal lobes and frontal/prefrontal cortex. The posterior part of the parietal lobe has been included in the "dorsal stream" of the visual systems, which is mainly concerned with the analysis of spatial relationships of objects, and the information about the position of the body in space (36) . With regard to the temporal lobe, the posterior part appears to be selectively involved in the FUN. From a structural standpoint, the inferior-longitudinal fasciculus (ILF), as well as an "indirect" stream of U-bundle fibers, connects the occipital and temporal areas (37) . Functionally, these regions are related to either the high-level analysis of images, such as the inferior temporal lobe, whose lesion compromises the ability to recognize facial expressions, or to the perception of-and attendance to auditory stimuli, as in the case of the superior temporal lobe (38) . Finally, in the frontal lobes, the FUN appears to involve the ventrolateral and dorsolateral prefrontal cortices, involved in higher functions such as allocation of attention, and typically considered the end of the ventral and dorsal streams, respectively (39,40) . In short, all the regions that are known to be relevant in the process of sensory information emerge as a temporally homogeneous fast network that quickly updates the information that is being processed, from visual and acoustic areas, through layers of abstraction, up to areas related to conscious perception.
The opposite network, to which we refer to as slow-updating network (SUN), clusters topographically in frontal and temporal regions. The regions involved in the SUN network appear to be linked anatomically by the uncinate fasciculus. In fact, the SUN mainly connects the orbitofrontal cortex within the frontal cortex to the temporal poles in the temporal lobes. Patients who underwent brain surgery involving the removal of the uncinate fasciculus showed impairment of verbal memory, naming of objects, verbal fluency, and name anomia. These symptoms did not appear in patients whose surgery did not encompass the removal of the connections between the orbitofrontal cortex and the temporal lobes (41) . Furthermore, the semantic variant of primary progressive aphasia and herpes encephalitis, both diseases that induce a damage to the temporal poles, cause disruptions in categorical discrimination, word comprehension and naming (42) . Recently, Warren et al. (43) , using fMRI showed that, during narrative speech comprehension, the left anterior basal temporal cortex shows high correlation with the left anterior basal frontal cortex, the left anterior inferior temporal gyrus as well as to the corresponding homotopic temporal cortex contralaterally. From a neurophysiological perspective, the N400 response is an event-related potential (ERP) evoked~400 ms after (potentially) meaningful material is presented. Using MEG, the N400 was localized in the superior temporal sulcus (44) , and intracranial recordings showed it originates in the anteroventral temporal lobe.
Furthermore, the FUN entails more long-range inter-hemispheric connections as compared to the SUN, which might suggest that inter-hemispheric coordination is specifically achieved via fast interactions (perhaps specifically relying on fast, white-matter bundles such as the corpus callosum).
Finally, we used multiplex -network analysis to distinguish regions that are important in both networks from those that are segregated in one layer only. We hypothesize that regions that are equally important in both networks would likely be the ones that allow functional integration between the FUN and the SUN, and this is why we shall refer to this group of nodes as the multi storage core (MSC). Regions that rank very high in the MSC are the Heschl's gyri and the Rolandic opercula, bilaterally. Superior and inferior frontal gyri are also mainly involved in the MSC. These regions are primarily concerned with language comprehension and retrieval, as well as secondary somatic and motor functions (45)(46)(47) . In conclusion, the MSC seems to localize mainly in regions that are high in the functional hierarchy mediating the cooperation of associative areas (interpretation) and lower areas (that convey and abstract the words). Being able to deal simultaneously with both fast and slow networks might underpin readiness to potentially meaningful stimuli. In fact, it has been proposed that acoustic stimuli must be analyzed at multiple timescales to correctly extract the meaning (48) . Hence, the MSC might represent a link between timescales that are proper of the environment (via bottom-up pathways) with intrinsic brain timescales (proper of top-down processes).
Together, our results are among the first ones to localize temporally coherent patterns of information degradation in segregated brain subnetworks. Importantly, such temporally coherent pathways involve either quickly evolving regions that are concerned with stimulus perception and abstraction, or slowly evolving regions dedicated to hierarchically higher processes. A specific network hinges both time-scales and localizes in regions that are generally involved in language comprehension and production. These subnetworks are found during rest, and might constitute the spatio-temporal scaffolding underpinning the constant readiness to new stimuli. Future work should describe in detail how such spatio-temporal structure supports efficient dynamics and state exploration.

Participants
Fifty-eight right-handed and native Italian speakers were considered for the analysis. To be included in this study, all participants had to satisfy the following criteria: a) to have no significant medical illnesses and not to abuse substances or use medication that could interfere with MEG/EEG signals; b) to show no other major systemic, psychiatric, or neurological illnesses; and c) to have no causes of focal or diffuse brain damage at routine MRI. The study protocol was approved by the local Ethics Committee. All participants gave written informed consent.

MEG acquisition
Subjects underwent magnetoencephalographic examination in a 163 -magnetometers MEG system placed in a magnetically shielded room (AtB Biomag UG -Ulm -Germany). The preprocessing was done similarly as in (49) . In short, the position of four coils and of four reference points (nasion, right and left pre-auricular point and apex) were digitized before acquisition using Fastrak (Polhemus®). The brain activity was recorded for 7 minutes, with eyes closed, with a break at 3.5 minutes, so as to minimize the chances of drowsiness. The head position was recorded at the start of each segment. The data were sampled at 1024 Hz and a 4th order Butterworth band-pass filter was applied to select components between 0.5 and 48 Hz. During the acquisitions, electrocardiogram (ECG) and electrooculogram (EOG) were also recorded (50) . These steps were done using Matlab 2019a and the Fieldtrip toolbox 2014 (51) .

Preprocessing
Principal component analysis (PCA) was performed to reduce the environmental noise (52,53) . Noisy channels were removed manually through visual inspection of the whole dataset by an experienced rater. Supervised independent component analysis (ICA) was performed to eliminate the ECG (and the EOG) component from the MEG signals (54) . Trials that did not contain artefacts (either system related or physiological) or excessive environmental noise were selected.

Source reconstruction
The data were co-registered to the native MRI. A modified spherical conductor model was used as a forward model (55) . The voxels in the MRI were labelled according to the Automated Anatomical Labelling (AAL) atlas (56,57) . We used the cortical regions for a total of 78 areas of interest. Subsequently, a linearly constrained minimum variance beamformer was used to compute 78 time series (one per area of interest) at a sampling frequency of 1024 Hz (58) . Reconstructed sources were again visually inspected by an experienced rater. Of the initial 58 subjects, 44 had enough artefact-free acquisitions and were selected for further analysis. The source reconstructed signals were downsampled to 256 Hz.

Edge-centric approach to MEG
In this work, we adopted an edge-centric approach that, rather than focusing on the local activity of the regions (nodes), represents the dynamics of the interactions between couples of brain regions (59) . This allowed us to characterize the whole brain network activity in terms of dynamical non-local interactions, highlighting the relational properties of each node. Given any couple of nodes and and their respective source-reconstructed signals and we defined a characteristic time series for the edge as the product of the z-scored signals, i.e., j i

Estimation of information decay time through Mutual Information
Shannon Entropy, defined as quantifies the uncertainty over the possible outcomes of a random variable X with x i probability distribution . If the uncertainty over future outcomes of decreases P X X as we measure the outcome of another random variable Y, we conclude that X and Y y i represent two processes that are not independent. The new resulting uncertainty over is then defined by X , The reduction in uncertainty (or -equivalently -the increase of information) over X given by the knowledge of is measured by the Mutual Information (MI) Y Unlike other measures, such as partial autocorrelation (PAC), Mutual Information (MI) evaluates statistical dependencies which take into account nonlinear interactions, which are ubiquitously found in brain data. In order to quantify the time span before the information in a signal is lost, we rely on the Auto Mutual Information (AMI) (t) X i.e., the MI between the signal and its time delayed copy . According to (t ) Y = X − τ previous works on M/EEG (60, 61) , a stable estimate of the probability distribution of any real-valued signal is obtained by dividing the data into 64 bins. The joint (t) X probability distribution for the pair , needed for the evaluation of the X(t), X(t )) ( − τ AMI, is given by a 64x64 contingency matrix which is the joint histogram of the two variables. The AMI decays as a function of the delay , from a maximal value at τ τ = 0 to a relatively stable lower value as . The more gentle ("slower") the decay, the τ → ∞ longer the information lasts in the signal. delay matrix twice, first by removing the edges starting from the slowest decaying ones, and then starting from the fastest ones. As a result, we obtained two equally dense matrices. In the former, only the fast-decaying edges are included, defining a fast updating subnetwork (FUN). The latter, containing the slow-decaying edges, identifies a slow updating subnetwork (SUN), which is complementary to the FUN . Finally, we defined a two-layered multiplex network, with the layers corresponding to the FUN and the SUN. Then, we evaluated the multiplex participation coefficient (MPC) to distinguish between nodes with edges mainly included in one of the two layers from nodes with edges that are projecting into both layers. The MPC, for a two-layered network, is defined as:

Information Storage Capability of the functional edges
where and denote the degrees of the -th node in layer FUN and SUN, respectively. The MPC is calculated per each node and is bounded between 0 and 1, where 1 indicates that the edges that are incident upon a given node are equally distributed on both layers, and 0 denotes a node that is only connected in one of the two layers (27) . The greater the MPC, the more a given node participates in both layers.

Parameter independent definitions
The above definitions of the FUN and SUN networks as well as of the MPC depend on the choice of a unique parameter, which is the density of the edges that we include ρ within each of the two layers (See Materials and Methods and Figure 3). In order to make our results independent of this choice, we repeat our analysis for several threshold densities , spanning 100 values within the density range 0.9-0.1 (each time keeping the density equal in both layers). For each density value, we evaluated the FUN and SUN binary matrices as well as the MPC. Averaging across all the density values, we obtained the MPC for each brain region (Fig.4.A) and the typical fast-updating and slow-updating subnetworks (Fig.4.B-C).

Null Model
To statistically validate the MPC results, we compared them to a null model.       In order to estimate the time after which the co-activation time series and its delayed version become maximally independent, we fit the last 80 points of the AMI profile (blue) to a straight line (black) and we find the first point (red) where the difference between the AMI decay and the fitted line is below a threshold. The results reported in the main text refer to the threshold set to 1 standard deviation from the AMI tail.