Quantitative Biology authors titles recent submissions

Network Controllability in the Inferior Frontal Gyrus

Relates to Controlled Language Variability and

Susceptibility to TMS

John D. Medaglia,1,2 Denise Y. Harvey,2,3 Nicole White,2 Danielle S. Bassett,4,5 Roy H. Hamilton2

1 _{Department of Psychology, Drexel University} Philadelphia, PA, 19104, USA

2

Department of Neurology, University of Pennsylvania Philadelphia, PA, 19104, USA

3

Moss Rehabilitation Research Institute Elkins Park, PA, 19027, USA 4

Department of Electrical and Systems Engineering, University of Pennsylvania Philadelphia, PA, 19104, USA

5

Department of Bioengineering, University of Pennsylvania Philadelphia, PA, 19104, USA

To whom correspondence should be addressed; E-mail: johnmedaglia@gmail.com. January 11, 2017

Number of pages: 38 Number of figures: 6 Number of tables: 1 Abstract words: 201 Introduction words: 630 Discussion words: 1499

Abstract

In language production, humans are confronted with considerable word selection demands. Often, we must select a word from among similar, acceptable, and competing alternative words in order to construct a sentence that conveys an intended meaning. In recent years, the left inferior frontal gyrus (IFG) has been identified as critical to this ability. Despite a recent emphasis on network approaches to

understanding language, how the left IFG interacts with the brain’s

complex networks to facilitate controlled language performance remains unknown. Here, we take a novel approach to understand word selection as a network control process in the brain. Using an anatomical brain network derived from high-resolution diffusion spectrum imaging (DSI), we compute network controllability underlying the site of transcranial magnetic stimulation in the IFG between administrations of two word

selection tasks. We find that a statistic that quantifies the IFG’s control

of difficult to reach states explains vulnerability to TMS in two open-response language tasks and a closed-response number naming

task. Moreover, we find that a statistic that quantifies the IFG’s control

of communication across modules in the human connectome explains changes in task performance following TMS. These findings establish a first link between network controllability, cognitive function, and TMS effects.

Significance Statement

This work illustrates that network control statistics applied to anatomical connectivity data demonstrate relationships with cognitive variability during controlled language tasks and TMS effects.

Introduction

Effective verbal communication depends on the ability to retrieve and select the appropriate

words that correspond to a speaker’s intended meaning. Often, the opportunity to select among several appropriate words challenges the speaker. Prior evidence in cognitive neuroscience indicates that the left inferior frontal gyrus (IFG) supports verbal selection [1, 2, 3, 4, 5, 6, 7, 8], and potentially a more domain-general role in selection in the context of competing representations [9]. Notably, the position of the IFG in the brain’s distributed anatomical networks is not unique to classically described language systems. Rather, it is positioned to mediate between several systems in the frontal associative, motor, insular, and temporal cortices as well as the basal ganglia [10]. This evidence suggests that the participation of the IFG in language function must operate in the context of many processing

demands in the brain’s distributed circuits.

While controlled language function is thought of as a network-level process [11, Error! Reference source not found., 9], putative mechanisms of this process in the context of the

brain’s complex structural architecture remain unclear. Recent theoretical work in network

control theory, an emerging area in engineering, provides one such mechanism. Network control theory is the study of how to design control strategies for networked systems [12], in which a set of nodes are connected by edges, and in which a particular dynamic process occurs atop those edges. In the context of the brain, this suggests that brain regions (nodes) are predisposed to drive or modulate neurophysiological dynamics in a manner consistent with their specific topological role in brain networks constructed from white matter tractography.

control functions [13, 14]. However, a mechanistic network control role for the IFG in language selection has not been evaluated.

Here we test whether network control is a putative mechanism for language control by asking whether the theoretically predicted control features of brain regions are related to cognitive performance on tasks with selection demands. In particular, we focus on word selection in open-ended semantic tasks, where participants can choose one of several appropriate words to complete the task [1]. This contrasts with a closed-ended task – number naming – that requires word retrieval but has only one correct response. We posit that controlled language function performance relates to the ability of the left IFG to control activity across human structural brain networks. To assess this view, we restrict our attention to two distinct network control features known as modal controllability (the ability of a node – here, a brain region – to drive a network into difficult-to-reach states) and boundary controllability (which describes the ability of a node to steer the system into states where modules are either coupled or decoupled). Here, modal controllability may contribute to selecting specific lexical representations, such as when a single word needs to be retrieved in the face of competing, alternative words. Variable boundary controllability in the IFG may contribute to inter-system coordination required for effective language selection.

We hypothesize that local inhibition via brain stimulation (i.e., using continuous theta-burst stimulation [15, 16]) will allow us to articulate the degree to which the IFG serves a domain-general versus domain-specific cognitive control role. More specifically, the degree to which the IFG serves a modal control role – specialized to drive the brain into difficult to reach states via sparse connections – may represent greater diversity in cognitive performance (i.e., differences in performance across tasks). We further anticipate that TMS may affect

performance more variably across the three tasks in individuals with higher modal controllability due to an anatomically sparse, and thus more specific role in driving the brain into difficult to reach states [17, 18]. In addition, we hypothesize that the degree to which the IFG serves a boundary control role – i.e., specialized to regulate gross inter-modular communication – will be related specifically to language tasks, representing the complex open-ended demands relative to the number task, and that TMS effects will be greater as IFG boundary control increases, thereby enabling IFG to impact multiple modules.

Materials & Methods

Overview of Methods

To address our hypotheses, we administer a form of noninvasive brain stimulation (transcranial magnetic stimulation) to a region within the left inferior frontal gyrus (pars triangularis) in each of 10 healthy adult subjects between repeated administrations of two language tasks with open-ended selection demands and one number naming task with a single appropriate response for comparison. We construct structural brain networks from diffusion spectrum imaging (DSI) data acquired for each subject (Methods, Fig. 1A). Each network contains 111 brain regions defined by the Lausanne anatomical parcellation and cerebellum (Fig. 1B), and each pair of regions is connected by an edge weighted by the number of streamlines linking those regions (Fig. 1C). We define a simplified model of brain dynamics and simulate network control to quantify modal and boundary controllability (Fig. 1D).

Figure 1: Overview of Methods (A) Continuous theta burst stimulation was administered to

each subject’s pars triangularis. (B) Diffusion tractography was computed for each subject. A

cortical parcellation was registered to each individual’s structural T1 image to identify

anatomical divisions. (C) A region x region structural adjacency matrix was constructed representing the streamline counts between pairs of regions. (D) We applied a community detection algorithm to identify an initial consensus partiation on the average network across subjects. (E) Modal and boundary controllability were computed for each node (brain region) in the network for each individual. Each node received a rank representing its strength of control in the network heirarchy within the individual. (F) Maps representing the variability in modal controllability (top) and boundary controllability (bottom). P

1...10 represent different participants. The relationship between controllability values at the IFG stimulation site and task response times before and after stimulation were examined using mixed effects models.

Subjects

Ten healthy individuals (mean age = 25.4, St.D. = 4.5, 6 female) from a larger neuroimaging study [19] returned to participate in the present study. All procedures were approved in a

convened review by the University of Pennsylvania’s Institutional Review Board and were

carried out in accordance with the guidelines of the Institutional Review Board/Human Subjects Committee, University of Pennsylvania. All participants volunteered with informed consent in writing prior to data collection.

Neuroimaging: Diffusion Tractography

Diffusion spectrum images (DSI) were acquired for a total of 10 subjects along with a T1-weighted anatomical scan at each scanning session. We followed a parallel strategy for data acquisition and construction of streamline adjacency matrices as in previous work applying network controllability statistics in human diffusion imaging networks [18]. DSI scans sampled 257 directions using a Q5 half-shell acquisition scheme with a maximum

b-value of 5,000 and an isotropic voxel size of 2.4 mm. We utilized an axial acquisition with the following parameters: repetition time (TR) = 5 s, echo time (TE)= 138 ms, 52 slices, field of view (FoV) (231, 231, 125 mm).

DSI data were reconstructed in DTI Studio (www.dsi-studio.labsolver.org) using q-space diffeomorphic reconstruction (QSDR)[20]. QSDR first reconstructs diffusion-weighted images in native space and computes the quantitative anisotropy (QA) in each voxel. These QA values are used to warp the brain to a template QA volume in Montreal Neurological

algorithm. Once in MNI space, spin density functions were again reconstructed with a mean diffusion distance of 1.25 mm using three fiber orientations per voxel. Fiber tracking was performed in DSI Studio with an angular cutoff of 35 , step size of 1.0 mm, minimum length of 10 mm, spin density function smoothing of 0.0, maximum length of 400 mm and a QA threshold determined by DWI signal in the colony-stimulating factor. Deterministic fiber tracking using a modified FACT algorithm was performed until 1,000,000 streamlines were reconstructed for each individual.

Anatomical (T1) scans were segmented using FreeSurfer [21] and parcellated using the connectome mapping toolkit [22]. A parcellation scheme including n=129 regions was

registered to the B0 volume from each subject’s DSI data. The B0 to MNI voxel mapping

produced via QSDR was used to map region labels from native space to MNI coordinates. To extend region labels through the grey-white matter interface, the atlas was dilated by 4 mm [23]. Dilation was accomplished by filling non-labelled voxels with the statistical mode of

their neighbors’ labels. In the event of a tie, one of the modes was arbitrarily selected. Each streamline was labelled according to its terminal region pair. From these data, we constructed a structural connectivity matrix, A whose element A

ij represented the number of streamlines

connecting different regions, divided by the sum of volumes for regions i and j [24].

Cognitive Testing

Participants performed two open-ended language tasks and one closed-ended number naming task (See Fig. 2).

Figure 2: Overview of Tasks (A) High verbal selection demands are introduced when a cuing noun is associated with multiple appropriate words (here, verbs). Top: Example of a

stimulus-response pairing with low selection demands. Bottom: a stimulus-response pairing with high selection demands. (B) Example items from the sentence completion task.

Participants were asked to provide an appropriate noun at the end of the sentence. Top: This

item has a low selection demand because “leash" is easily and dominantly recalled in the

context of this sentence. Bottom: This item has a high selection demand because several alternate words may be appropriate to complete the sentence. (C) Example items from the verb generation task. Participants were asked to provide an appropriate verb associated with the noun. Left: This item has a low selection demand because “cut" is the most dominant verb

associated with “scissors". Right: This item has a high selection demand because several verbs

are highly associated with the mouth, such as “eat", “talk", and “kiss".

The language tasks included a verb generation task [25] and a sentence completion task [26]. For the verb generation task, subjects were instructed to generate the first verb that came to mind when presented with a noun stimulus (e.g., “cat”). The verb could be either something

the noun does (e.g., “meow”) or something you do with it (e.g., “feed”). Response times (RTs)

were collected from the onset of the noun cue to the onset of the verb response. For the

sentence completion task, participants were presented with a sentence, such as “They left the

dirty dishes in the ---?”, and were instructed to generate a single word that appropriately

completes the sentence, such as “sink”. Words in the sentences were presented serially in 1s segments consisting of one or two words. RTs were computed as the latency between the onset of the last segment, which always contained a two-word segment (i.e., a word and an

underline), and the onset of the participant’s response. For all items in the sentence completion task, items in the high vs. low selection demand conditions were matched on retrieval demands (association strength) [26]. For both language tasks, each trial began with the presentation of a fixation point (+) for 500 ms, followed by the presentation of the target stimulus, which remained on the screen for 10 s until the subject made a response. Subjects were given an example and five practice trials in the first administration of each language task (i.e., before TMS), and were reminded of the instructions before performing the task a second time (i.e., after TMS). In each of the before and after TMS conditions, subjects completed 50 trials for a total of 100 trials.

The comparison task was a number naming task where participants produced the English names for strings of Arabic numerals presented on the screen. On each trial, a randomized number (from tens of thousands to millions; e.g., 56395, 614592, 7246856) was presented in black text on a white background. The numbers were uniformly distributed over three lengths (17 per length for each task administration). The position of items on the screen was randomized between the center, left, and right of the screen to reduce the availability of visual cues to number length and syntax [25]. RTs were collected from the onset of the stimulus

presentations to the onset of the subject’s response. The number appeared in gray following

the detection of a response (i.e., voice key trigger), and remained on the screen thereafter to reduce the working memory demands required for remembering the digit string. At the start of the experiment, subjects performed 50 trials of the number naming task to account for initial learning effects [25]. Prior to performing the task for the first time, subjects were given an example and five practice trials, and were later reminded of the instructions before performing

the task a second (i.e., before TMS) and a third time (i.e., after TMS). In each of the before and after TMS conditions, subjects completed 51 trials for a total of 102 experimental trials.

The items for the verb generation task were identical to those used in [4] and the items for the sentence completion task were those from [27]. The difficulty of items was sampled to cover a distribution of values computed via latent semantic analysis (LSA) applied to corpus data. In particular, items were sampled to represent a range of LSA entropy and LSA association strength [26], which represent the selection and retrieval demands of each item, respectively [26]. An LSA association value of 0 means that the cue word or sentence is not strongly associated with any word in particular, whereas a value of 1 means that the cue word or sentence is strongly associated with at least one word, implying that it is easy to retrieve. An LSA entropy value of 0 indicates that the word is not related to any words, whereas higher values indicate higher relatedness to many words, which theoretically increases competition among appropriate words [26].

Verbal responses for all tasks were collected from a computer headset microphone. The microphone was calibrated to reduce sensitivity to environment background noise prior to the collection of data for each session such that the recording software was not triggered without clear verbalizations. List order (before or after TMS) was counterbalanced across participants. Item presentation order within each task was fully randomized across participants.

Transcranial Magnetic Stimulation.

The Brainsight system (Rogue Research, Montreal) was used to co-register MRI data with the location of the subject and the TMS coil. The stimulation site was defined as the posterior extent of the pars triangularis in each individual subject’s registered T1 image. A Magstim

Super Rapid2 Plus1 stimulator (Magstim; Whitland, UK) was used to deliver cTBS via a 70 mm diameter figure-eight coil. To calibrate the intensity of stimulation, cTBS was delivered at

80% of each participant’s active motor threshold [16]. Each participant’s threshold was determined prior to the start of the experimental session using a standard up-down staircase procedure with stimulation to the motor cortex [M1].

Mathematical Models

Network Control Theory

We follow a previous application of network control theory in diffusion weighted imaging data as the basis for our examination of controllability and cognitive control. We briefly describe the mathematical basis for the approach taken here. For a full discussion of structural network controllability in the context of diffusion weighted imaging networks, see [13]. For a full discussion of the mathematical basis for structural network controllability see [28, 29, 17]. Our ability to understand neural systems is fundamentally related to our ability to control them [30]. Network control theory is a branch of traditional control theory in engineering that examines how to control a system based on the links between its components, and based on a

model of the system’s dynamics. Here, we interpret the word control to mean perturbing communication in an anatomical brain network. To apply a network control perspective, we require (i) knowledge of the network connectivity linking system components, and (ii) knowledge regarding how system components function, i.e., their dynamics, rather than

mechanistic models allows us enrich descriptive approaches to examine the human connectome [31] with statistics that explicitly include a dynamic model.

Mathematically, we can study the controllability of a networked system by defining a network represented by the graph =(,), where and are the vertex and edge sets, respectively. Let a

ij be the weight associated with the edge (i,j)∈, and define the weighted adjacency

matrix of as A=[a

ij], where aij=0 whenever (i,j)/∈. We associate a real value (state) with

each node, collect the node states into a vector (network state), and define the map x:N_≥0→Rn

to describe the evolution (network dynamics) of the network state over time. Given the network and node dynamics, we can use network control theory to quantitatively examine how the network structure relates to the types of control that nodes can exert.

Dynamic Model of Neural Processes

We begin with an analogous approach to prior work [13]. We define structural brain networks by subdividing the entire brain into anatomically distinct brain areas (network nodes) in a commonly used anatomical atlas [24]. Consistent with prior work [32, 33, 34, 13], we connect nodes by the number of white matter streamlines identified by a commonly used deterministic tractography algorithm (for details on the tractography implementation, see [35]). This procedure results in sparse, weighted, undirected structural brain networks for each subject. Properties of this network include high clustering, short path length, and strong modularity, consistent with prior studies of similar network data [32, 24]. The definition of structural brain networks based on tractography data in humans follows from our primary hypothesis that

control features of neural dynamics are in part determined by the structural organization of the

brain’s white matter tracts.

To define the dynamics of neural processes, we draw on prior models linking structural brain networks to resting state functional dynamics [36, 37, 38]. Although neural activity evolves through neural circuits as a collection of nonlinear dynamic processes, these prior studies have demonstrated that a significant amount of variance in neural dynamics as measured by resting state fMRI can be predicted from simplified linear models. Based on this literature, we employ a simplified noise-free linear discrete-time and time-invariant network model:

x(t+1)=Ax(t)+Bu(t), (1)

where x:R_≥0→RN describes the state (e.g., a measure of the electrical charge, oxygen level, or firing rate) of brain regions over time, and A∈RN×N is a symmetric and weighted adjacency matrix. In this case, we construct a weighted adjacency matrix whose elements indicate the number of white matter streamlines connecting two different brain regions – denoted here as i and j – and we stabilize this matrix by dividing by the mean edge weight. While the model employed above is a discrete-time system, we find that the controllability Gramian is statistically similar to that obtained in a continuous-time system [13].

The diagonal elements of the matrix A satisfy A

ii=0. The input matrix B identifies the

control points in the brain, where ={k

1,…,km} and

, (2)and e

i denotes the i-th canonical vector of dimension N. The input

u:R_≥0→Rm denotes the control energy.

Network Controllability

To study the ability of a certain brain region to influence other regions in arbitrary ways we adopt the control theoretic notion of controllability. Controllability of a dynamical system refers to the possibility of driving the state of a dynamical system to a specific target state by means of an external control input [39]. In the current paper, we follow the procedures applied in [18] and focus on two network controllability statistics: modal and boundary controllability. Modal Controllability

Modal controllability refers to the ability of a node to control each evolutionary mode of a dynamical network [40], and can be used to identify the least controllable state from a set of control nodes. Modal controllability is computed from the eigenvector matrix V=[v

ij] of the

network adjacency matrix A. By extension from the PBH test [41], if the entry v

ij is small,

then the j-th mode is poorly controllable from node i. Following [42], we define

φ

i=



j=1

N

(1−λ2_j(A))v2_ij as a scaled measure of the controllability of all N modes

λ₁(A),…,λ

N(A) from the brain region i. Regions with high modal controllability are

able to control all the dynamic configurations of the network, and hence to drive the dynamics towards hard-to-reach configurations.

Boundary Controllability

Boundary controllability, a metric developed in network control theory, quantifies the role of a network node in controlling dynamics between modules in hierarchical networks [17]. Boundary controllability identifies brain areas that can steer the system into states where different cognitive systems are either coupled or decoupled. Here, we apply a similar approach to that taken in [13] to quantify boundary controllability in our diffusion tractography networks and associate controllability variability with cognitive performance. Specifically, we partition the brain into modules by maximizing the modularity quality function [43] using a Louvain-like [44] locally greedy algorithm [45]. Because the modularity quality function has many near-degeneracies, we perform the optimization algorithm multiple times [46]. We observed that the mean partition similarity was high and the variance of the partition similarity

was low for a value of γ at 1.6 (mean z-Rand score = 60.4, standard deviation = 3.7), which is within the range of stable partitions found in our prior analyses in diffusion spectrum imaging data [13]. We therefore used the consensus partition at γ=1.6 for the remainder of the analysis in this study.

Examining the Relationship Between Controllability, Cognition,

and TMS effects

All data were analyzed using R [47], and the R packages lme4 v.1.1-9 [48], languageR v.1.4.1 [49], lmerTest v.2.0-29 [50], effects v.1.27 [51], and LMERConvenienceFunctions v.2.10 [52], using multilevel modeling with maximum-likelihood estimation [53]. This technique

accounting for the non-independence of observations collected from each participant in a within-subjects design, without resorting to computing separate regression equations for each subject (e.g., [54, 53, 55]. Multilevel modeling also accounts for violations of the sphericity assumption by modeling heteroskedasticity in the data when necessary, improving statistical power over other methods commonly employed for analyzing repeated-measures data. Prior to analysis, trials on which participants responded incorrectly were excluded from the data in addition to any responses of less than 200ms (1% of trials). Response times (RT) across all three tasks were transformed by computing the cumulative density function of the observed RT data over all trials, calculating a transformation to a gaussian distribution, and application of the transformation to the original data. Treating RT data from all three tasks as one distribution allows us to examine cross-task differences in RT, since we expect responses to be faster or slower based on the difficulty of the task and before and after TMS. All continuous variables were grand-mean-centered prior to data analysis.

Normalized RT was modeled as a function of the categorical variables Task (Number naming, Sentence Completion, Verb Generation), and TimePoint (Pre-TMS, Post-TMS), as well as the continuous variables Modal Controllability and Boundary Controllability and all interaction terms. A 2-level multilevel model was used to account for the non-independence of observations by estimating a random intercept for each participant using an unstructured covariance matrix and the between-within method of estimating degrees of freedom. We also modeled by-item random intercepts, and by-subjects random slopes for the effect of trial number (in order to index individual learning rates over the course of each task). All results are reported using the normalized RT z-scores.

Results

We aimed to test the hypothesis that IFG anatomical network controllability would relate to the domain generality of the IFG in language processing. We anticipated that individuals with high modal controllability would present with greater diversity in performance across tasks, and that TMS may affect performance more variably across the three tasks in individuals with higher modal controllability. In addition, we hypothesized that IFG boundary controllability would relate specifically to language tasks, representing the complex open-ended demands relative to the number task, and that TMS effects will be greater as IFG boundary control increases. We used mixed effects models to test these hypotheses. See Table 1 for the full mixed effects model results including parameter values and significance estimates.

There was a significant main effect of Task: F(2,2559) = 163.39, p<0.0001, partial R2 = 0.529. The RTs for each task were all significantly different from one another (all ps<0.0003). The fastest RTs were recorded in the Sentence Completion task (M = -0.88, SD = 1.07), while participants were slower in the Number naming task (M = -0.66, SD = 0.82) and even slower in the Verb Generation task (M = 0.229, SD = 0.69). There was also a main effect of TMS:

F(1,2559)=8.32, p=0.004, partial R2=0.003. Participants were faster to respond Post-TMS, whic could either be interpreted as an effect of TMS or an effect of learning more generally.

In addition, there were several significant interactions. Task interacted with IFG modal controllability (theoretically: the predicted ability of the IFG to drive the brain into hard to reach states) and IFG boundary controllability (theoretically: the predicted ability of the IFG to drive the brain into states where putative functional modules are either coupled or

effect. Finally, a three-way interaction was observed between task, the TMS effect, and IFG boundary controllability.

Table 1. Mixed effects model for the effects of task, TMS, and controllability Df Sum of Sq. Mean Sq. Error F Lower Den. Df p

Task

2 157.379 78.690 163.391 2559 <0.001***

TMS 1 4.006 4.006 8.318 2559 0.004**

Modal 1 0.005 0.005 0.011 2559 0.916

Boundary 1 0.415 0.415 0.862 2559 0.353

Task*TMS 2 0.906 0.453 0.940 2559 0.391

Task*Modal 2 15.430 7.715 16.020 2559 <0.001***

Task*Boundary 2 7.060 6.658 14.658 2559 <0.001***

TMS*Modal 2 13.317 7.706 13.826 2559 <0.001***

TMS*Boundary 1 6.547 6.547 13.595 2559 <0.001***

Task*TMS*Modal 2 0.337 0.169 0.350 2559 0.705

Task*TMS*Bound ary

2 5.549 2.775 5.761 2559 0.003**

TMS = transcranial magnetic stimulation effect. *Denotes significance at p<0.05, **denotes significance at p<0.01, and ***denotes significance at p<0.001.

Post hoc tests for all interactions were examined by estimating simple slopes at one standard deviation above and below the means (or in the case of categorical variables such as task and TMS effects, estimating effects at each level) of the predictor variables in the interaction term [56].

In the post hoc tests for the task interaction with IFG modal controllability, each test asks whether the differences between tasks are different as a function of modal controllability. We found that individuals with higher, as compared to lower, modal controllability were relatively faster in sentence completion compared to verb generation (t(2569)=3.065, p=0.002), relatively faster in sentence completion compared to number naming (t(2571)=5.438,

p<0.001), and relatively faster in number naming compared to verb generation (t(2752)=2.370, p=0.018). See Fig. 3.

Figure 3: IFG Modal Controllability and Task Performance Interact. In individuals with higher IFG modal controllability, performance was more distinct across the three tasks than in individuals with lower modal controllability. Delta symbols indicate that the differences between tasks were the values compared in each post hoc statistical test. Asterisks indicate statistically significant post hoc effects (differences in performance between tasks) at p<0.05, corrected for multiple comparisons. Each bar in this effect estimate plot represents the

estimated response times at +/- 1 standard deviation along the modal controllability dimension at which post-hoc tests were performed; see Table 1 for model results. Numbers = Number Naming, SentComp = Sentence Completion, VerbGen = Verb Generation.

In the post hoc tests for the task interaction with IFG boundary controllability, each test asks whether the differences between tasks are related to boundary controllability. We found that individuals with lower, as compared to higher, boundary controllability were relatively slower to generate responses during the verb generation task compared to number naming (t(2577)=−4.534, p<0.001) and sentence completion (t(2572)=−4.583, p<0.001). See Fig. 4.

Figure 4: IFG Boundary Controllability and Task Performance Interact. In individuals with higher IFG boundary controllability, performance on number naming and sentence completion was closer to performance on verb generation, mostly driven by slower

performance on number naming and sentence completion in individuals with higher boundary controllability. Delta symbols indicate that the differences between tasks were the values compared in each post hoc statistical test. Asterisks indicate statistically significant post hoc

effects (differences in performance between tasks) at p<0.05, corrected for multiple

comparisons. Each bar in this effect estimate plot represents the estimated response times at +/- 1 standard deviation along the boundary controllability dimension at which post-hoc tests were performed; see Table 1 for model results. Numbers = Number Naming, SentComp = Sentence Completion, VerbGen = Verb Generation.

Taken together, these results indicate that performance differences across tasks were more pronounced in higher modal controllability, whereas performance was more similar across tasks in individuals with higher boundary controllability due to slowed responses on the sentence completion and number naming tasks.

In the post-hoc tests for the TMS by IFG modal controllability interaction, each test asks whether the effects of TMS was observed in low or high boundary controllability. We found that TMS effects were greater in individuals with lower modal controllability overall (post-hoc test: t(2876) = 4.797, p<0.001). Individuals with high modal controllability did not show an effect of TMS. Similarly, in post-hoc testing within the TMS by boundary controllability interaction, we found that TMS effects were greater in individuals with lower boundary controllability overall (post-hoc test: t(2682) = 4.275, p<0.001). Individuals with high boundary controllability did not show an effect of TMS (see Fig. 5).

Figure 5: IFG Controllability and Brain Stimulation Interact. (A) In individuals with low modal controllability, response times were faster following TMS, whereas no change in response times was observed in individuals with high modal controllability. (B) Consistent with findings in modal controllability, in individuals with low boundary controllability, response times were faster following TMS, whereas no change in response times was observed in individuals with high boundary controllability. Asterisks indicate statistically significant effects at p<0.05, corrected for multiple comparisons. Each bar in this effect estimate plot represents the estimated response times at +/- 1 standard deviation along the controllability dimensions (either modal or boundary); see Table 1 for model results.

Finally, we identified a three-way interaction between task, TMS effect, and IFG boundary controllability. Post hoc tests asked whether task performance differed before and after

practice for each task. The effects of TMS across the tasks differed depending on individuals’

boundary controllability: sentence completion (t(2712)=2.86, p=0.004) and verb generation (t(2741)=3.75, p=0.0002) were faster following TMS only in the low boundary controllability condition. Number naming (t(2702)=2.23, p=0.005) was faster following TMS only in the high boundary controllability condition (see Fig. 6).

Figure 6: IFG Boundary Controllability, Task, and Brain Stimulation Interact. Individuals with low IFG boundary controllability demonstrate faster response times following TMS in verbal tasks but not the number naming task, whereas the opposite was observed among individuals with higher boundary controllability. Each bar in this effect estimate plot represents the estimated response times at +/- 1 standard deviation of boundary controllability values; see Table 1 for model results. Asterisks indicate statistically significant effects at p<0.05, corrected for multiple comparisons.

Discussion

In this paper, we examine the hypothesis that network controllability in the IFG is related to language selection in open- and closed-ended tasks. We explicitly test this hypothesis by linking variability in the vulnerability of controlled language function to perturbation by TMS to IFG controllability. In this study, we integrate two separately developing theoretical frameworks from cognitive neuroscience and emerging applications of control theory to human brain networks [18]. In cognitive neuroscience, the IFG is identified as a site that mediates controlled language function; however, the processes by which the IFG executes this role in brain networks is unknown. Network control theory is postulated to be a useful framework to understand the organization for human cognitive control and performance variability based on the role of anatomical regions in the structural connectome [18].

To test this experimentally, we constructed structural brain networks from diffusion spectrum imaging data acquired in 10 healthy adult individuals and administered inhibitory TMS between two repetitions of language tasks and a comparison number task. We anticipated that higher modal controllability would be related to greater diversity across the tasks regardless of brain stimulation. We also anticipated that the effect of TMS to the IFG on behavioral performance would be more variable as a function of modal controllability. In addition, we predicted that individual variability in boundary controllability would be related specifically to performance on language tasks, and finally that TMS effects would be greater in individuals with high boundary control in the IFG.

Overall, we found that individuals with higher IFG modal controllability – the tendency to drive the brain into difficult to reach states – demonstrated greater inter-task performance variability. Specifically, higher modal controllability was associated with greater differences in performance across tasks. This is consistent with the notion that as IFG connection sparsity increases, performance diversifies across tasks due to its specialized role in driving the brain to difficult to reach states. In human structural brain networks, the increasing specialization of the IFG in achieving difficult-to-reach states may be associated with increasingly variable domain involvement of the IFG. In contrast, increases in boundary controllability were associated with more similar performance between verb generation and the other tasks. Thus, increased burden to the IFG to integrate and segregate information may lead performance on easier tasks toward the relatively more difficult verb generation task, potentially as a result of neural interference. Taken together, this establishes an important dual control role of the IFG in the human anatomical connectome that varies across individuals: higher modal controllability drives domain specificity and diversity in performance across tasks, whereas higher boundary controllability drives a domain general role as a function of strong intermodule control.

We additionally found that reduced IFG modal and boundary controllability is associated with faster performance following TMS. These findings indicate that for individuals in which the IFG less specifically drives the brain into rare, integrated, or segregated states, TMS effects are more generally evident across cognitive domains. These effects were not observed in individuals higher in either control type. These findings may suggest that the extent to which the IFG specializes in a strong control roles of these types results in particular sensitivity to perturbation across both open- or closed-ended tasks. While prior work has

revealed that the IFG participates in a distributed language system [9], the current results suggest an important principle: if the IFG is less specialized to drive the brain toward specific states, more diffuse effects across cognitive processes may occur. While we use a simplified dynamic model paired with diffusion imaging data, future studies could examine local neural model dynamics at IFG [57] in the context of distribute network control processes to examine local versus distributed network influences on cognitive change.

Lastly, we observed a three-way interaction between TMS, IFG boundary controllability, and task, whereas no three-way interaction was observed for modal controllability. We speculate that this is related to the difference in complexity across the two measures. In human brain networks, preliminary studies suggest that ranked modal controllability is strongly related to the strength of nodes across the network [18]. This suggests that in the human brain, hub regions are situated to drive specific and difficult to reach states [18]. However, boundary controllability inherently represents the rich heirarchically modular organization of the brain, which is difficult to represent in a concise measure; indeed, one goal of network neuroscience is to better characterize this organization [Error! Reference source not found., 58] and associating it with cognition [59, 60]. This possibility could be more thoroughly explored in future studies with more comprehensive cognitive and stimulation manipulations.

Within this interaction, we found that inhibitory TMS in individuals with lower IFG boundary controllability may facilitate performance in tasks requiring language selection. This can potentially be understood in the context of prior findings suggesting a role of GABA-mediated inhibition in word selection [57]. In particular, locally upregulating the influence of GABA-mediated neurons with theta-burst stimulation may release inhibitory

detrimental activation of competing alternative responses downstream, presumably processed in the temporal lobe. We speculate that inhibiting a node with a lower – or more circumscribed – role in controlling intermodular dynamics provides benefits across the network, facilitating improvements in function in the open- and closed-ended tasks used here.

Notably, these results provide suggest that part of the IFG’s local function in language control is related to its ability to drive dynamics across the brain’s modular anatomical network.

Taken together, in the context of the brain’s structural triple dissociation in IFG

controllability, this indicates that (i) different network control roles in a given region may serve specific cognitive roles and (ii) the topological role of regions in the brain’s structural networks confer differing degrees of robustness to noninvasive neural stimulation. Here, the degree to which the IFG drives the brain into difficult to reach states and integrated or segregated states increases vulnerability to exogenous TMS across open- and closed-ended tasks. Conversely, the lower the controllability of the IFG, the more local inhibition of the IFG facilitates language function. While the IFG may be related to control functions generally [62], future students can pair TMS, diffusion imaging, and task manipulations to dissociate specific contributions. In addition, the executive processes involved in language may not be unique to the frontal lobe [63], and whether or not similar network controllers in other parts of the brain influence controlled language function remains to be seen.

Beyond this study, network control theory may link classical models in cognitive neuroscience and modern techniques from statistical physics. In particular, the brain expresses numerous parallel control circuits in major models of cognitive control [64]. In a network

control view, it is possible to simultaneously consider the role of a local region’s computations and its role in the brain’s intricately interactive control pathways. Thus, as researchers apply

TMS in experimental and clinical contexts, similar analyses may produce a more fundamental understanding of the effects of TMS to specific categories of cognitive function when applied to individual or sets of regions [19], such as by representing functional states along an energy landscape to be controlled for experimental or clinical gains [65]. While at this point still speculative, such control strategies might eventually be applied in vivo to quantify personalized energy landscapes and control-based brain stimulation treatments. The current findings suggest that understanding whether the IFG serves as a modal or boundary controller can help us predict how an individual may respond to TMS to this region depending on cognitive domain. This may eventually facilitate personalized network analyses to support neurorehabilitation.

Future studies could examine larger cohorts, including the effects of TMS at the IFG over broader age ranges and in patients with neuropsychiatric conditions. In addition, while the current results establish a link between TMS boundary controllability and response times during controlled language function, they are not specific to classically examined selection or retrieval demands at the item level. Future analyses could thus examine the interactions between the IFG and specific controllable subnetworks of the brain involved in more general or specific control processes [9], and different behavioral task designs such as open-ended number generation and closed-ended sentence paradigms to examine relationships between network controllability and item selection and retrieval demands. While we were interested in broad inter-task performance differences representing different cognitive processes involving the IFG, future studies may use sham or vertex conditions to better elucidate specific effects (e.g., examining the uniqueness of effects to IFG stimulation). Finally, we applied a

to influence cognitive-emotional functioning, including in the IFG. Future studies could use varying stimulation parameters to examine sensitivity of controlled language function to different stimulation intensities, as well as their interaction with network controllability.

By examining the relationship between inter-individual variability in IFG controllability and controlled language function before and after brain stimulation, we establish a bridge

between a neuroscientist’s notion of a controlled language process and an engineer’s notion of

network control. The current results demonstrate that linking network controllability in white matter networks with experimental manipulation involving TMS can reveal associations between regional network control roles and cognitive susceptibility to brain stimulation. Inter-individual variability in performing control-demanding tasks is related to the theoretically predicted specialization of regions in driving the brain into difficult to reach states. Moreover, changes following TMS similarly dissociate according to the strength of two distinct control roles in the human connectome. In particular, the degree of dynamic specialization of the IFG may result in diverse performance across language tasks, and its ability to govern intermodular dynamics may mediate the cognitive effects of TMS. Similar experiments may elucidate the role of the IFG in specific and general cognitive control functions in the human connectome.

Acknowledgments

JDM acknowledges support from the Office of the Director at the National Institutes of Health through grant number 1-DP5-OD-021352-01. DSB acknowledges support from the John D. and Catherine T. MacArthur Foundation, the Alfred P. Sloan Foundation, the Army Research Laboratory and the Army Research Office through contract numbers W911NF-10-2-0022 and W911NF-14-1-0679, the National Institute of Mental Health (2-R01-DC-009209-11), the National Institute of Child 415 Health and Human Development (1R01HD086888-01), the Office of Naval Research, and the National Science Foundation (BCS-1441502, BCS-1430087, and CAREER PHY-1554488).

References and Notes

[1] M. M. Botvinick, T. S. Braver, D. M. Barch, C. S. Carter, J. D. Cohen, Psychological review108(3), 624 (2001).

[2] H. Moss, et al., Cerebral Cortex15(11), 1723 (2005).

[3] J. K. Nelson, P. A. Reuter-Lorenz, J. Persson, C.-Y. C. Sylvester, J. Jonides, Brain research1256, 92 (2009).

[4] H. R. Snyder, M. T. Banich, Y. Munakata, Journal of cognitive neuroscience23(11), 3470 (2011). [5] S. L. Thompson-Schill, M. D’Esposito, G. K. Aguirre, M. J. Farah, Proceedings of the National Academy of Sciences94(26), 14792 (1997).

[6] S. L. Thompson-Schill, M. D’Esposito, I. P. Kan, Neuron23(3), 513 (1999).

[7] S. L. Thompson-Schill, M. M. Botvinick, Psychonomic Bulletin & Review13(3), 402 (2006). [8] L. J. Tippett, A. Gendall, M. J. Farah, S. L. Thompson-Schill, Neuropsychology18(1), 163 (2004). [9] E. Fedorenko, S. L. Thompson-Schill, Trends in cognitive sciences 18(3), 120 (2014).

[10] D. Saur, et al., Proceedings of the national academy of Sciences 105(46), 18035 (2008). [11] K. W. Doron, D. S. Bassett, M. S. Gazzaniga, Proceedings of the National Academy of Sciences109(46), 18661 (2012).

[12] J. Ruths, D. Ruths, Science343(6177), 1373 (2014). [13] S. Gu, et al., Nature Communications6, 8414 (2015).

[14] J. D. Medaglia, F. Pasqualetti, R. H. Hamilton, S. L. Thompson-Schill, D. S. Bassett, arXiv preprint arXiv:1604.04683 (2016).

[15] A. Benali, et al., The Journal of Neuroscience31(4), 1193 (2011).

[16] Y.-Z. Huang, M. J. Edwards, E. Rounis, K. P. Bhatia, J. C. Rothwell, Neuron45(2), 201 (2005).

[17] F. Pasqualetti, S. Zampieri, F. Bullo, IEEE Transactions on Control of Network Systems1(1), 40 (2014).

[19] R. F. Betzel, S. Gu, J. D. Medaglia, F. Pasqualetti, D. S. Bassett, arXiv preprint arXiv:1603.05261 (2016).

[20] F.-C. Yeh, V. J. Wedeen, W.-Y. I. Tseng, Neuroimage55(3), 1054 (2011). [21] B. Fischl, Neuroimage62(2), 774 (2012).

[22] L. Cammoun, et al., Journal of neuroscience methods203(2), 386 (2012). [23] M. Cieslak, S. Grafton, Brain imaging and behavior8(2), 292 (2014). [24] P. Hagmann, et al., PLoS Biology6(7), e159 (2008).

[25] K. Krieger-Redwood, E. Jefferies, Neuropsychologia64, 24 (2014).

[26] H. R. Snyder, Y. Munakata, Psychonomic Bulletin & Review15(6), 1083 (2008). [27] H. R. Snyder, et al., Cognition & emotion28(5), 893 (2014).

[28] Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási, Nature473(7346), 167 (2011). [29] J. Ruths, D. Ruths, Science343(6177), 1373 (2014).

[30] S. J. Schiff, Neural Control Engineering. The MIT Press (2012).

[31] J. D. Medaglia, M. E. Lynall, D. S. Bassett, J Cogn Neurosci27(8), 1471 (2015).

[32] D. S. Bassett, J. A. Brown, V. Deshpande, J. M. Carlson, S. T. Grafton, Neuroimage54(2), 1262 (2011).

[33] A. M. Hermundstad, et al., Proc Natl Acad Sci U S A110(15), 6169 (2013). [34] A. M. Hermundstad, et al., PLoS Comput Biol10(5), e1003591 (2014). [35] M. Cieslak, S. T. Grafton, Brain Imaging Behav8(2), 292 (2014).

[36] C. Honey, et al., Proceedings of the National Academy of Sciences 106(6), 2035 (2009). [37] C. J. Honey, J.-P. Thivierge, O. Sporns, Neuroimage52(3), 766 (2010).

[38] F. Abdelnour, H. U. Voss, A. Raj, Neuroimage90, 335 (2014).

[39] R. E. Kalman, Y. C. Ho, S. K. Narendra, Contributions to Differential Equations1(2), 189 (1963).

[40] A. M. A. Hamdan, A. H. Nayfeh, AIAA Journal of Guidance, Control, and Dynamics12(3), 421 (1989).

[42] F. Pasqualetti, S. Zampieri, F. Bullo, IEEE Transactions on Control of Network Systems1(1), 40 (2014).

[43] M. E. Newman, Proc Natl Acad Sci U S A103(23), 8577 (2006).

[44] V. D. Blondel, J.-L. Guillaume, R. Lambiotte, E. Lefebvre, Journal of Statistical Mechanics: Theory and Experiment10, P1000 (2008).

[45] I. S. Jutla, L. G. S. Jeub, P. J. Mucha, ‘A generalized Louvain method for community detection implemented in MATLAB’ (2011–2012).

[46] B. H. Good, Y. A. de Montjoye, A. Clauset, Phys Rev E81(4 Pt 2), 046106 (2010).

[47] R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2016).

[48] D. Bates, M. Maechler, B. Bolker, S. Walker, et al., R package version1(7) (2014). [49] R. H. Baayen, R package version1(1) (2011).

[50] A. Kuznetsova, P. B. Brockhoff, R. H. B. Christensen, R package version2(6) (2013). [51] J. Fox, et al., Journal of statistical software8(15), 1 (2003).

[52] A. Tremblay, J. Ransijn, R Package Version2 (2015).

[53] R. H. Baayen, D. J. Davidson, D. M. Bates, Journal of memory and language59(4), 390 (2008).

[54] R. F. Lorch, J. L. Myers, Journal of Experimental Psychology: Learning, Memory, and Cognition16(1), 149 (1990).

[55] R. H. Baayen, Analyzing linguistic data: A practical introduction to statistics using R. Cambridge University Press (2008).

[56] L. S. Aiken, S. G. West, R. R. Reno, Multiple regression: Testing and interpreting interactions. Sage (1991).

[57] H. R. Snyder, et al., Proceedings of the National Academy of Sciences107(38), 16483 (2010). [58] D. S. Bassett, et al., PLoS Comput Biol6(4), e1000748 (2010).

[59] D. S. Bassett, E. Bullmore, The neuroscientist12(6), 512 (2006).

[61] J. Trippe, A. Mix, S. Aydin-Abidin, K. Funke, A. Benali, Experimental brain research 199(3-4), 411 (2009).

[62] M. Brass, J. Derrfuss, B. Forstmann, D. Y. von Cramon, Trends in cognitive sciences9(7), 314 (2005).

[63] C. Whitney, M. Kirk, J. O’Sullivan, M. A. L. Ralph, E. Jefferies, Cerebral Cortex p. bhq180 (2010).

[64] T. A. Niendam, et al., Cognitive, Affective, & Behavioral Neuroscience12(2), 241 (2012). [65] T. Watanabe, N. Masuda, F. Megumi, R. Kanai, G. Rees, Nature communications5 (2014).

to influence cognitive-emotional functioning, including in the IFG. Future studies could use

varying stimulation parameters to examine sensitivity of controlled language function to

different stimulation intensities, as well as their interaction with network controllability.

By examining the relationship between inter-individual variability in IFG controllability

and controlled language function before and after brain stimulation, we establish a bridge

between a neuroscientist’s notion of a controlled language process and an engineer’s notion of

network control. The current results demonstrate that linking network controllability in white

matter networks with experimental manipulation involving TMS can reveal associations

between regional network control roles and cognitive susceptibility to brain stimulation.

Inter-individual variability in performing control-demanding tasks is related to the

theoretically predicted specialization of regions in driving the brain into difficult to reach

states. Moreover, changes following TMS similarly dissociate according to the strength of two

distinct control roles in the human connectome. In particular, the degree of dynamic

specialization of the IFG may result in diverse performance across language tasks, and its

ability to govern intermodular dynamics may mediate the cognitive effects of TMS. Similar

experiments may elucidate the role of the IFG in specific and general cognitive control

functions in the human connectome.

Acknowledgments

JDM acknowledges support from the Office of the Director at the National Institutes of Health

through grant number 1-DP5-OD-021352-01. DSB acknowledges support from the John D.

and Catherine T. MacArthur Foundation, the Alfred P. Sloan Foundation, the Army Research

Laboratory and the Army Research Office through contract numbers W911NF-10-2-0022 and

W911NF-14-1-0679, the National Institute of Mental Health (2-R01-DC-009209-11), the

National Institute of Child 415 Health and Human Development (1R01HD086888-01), the

Office of Naval Research, and the National Science Foundation (BCS-1441502,

BCS-1430087, and CAREER PHY-1554488).

References and Notes

[1] M. M. Botvinick, T. S. Braver, D. M. Barch, C. S. Carter, J. D. Cohen, Psychological review 108(3), 624 (2001).

[2] H. Moss, et al., Cerebral Cortex 15(11), 1723 (2005).

[3] J. K. Nelson, P. A. Reuter-Lorenz, J. Persson, C.-Y. C. Sylvester, J. Jonides, Brain research 1256, 92 (2009).

[4] H. R. Snyder, M. T. Banich, Y. Munakata, Journal of cognitive neuroscience 23(11), 3470 (2011). [5] S. L. Thompson-Schill, M. D’Esposito, G. K. Aguirre, M. J. Farah, Proceedings of the National Academy of Sciences 94(26), 14792 (1997).

[6] S. L. Thompson-Schill, M. D’Esposito, I. P. Kan, Neuron 23(3), 513 (1999).

[7] S. L. Thompson-Schill, M. M. Botvinick, Psychonomic Bulletin & Review 13(3), 402 (2006). [8] L. J. Tippett, A. Gendall, M. J. Farah, S. L. Thompson-Schill, Neuropsychology 18(1), 163 (2004). [9] E. Fedorenko, S. L. Thompson-Schill, Trends in cognitive sciences 18(3), 120 (2014).

[10] D. Saur, et al., Proceedings of the national academy of Sciences 105(46), 18035 (2008). [11] K. W. Doron, D. S. Bassett, M. S. Gazzaniga, Proceedings of the National Academy of Sciences 109(46), 18661 (2012).

[12] J. Ruths, D. Ruths, Science 343(6177), 1373 (2014). [13] S. Gu, et al., Nature Communications 6, 8414 (2015).

[14] J. D. Medaglia, F. Pasqualetti, R. H. Hamilton, S. L. Thompson-Schill, D. S. Bassett, arXiv preprint arXiv:1604.04683 (2016).

[15] A. Benali, et al., The Journal of Neuroscience 31(4), 1193 (2011).

[16] Y.-Z. Huang, M. J. Edwards, E. Rounis, K. P. Bhatia, J. C. Rothwell, Neuron 45(2), 201 (2005).

[19] R. F. Betzel, S. Gu, J. D. Medaglia, F. Pasqualetti, D. S. Bassett, arXiv preprint arXiv:1603.05261 (2016).

[20] F.-C. Yeh, V. J. Wedeen, W.-Y. I. Tseng, Neuroimage 55(3), 1054 (2011). [21] B. Fischl, Neuroimage 62(2), 774 (2012).

[22] L. Cammoun, et al., Journal of neuroscience methods 203(2), 386 (2012). [23] M. Cieslak, S. Grafton, Brain imaging and behavior 8(2), 292 (2014). [24] P. Hagmann, et al., PLoS Biology 6(7), e159 (2008).

[25] K. Krieger-Redwood, E. Jefferies, Neuropsychologia 64, 24 (2014).

[26] H. R. Snyder, Y. Munakata, Psychonomic Bulletin & Review 15(6), 1083 (2008). [27] H. R. Snyder, et al., Cognition & emotion 28(5), 893 (2014).

[28] Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási, Nature 473(7346), 167 (2011). [29] J. Ruths, D. Ruths, Science 343(6177), 1373 (2014).

[30] S. J. Schiff, Neural Control Engineering. The MIT Press (2012).

[31] J. D. Medaglia, M. E. Lynall, D. S. Bassett, J Cogn Neurosci 27(8), 1471 (2015).

[32] D. S. Bassett, J. A. Brown, V. Deshpande, J. M. Carlson, S. T. Grafton, Neuroimage 54(2), 1262 (2011).

[33] A. M. Hermundstad, et al., Proc Natl Acad Sci U S A 110(15), 6169 (2013). [34] A. M. Hermundstad, et al., PLoS Comput Biol 10(5), e1003591 (2014). [35] M. Cieslak, S. T. Grafton, Brain Imaging Behav 8(2), 292 (2014).

[36] C. Honey, et al., Proceedings of the National Academy of Sciences 106(6), 2035 (2009). [37] C. J. Honey, J.-P. Thivierge, O. Sporns, Neuroimage 52(3), 766 (2010).

[38] F. Abdelnour, H. U. Voss, A. Raj, Neuroimage 90, 335 (2014).

[39] R. E. Kalman, Y. C. Ho, S. K. Narendra, Contributions to Differential Equations 1(2), 189 (1963).

[40] A. M. A. Hamdan, A. H. Nayfeh, AIAA Journal of Guidance, Control, and Dynamics 12(3), 421 (1989).

[42] F. Pasqualetti, S. Zampieri, F. Bullo, IEEE Transactions on Control of Network Systems 1(1), 40 (2014).

[43] M. E. Newman, Proc Natl Acad Sci U S A 103(23), 8577 (2006).

[44] V. D. Blondel, J.-L. Guillaume, R. Lambiotte, E. Lefebvre, Journal of Statistical Mechanics: Theory and Experiment 10, P1000 (2008).

[45] I. S. Jutla, L. G. S. Jeub, P. J. Mucha, ‘A generalized Louvain method for community detection

implemented in MATLAB’ (2011–2012).

[46] B. H. Good, Y. A. de Montjoye, A. Clauset, Phys Rev E 81(4 Pt 2), 046106 (2010).

[47] R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2016).

[48] D. Bates, M. Maechler, B. Bolker, S. Walker, et al., R package version 1(7) (2014). [49] R. H. Baayen, R package version 1(1) (2011).

[50] A. Kuznetsova, P. B. Brockhoff, R. H. B. Christensen, R package version 2(6) (2013). [51] J. Fox, et al., Journal of statistical software 8(15), 1 (2003).

[52] A. Tremblay, J. Ransijn, R Package Version 2 (2015).

[53] R. H. Baayen, D. J. Davidson, D. M. Bates, Journal of memory and language 59(4), 390 (2008).

[54] R. F. Lorch, J. L. Myers, Journal of Experimental Psychology: Learning, Memory, and Cognition 16(1), 149 (1990).

[55] R. H. Baayen, Analyzing linguistic data: A practical introduction to statistics using R. Cambridge University Press (2008).

[56] L. S. Aiken, S. G. West, R. R. Reno, Multiple regression: Testing and interpreting interactions. Sage (1991).

[57] H. R. Snyder, et al., Proceedings of the National Academy of Sciences 107(38), 16483 (2010). [58] D. S. Bassett, et al., PLoS Comput Biol 6(4), e1000748 (2010).

[61] J. Trippe, A. Mix, S. Aydin-Abidin, K. Funke, A. Benali, Experimental brain research

199(3-4), 411 (2009).

[62] M. Brass, J. Derrfuss, B. Forstmann, D. Y. von Cramon, Trends in cognitive sciences 9(7), 314 (2005).

[63] C. Whitney, M. Kirk, J. O’Sullivan, M. A. L. Ralph, E. Jefferies, Cerebral Cortex p. bhq180 (2010).

[64] T. A. Niendam, et al., Cognitive, Affective, & Behavioral Neuroscience 12(2), 241 (2012). [65] T. Watanabe, N. Masuda, F. Megumi, R. Kanai, G. Rees, Nature communications 5 (2014).