Dynamic neural circuit disruptions associated with antisocial behaviors

Abstract Antisocial behavior (ASB) is believed to have neural substrates; however, the association between ASB and functional brain networks remains unclear. The temporal variability of the functional connectivity (or dynamic FC) derived from resting‐state functional MRI has been suggested as a useful metric for studying abnormal behaviors including ASB. This is the first study using low‐frequency fluctuations of the dynamic FC to unravel potential system‐level neural correlates with ASB. Specifically, we individually associated the dynamic FC patterns with the ASB scores (measured by Antisocial Process Screening Device) of the male offenders (age: 23.29 ± 3.36 years) based on machine learning. Results showed that the dynamic FCs were associated with individual ASB scores. Moreover, we found that it was mainly the inter‐network dynamic FCs that were negatively associated with the ASB severity. Three major high‐order cognitive functional networks and the sensorimotor network were found to be more associated with ASB. We further found that impaired behavior in the ASB subjects was mainly associated with decreased FC dynamics in these networks, which may explain why ASB subjects usually have impaired executive control and emotional processing functions. Our study shows that temporal variation of the FC could be a promising tool for ASB assessment, treatment, and prevention.


| INTRODUCTION
Antisocial behavior (ASB) is an important public health concern due to its serious societal cost, not only involving directly financial loss but also intangible mental pain and injury. There is increasing interest in research on the neural associations of ASB and the risk prediction for future ASB (Poldrack et al., 2017). Numerous studies in the field of behavioral research have provided evidence that indicates disruptions in cognitive functions in ASB subjects (Klapwijk, van den Bos, & Güro glu, 2017). These cognitive function disruptions include difficulties in behavioral control (Murray, Waller, & Hyde, 2018), increased impulsivity (Mackey et al., 2017), risk-taking decisions (Syngelaki, Moore, Savage, Fairchild, & Van Goozen, 2009), and excessive reward-driven behavior (Murray, Shaw, Forbes, & Hyde, 2017), among others.
Neuropsychological deficits in the cognitive functions are thought to contribute to antisocial and aggressive behaviors according to in vivo brain research using structural and functional magnetic resonance imaging (MRI; Ogilvie, Stewart, Chan, & Shum, 2011). Increasing studies using structural MRI have suggested that ASB might be associated with structural or morphometric abnormalities in the highorder cognitive function-related regions. For example, Raine, Lencz, Bihrle, LaCasse, and Colletti (2000) found that individuals with severe ASB had reduced gray matter volume in the dorsolateral and medial prefrontal cortices, further confirmed by their subsequent study (Raine, Yang, Narr, & Toga, 2011). Narayan et al. (2007) found medial frontal cortex thinning in violent ASB individuals. A large cohort study of ASB (N = 1,830) revealed that a higher impulsivity level was associated with decreased gray matter volume in the mediofrontal cortex (Mackey et al., 2017). Sundram et al. (2012) used diffusion-weighted imaging (DWI) and found abnormalities of the fibers in the frontal lobe in ASB. While informative, the fact that ASB subjects usually have impaired behavioral control calls for more functional studies.
The functional abnormalities in the high-level cognitive functionrelated areas were also found in ASB subjects during task-based functional MRI (fMRI) while the subjects were involved in decision making and reward-based learning tasks (Klapwijk et al., 2017;Mackey et al., 2017;Murray et al., 2017). For instance, during a monetary reward/loss task, Murray et al. (2017) found that ASB was related to less activation of the ventral striatum during reward anticipation and less activation of the ventrolateral prefrontal cortex during reward and loss anticipation. During decision making with morally distressful stimuli, reduced activations were consistently found in the medial prefrontal cortex, posterior cingulate cortex, amygdala, and anterior temporal areas in individuals with severe ASB (Harenski, Harenski, Shane, & Kiehl, 2010;Marsh & Cardinale, 2014;Pujol et al., 2012).
Recently, to investigate brain function in more natural circumstances and thus rule out potential confounding factors raised by the task executions, our group has been using resting-state fMRI (rs-fMRI) to investigate abnormal synchronizations of the spontaneous neural activities among different brain regions with functional connectivity (FC) metrics in subjects with severe ASB, that is, antisocial personality disorders (Tang, Jiang, Liao, Wang, & Luo, 2014). Similar to our findings, Yoder, Harenski, Kiehl, and Decety (2015) suggested that executive function-related networks could be the most targeted brain functional system in ASB individuals.
Despite the progress in understanding of ASB, previous research was mainly based on group-level analysis with statistical analysis, and most of the work focused on subjects with severe ASB, for example, those with violent behaviors (Poldrack et al., 2017), antisocial personality disorders (Jiang et al., 2016;Jiang et al., 2017;Tang et al., 2014), and psychopathy (Blair, 2012;Ly et al., 2012). Despite these studies focused on contrasting severe ASB with normal controls, few studies investigated how the brain structure or function changes with different ASB severity levels, that is, the association between brain and ASB scores. Specifically, traditional rs-fMRI-based FC studies of ASB usually calculated a single FC matrix or map with the entire rs-fMRI scan (Contreras-Rodríguez et al., 2015; Tang et al., 2014). The resultant FC metrics have been interpreted as stable FC or timeinvariant (Lurie et al., 2018;Fan et al., 2008;Fan et al., 2007) which is now considered to reflect "core connections" in the brain functional networks and could not be used to characterize adaptive, complex task control-related, "dynamic" brain functional organizations Liu, Zhang, Chang, & Duyn, 2018). Therefore, it is less likely to identify any abnormalities based on such stable FC metrics from the subjects with different ASB severity levels.
To reveal such subtle brain functional changes, dynamic FC (dFC) studies have been recently proposed (Hutchison & Morton, 2016;Medaglia et al., 2018). For example, the temporal variability of the dFC has been found quite informative in detecting the switch of cognitive states (Allen et al., 2014;Lurie et al., 2018) and sensitive to many brain diseases (Jie, Liu, & Shen, 2018;Li, Zang, & Zhang, 2015;Liao et al., 2014;Liu et al., 2018;Suk, Wee, Lee, & Shen, 2016;Yan, Zhang, Sui, & Shen, 2018;. Hutchison, Womelsdorf, Gati, Everling, and Menon (2013) suggested that dFC may reflect an intrinsic brain property with a neural origin and could index changes in large-scale neural activity patterns underlying cognition and behavior. Preti, Bolton, and Van De Ville (2017) provided a comprehensive description of the state-of-the-art dFC analysis approaches, including a widely adopted sliding window-based correlation analysis for capturing time-resolved FC. By descriptive FC measures over subsequent time windows, fluctuations in FC can be captured (Preti et al., 2017). Currently, investigating temporal variability of dFC is believed as an effective method to characterize FCs' intrinsic temporal fluctuations and to associate functional networks' activities and behaviors (Thompson et al., 2013). In their seminal works, Kucyi et al. used standard deviation of a dFC time course to track mind wandering (Kucyi, Salomons, & Davis, 2013) and daydreaming (Kucyi & Davis, 2014). However, the standard deviation of the dFC measures their temporal variability within the full frequency range. To better remove spurious fluctuations and keep those originated from neural activity and involved in changes in cognitive states or brain diseases (Betti et al., 2013;Leonardi & Van De Ville, 2015;Thompson et al., 2013;Wilson et al., 2015 measured only low-frequency component of the dFC time series (dFC-ALFF, amplitude of the low-frequency fluctuations of dFC) for investigating taxi drivers' vigilance network and its experience-related changes. Using dFC-ALFF to characterize ASBrelated brain functional changes is suitable to better understand the neural associations of ASB.
In this study, we focused on ASB subjects with different severity (including mild and severe ASB, measured by a continuous behavioral scale, Antisocial Process Screening Device [APSD]) and tried to establish the individual-level associations between dFC-ALFF and the APSD scores. Specifically, we adopted a recently established machine learning method, namely connectome-based predictive modeling (CPM; Finn et al., 2015;Fong et al., 2019;Scheinost et al., 2019), to the dFC-based individualized ASB association analysis. Based on the literature, we have the following hypotheses: (a) dFC-ALFF can be associated with ASB severity levels, or the ASB score of a single subject can be reflected by his/her dFC pattern; (b) ASB severity could be mediated by the deteriorated dynamic interactions among the highlevel cognitive function-related brain regions; and (c) There exist specific functional networks (mostly high-order cognition-related) that might be more probably targeted by ASB than others.

| Participants and antisocial behavior measure
A hundred and fifteen native Chinese male participants (age range 18-26 years old, 23.29 ± 3.36) were recruited from the School for Youth Offender of Hunan Province. They were sentenced to receive an "enclosed-style" reformatory education. Based on their self-reporting, none of them was excluded due to any brain injury history or any major mental illness, such as schizophrenia, depression, or anxiety neurosis.
All the subjects were right-handed with normal intelligence quotient (IQ, according to the Wechsler Adult Intelligence Scale (Table 1) and without any history of substance abuse.
Two senior psychiatrists assessed the ASB severity for all the subjects. The antisocial behavior and psychopathic traits were quantitatively estimated using the APSD, a 20-item questionnaire based on the Psychopathy Checklist-revised (PCL-R; Frick & Hare, 2001;Goodwin, Sellbom, & Salekin, 2015). APSD measures antisocial behavior and psychopathic traits with regards to impulsivity, narcissism, and callousness-unemotionality, which has been extended to younger adults (Goodwin et al., 2015). Recent (Wang, Deng, Armour, Bi, & Zeng, 2015). The total APSD score reflects the severity of ASB and was used as the target in our study, which ranged from 6 to 29, with a mean of 16.69 and a median of 17 ( Figure S1).
In this experiment, we also screened individual emotional status using the Self-rating Anxiety Scale (SAS; Zung, 1971), which holds good psychometric credentials (Tanaka-Matsumi & Kameoka, 1986). The SAS has been extensively used in the research of emotional disorders (Dunstan & Scott, 2018). Our subjects had the SAS scores ranging from 24 to 57, with a mean of 37.41 and a median of 36 ( Figure S2A). None of the subjects had access to alcohol for at least 6 months before the MRI scan. Each of them was chaperoned by three regulators while going out for the MRI scan. This study was approved by the Ethical Committee of the School for Youth Offender of Hunan Province and by the Ethical Committee of the Third Xiangya Hospital of Central South University. Written informed consent was obtained from each subject.

| Data acquisitions and preprocessing
All rs-fMRI data were acquired on a 3.0-T Philips scanner at the Third Xiangya Hospital of Central South University. Before the scan, subjects were instructed to relax, close their eyes, remain awake, and refrain from any specific thinking. After the scan, a brief survey was carried out to confirm that they did not fall asleep during the scan.
The rs-fMRI scans were performed using a gradient-echo echo-planar imaging (EPI) sequence with the following parameters: repetition time The rs-fMRI data were preprocessed based on an in-house resting-state BOLD fMRI preprocessing pipeline as used by previous studies Zeng et al., 2014Zeng et al., , 2018 based on SPM12 (www.fil.ion.ucl.ac.uk/spm). The first five volumes of the scanned data were removed in consideration of the magnetic saturation, and the remaining volumes were slice timing-corrected and head motioncorrected. The corrected volumes were normalized to the standard EPI template in the Montreal Neurological Institute (MNI) space and resampled to 3 × 3 × 3 mm 3 voxels (Luan, Qi, Xue, Chen, & Shen, 2008;Wu, Qi, & Shen, 2006). Spatial smoothing and temporal filtering were performed using a Gaussian filter of 8-mm full-width halfmaximum kernel and a Chebyshev band-pass filter (0.01-0.08 Hz), respectively. Linear detrending was carried out to remove any signal drift. Both filtering and detrending were conducted in a voxel-wise manner, including the voxels in the white matter and cerebrospinal fluid; therefore, the covariates used in the later step were also filtered and detrended in the same way. Finally, potential influences of physiological noise and artifacts were further reduced by regressing out the nuisance covariates, including six head motion parameters and the mean signals from the white matter, cerebrospinal fluid, and the whole brain, as well as their first-order derivatives .

| Calculation of dynamic FC and its temporal variability
The processing flowchart is plotted in Figure 1. First, we segmented the preprocessed rs-fMRI data into 160 regions of interest (ROIs) by using a predefined atlas (Dosenbach et al., 2010). The regional rs-fMRI signal of each ROI was calculated by averaging the blood-oxygen- To quantify the variability of each dFC time series over time, we calculated the dFC-ALFF for each of the 12,720 dFC time series. The dFC-ALFF reflects the total fluctuation power of a dFC time series within a certain low-frequency range. Of note, ALFF has been traditionally widely used to measure the fluctuations of the BOLD rs-fMRI signals and recently, was adopted to measure the temporal variability of the dFC by our group and other researchers (Leonardi & Van De Ville, 2015;Shen et al., 2016). The dFC-ALFF calculation includes the following steps. First, a fast Fourier transformation (FFT) of each dFC time series was conducted. Second, the ALFF was calculated by summing the amplitudes of the dFC frequency spectrum within a predefined frequency band (in this study, it is 0-1/w Hz, where w = 40 s, that is, the length of the sliding windows). Third, each dFC-ALFF value was standardized to be a z-score by subtracting the mean of all 12,720 dFC-ALFFs of the same subject and dividing by their standard deviation. These z-scores of the dFC-ALFF were used as the features of the following associative model ( Figure 1b).

| ASB associative analysis based on wholebrain dFC-ALFF
We used an SVM (support vector machine)-based regression (SVR) to associate each subject's ASB score with the dFC-ALFF features.
SVM/SVR has been widely used to handle high-dimensional data.
Soft-margin SVM tries to find the maximal margin between two groups while allowing some misclassifications. Theoretical and experi- The inner LOOCV was used to optimize the predictive model by feature selection (p-value from a predefined range .005-.05, with a step of .001), then the optimal model (the selected features with the optimized p-value) was used to generate the result for the left-out sample in an outer LOOCV decision boundary that is nonlinear in the original space but linear in a higher-dimensional space using the "kernel trick" (Jäkel, Schölkopf, & Wichmann, 2009). SVR retains the main features of SVM with only a difference in loss penalty calculation. Here, we used an epsiloninsensitive loss, which defines a "tube" with a width of epsilon around the regression line in the hyperspace and there is no penalty for data points far away from the regression line (Dosenbach et al., 2010).
To obtain the optimal model, we adopted a nested leave-one-out cross-validation (LOOCV) strategy ( The features with p values less than the predefined p threshold were used to train an SVR model that was then used to predict the testing sample of the inner LOOCV. The p threshold that obtains the best association performance throughout the inner SVR prediction was used for predicting ASB scores with the testing data in the outer LOOCV. In this study, the selected features from the training data were used to fit the SVR model with a linear kernel and a hyperparameter C = 1 (Dosenbach et al., 2010;Finn et al., 2015). We did not optimize the hyperparameter but rather fixed it because involving too many freely estimable parameters could make the model less robust (Zhou et al., 2020). For other hyperparameters, we kept them as defaults, including insensitivity = 0 and an eInsensitive loss function (Dosenbach et al., 2010;Finn et al., 2015). After the full outer LOOCV iterations, each of the subjects had a model-generated ASB score. The final performance of the model was assessed by using Pearson's correlation between the model-generated ASB scores and the real ASB scores across all the subjects. Of note, in the original CPM paper, feature selections were carried out for the positively correlated (with the behavior score) features and negatively correlated features to train different associative models, separately (Finn et al., 2015). However, we propose that both types of features should be included in the same SVR model as an "integrated model" (using both positively and negatively correlated features) to reach a relatively unbiased result.
2.5 | Identification of the consistently associative dFC links

| Link-wise contribution evaluation
To reveal potential imaging features that are associated with ASB, we identified the consensus dFC links that were consistently (100%) selected across all the outer LOOCV loops in the integrated model.
For each consensus dFC, we further calculated the averaged Pearson's correlation between its dFC-ALFF and the ASB score across all the outer LOOCV loops, representing the contribution of each dFC link (we hereby called it "link-wise contribution"). Specifically, we separately evaluated the links where weakened dFC-ALFFs were associated with severer ASB scores, and those where abnormally strengthened dFC-ALFFs were associated with severer ASB scores.

| Region-wise contribution evaluation
Of all the consistently selected dFC links, we then determined which brain regions were more associated with ASB. For each ROI, its "degree of contribution" was defined by a sum of half of the absolute values of the "link-wise contributions" across all the dFC links that were connected to this region (Dosenbach et al., 2010). In this way, the ROIs with higher "degree of contributions" were deemed to be more important for ASB-brain association.

| Network-wise contribution evaluation
It is also important to identify which functional network(s) could be more associated with ASB. Therefore, in addition to the link-wise and region-wise contributions, we further summarized a "network-level" degree of association for each predefined large-scale functional network. Such a network-level degree of association included an intranetwork, an inter-network, and pairwise inter-network ASB association index. The intra-network ASB association index was calculated by a sum of the link-wise contribution across all selected intra-network dFC links, while an inter-network ASB association index was calcu- Six well-known functional networks were chosen from a previous study (Dosenbach et al., 2010). They are the cingulo-opercular network (CON), frontoparietal network (FPN), default mode network (DMN), sensorimotor network (SMN), occipital network (OcN), and cerebellum network (CereN). For each network, an intra-and inter-network ASB association indices were generated, and the percentage of each pairwise networks was also calculated. In this way, we generated intranetwork, inter-network, and pairwise-network contributions.
2.6 | ASB association based on network-specific dFC-ALFF In Section 2.4, whole-brain dFC-ALFFs were used to be individually associated with ASB; to further look into which brain functional network(s) might be better associated with ASB scores, we investi- correction was adopted to indicate (a) good associative model(s).

| Validation
To validate the effectiveness of the dFC-based ASB association, we also used the traditional static FCs to associate with ASB scores and compared the results with the dFC-ALFF-based results. The difference between the two methods is that, for static FC-based ASB association, Pearson's correlation of the entire regional rs-fMRI signals was calculated (Shen, Wang, Liu, & Hu, 2010). For each subject, the lower triangular entries in the 160 × 160 static FC matrix were standardized to zscores as we did for standardizing dFC-ALFF features. These z-score transformed static FC features were used as features to feed into the associative model for result comparison instead of the dFC-ALFF values.
To investigate the influence of head motion on the results, we calculated Pearson's correlation between the extent of head motion of the individuals and the 103 dFC-ALFF features that were identified to be most contributive in the brain-behavior association analysis. To measure head motion, we calculated the mean absolute displacement of each volume compared with the previous volume, that is, the Euclidean norm of their first-order derivative terms ( ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Δx 2 + Δy 2 + Δz 2 p ) (Power, Barnes, Snyder, Schlaggar, & Petersen, 2012;Zeng et al., 2014).
To test whether specific mood states can alter the brain dFC and Kuppens and Verduyn (2017), we used SAS scores as targets in a control correlation analysis, where SAS scores were used as targets to feed into the associative model instead of the ASB scores. The same analysis was conducted as that for dFC-ASB association study and compared with the latter.

| Performance of dFC-ALFF-based ASB association
Based on the dFC-ALFF, we used nested LOOCV to investigate the brain-behavior association and found that the SVR model achieved a good performance, with r = .41 (p = 5.77 × 10 −6 ) between the modelgenerated and the observed ASB scores (Figure 2a). works. Only a few intra-network dFC links consistently contributed to the ASB-brain association (Figures 3 and 5a).

| Region-wise contribution
Based on the consistently selected dFC features, the ROI-level degree of association with ASB scores was obtained for each brain region and they were visualized in Figure 4 (see Table 2 for details). In Figure 4, the size of an ROI was proportional to its ASB associative level (i.e., the degree of contribution or importance to the associative model

| Network-wise contribution
The network-level degree of association with ASB score showed more network specificity and more correlation direction specificity.
That is, different large-scale functional networks were found to differently contribute to the ASB-brain association. Generally, the high-order function-related networks, such as CON (cinguloopercular network) and FPN (frontoparietal network), as well as one of the primary networks (sensorimotor network, or SMN), contained more negatively associated features (Figure 5a). This indicates that the severer ASB the subjects had, the lesser their dFC fluctuations were. On the other hand, the OcN (occipital network) had more positively associated features than the negatively associated ones, meaning that the greater the OcN's dFC fluctuations were, the severer ASB the subjects had. While the default mode network (DMN) and the cerebellar network (CereN) did not have such specificity regarding the positive or negative associations with the ASB scores (Figure 5a), the DMN seemed more important than the CereN in the ASB-brain association analysis in terms of the normalized weight. Of all the six large-scale networks, CON appeared to be more informative and more significantly associated with the ASB scores. In addition, we observed a large difference between the involvement of the inter-network and that of the intra-network dFC links, with the former more contributive to the ASB-brain association than the latter.

F I G U R E 3
The dFC-ALFF links that were consistently selected during ASB-brain association, including (

| Performance of network-specific ASB score association
When using intra-network dFC links of each network to associate with ASB, none of the six networks showed any significant associative ability (p > .05). When using pairwise inter-network connections to associate with ASB, the dFC between CON and FPN presented good associative ability (r = .23, p < .05, FDR corrected, Figure 2b), while the dFC between DMN and FPN showed an even better associative ability (r = .41, p < .05, FDR corrected, Figure 2c and Figure S3). Other pairwise networks did not show a significant relationship with ASB (for details, see the Supplemental Document and Table S1).

| Performance of static FC-based ASB association and validation
Compared to the success of the dFC-ALFF-based ASB association, the traditional static FC was not able to generate any valid result (r = −.0577, p = .54).
Among all the 103 contributive dFC-ALFF features, most of them (100, 97.09%) had insignificant correlations with the extent of head motion, while only three (2.91%) showed weak correlation but they were not significant after FDR correction (Table S2). These results imply that head motion may not play an important role in our study (for details, refer the Supporting Information).
In the control correlation experiment, we used SAS scores as targets to feed into the associative model for dFC-SAS association study.
The results showed insignificant association between the dFC-ALFF F I G U R E 4 ROI-level degree of associations with ASB scores. The size of each ROI was proportional to its ASB associative level (i.e., the degree of contributions to ASB-brain association  Figure S2B). From such results, we concluded that the individual emotional status as measured by SAS could not play a significant role in our study.

| General discussions
In this study, we used temporal variations of the dFC from rs-fMRI to investigate the ASB-brain association. As far as we know, it is the first study that uses a dFC technique for individualized association with ASB scores. Compared to static FC, time-varying, dynamic FC was proved to be more sensitive and informative for ASB-brain association. A simple and intuitive dFC metric, that is, dFC-ALFF (Leonardi & Van De Ville, 2015;Shen et al., 2016), showed its promise in individualized trait (ASB) association. More importantly, we revealed specific patterns of dFC-ALFF associated with ASB. Based on the analysis at different spatial scales, we found that (a) ASB score was mainly negatively correlated with the degree of dFC's temporal variation, that is, severer ASB corresponds to less fluctuation of the dFC; (b) All the three high-order cognition-related functional networks (the DMN, CON, and FPN) might be closely associated with the behavioral abnormality in ASB subjects; (c) The inter-network dFCs might contribute more than the intra-network dFCs to the ASB-brain association; and (d) One of the primary networks, SMN, seems also informative to ASB-brain association. Our results provide useful information for the understanding of the potential neural influences on ASB, and for guiding the future interventions or treatment for subjects with severe ASB. In addition, we also found that such a brain dFC-ASB association was less likely affected by head motion and an individual's emotional status.

| Significantly improved ASB-brain association based on dFC
Temporal variations of the dFC (dFC-ALFF) were considerably better than the traditional static FC in the task of ASB-brain association. A possible reason is that the dFC variation and the static FC amplitude may reflect different network characteristics. The dFC was proposed to be related to much higher-level cognitive functions, such as attention levels (Madhyastha, Askren, Boord, & Grabowski, 2015), consciousness (Wang, Ong, Patanaik, Zhou, & Chee, 2016), and task adaptive control (Reddy et al., 2018). The fluctuation of the FC along time could reflect brain network flexibility (Medaglia et al., 2018).
Since most of our subjects had mild ASB, their dFC could be more easily affected than the static FC.
In this study, dFC was found more sensitive to ASB scores than static FC for the mild ASB subjects. Compared to the previous studies, we found that the sensitivity could vary in different ASB-brain association tasks. For example, our previous study has shown that static FC could be useful for classifying subjects with severe ASB (i.e., antisocial personality disorders) from normal controls (Tang et al., 2014). Such a patient versus healthy control classification task is easier than discriminating different degrees of ASB in the current regression analysis. As for disease detection sensitivity, other groups also found that dFC   Shen et al., 2016) or other brain diseases or disorders (Rashid et al., 2016;Rashid, Damaraju, Pearlson, & Calhoun, 2014;Su et al., 2016). Our study suggests that it is better to use dFC as features if the effect of interest is subtle (e.g., mental disorders at their preclinical stages).

| Inter-network dFC deteriorations in ASB
Regarding the brain functional connections that show dFC-ASB correlation, one of the major findings is that the inter-network dFC links are mainly involved. It may suggest that it is the inter-network dFC that could be mainly associated with behavioral deficits, while the intra-network dFCs could be largely intact and resilient (Figures 3 and   5). Such difference might indicate that ASB could mainly target internetwork communications, therefore making the subjects manifesting difficulties in handling social behaviors. Inter-network communications have been regarded essential in maintaining healthy executive control functions (Gallen, Turner, Adnan, & D'Esposito, 2016;Schultz & Cole, 2016). Poor executive control functions might introduce externalizing antisocial behaviors of the offenders (Klapwijk et al., 2017). On the other hand, intra-network connections are mainly for certain specialized brain functions that are less complex than those mediated by or relying on the inter-network connections (Gallen et al., 2016;Schultz & Cole, 2016). The largely intact intra-network dFCs could be the reason that these ASB subjects still look normal in a general sense.
The network-specific ASB association revealed three higher-order networks (CON, FPN, and DMN) that were more strongly associated with ASB than the other functional networks. Interestingly, these three networks have also been mentioned and studied as a triple network model (Menon, 2011), which relies on the assumption that the aberrant inter-network connections could underlie a wide range of psychiatric and neurological disorders (Wu et al., 2016). Our results showed that the temporal variability of the inter-network dFCs, especially those among the three networks, might be more important in maintaining normative cognitive functions and affective statuses, such as healthy social behaviors. Therefore, we provided another support to the importance of the triple network model from the dFC point of view.

| Disruptions of the network-specific dFC
The CON and FPN are considered as two major networks related to control functions (Dosenbach et al., 2010). In our study, both CON and FPN showed less dFC variability with each other and with other networks for the subjects with severer ASB. These two control networks may contribute to the flexible control of the goal-directed behaviors, such as executive control, attentional control, and emotional control through their moment-to-moment interactions and those with other regions (Coste & Kleinschmidt, 2016;Dosenbach et al., 2010;Dosenbach, Fair, Cohen, Schlaggar, & Petersen, 2008;Sadaghiani & D'Esposito, 2015). The CON was believed to provide stable task control over entire task epochs, while the FPN seems to be able to initiate and adjust control in response to feedbacks (Dosenbach et al., 2008;Duncan, 2010;Spreng, Sepulcre, Turner, Stevens, & Schacter, 2013). In a recent study investigating executive functions, the CON and FPN were consistently engaged across switching, updating, and inhibiting tasks (Engelhardt, Harden, Tucker-Drob, & Church, 2018). The impaired dFC variability between the two control networks and between them and other networks in the ASB subjects may result in insufficient control and dysregulation of behaviors, thus leading to more impulsive or involuntary behaviors. Note: Brain region names were adopted from a predefined atlas (Dosenbach et al., 2010). The related links are consistently selected by the associative model. Weight was calculated by a sum of 0.5 × absolute value of the "link-wise contribution" across all the dFC links that connected to this ROI (Dosenbach et al., 2010 (Mak et al., 2017). Apathy, defined as loss or reduction of motivation and associated with decreases in at least two out of three of goal-directed behavior, cognitive activity, or emotion (Husain & Roiser, 2018), has been regarded mainly related to the alterations of the DMN (Husain & Roiser, 2018 The SMN is the only primary functional system that was found to be responsible for ASB, where its dFC variability with CON was found to be negatively associated with ASB, while its dFC variability with DMN was found to be positively associated with ASB. This might imply that it is difficult for the ASB subjects to receive control information sent from these high-level networks to maintain behavioral adaption to the fast-changing environment. It is also possibly associated with abnormal behavioral responses, which could be externalized as antisocial behavior performance, including impulsivity, risk-taking, violent, aggressive behavior, and affective instability. It should be noted that, due to the nature of multivariate machine learning analysis with nested LOOCV, the predictive results and the contributive features between the whole brain-based and specific network-based ASB associations were not strictly the same. We used embedded-(or nested-) LOOCV to select features and the selected features were fed into an SVR model for training the association model. When different features were considered, the complex relationship among them also changed, which resulted in different classification hyperplane and "weights" on the selected features derived from the SVR training. This multivariate analysis will generate different results compared to the mass-univariate analysis such as regression (as each link will be evaluated independently in the latter method). Nevertheless, we found that the results are still consistent to a large extent. On one hand, almost all the predictive links are inter-network links based on whole-brain-based association analysis, which is consistent with the network-wise association analysis with only significant inter-network link-based associations. On the other hand, the CON, DMN, and FPN are among the most useful functional networks compared to the others (Figure 5a), which is consistent with the network-wise association results (only links between CON and FPN, as well as those between DMN and FPN, show significant associative abilities with the ASB scores; Figure 2b,c).

| Possible compensatory effect of cognitive function damage in ASB
In our study, we found that several connectivities showed positively correlated dFC variation with ASB severity, which might indicate a possible compensatory effect against the impaired executive control functions in ASB subjects. These dynamic links are mainly inter-network connections (Figures 3 and 5). Neuroscience research has revealed strong brain plasticity in motor, sensory, and cognitive domains, even in the social capacities (Valk et al., 2017). This type of functional compensation is considered as a neural plastic effect of structural or functional disturbances (Iraji et al., 2016;Tomassini et al., 2016). Therefore, we assume that these increased dFC links in the subjects with severer behavioral disturbance are more likely to be related to functional compensation.

| Limitations and future work
In this study, the low-frequency fluctuations of dFC were used as features to be associated with ASB scores. This metric characterizes the temporal variability of the dFC but might ignore other rich information in the dFC, such as the covariance among different dFC time series (i.e., "high-order FC"; . The sample size of the mild ASB participants is also relatively small for the associative analysis. We will carry out a further experiment and use a large sample size to validate our findings. Additionally, we followed the previous studies to perform within-subject standardization to the dFC-ALFF features, because it is suggested for reducing undesirable relationships with nuisance variables and increasing test-retest reliability of ALFF metrics (Yan, Craddock, Zuo, Zang, & Milham, 2013). In the future, we will investigate the differences between subject-specific z-scoring and other commonly used feature standardization methods in the machine learning field. Since resting state is a less constrained "status" where it is difficult to monitor or maintain subjects' status during the rs-fMRI scan, the interpretation of the rs-fMRI-based findings should be carefully made. Many studies have indicated that varying emotional or cognitive events during the so-called "resting state" could modulate dFC (Barnes, Bullmore, & Suckling, 2009;Cole, Bassett, Power, Braver, & Petersen, 2014;Gonzalez-Castillo et al., 2015;Grigg & Grady, 2010). However, due to technical limitations, monitoring subjects' emotional and cognitive statuses during rs-fMRI scan was not achieved at the time when the data was collected. More careful experimental design, such as monitoring and controlling emotional and cognitive statuses, should be conducted in our future study.
Finally, we did not investigate whether the associations between brain dFC and ASB may be modulated by the severity of ASB. Such a study, however, is interesting and will be investigated in the future when we enrolled enough samples.

| CONCLUSIONS
Our study demonstrated the effectiveness of using dynamic FC in antisocial behavior severity association in a machine learning framework. Dynamic neural circuit disruptions were found to possibly be associated with less cognitive control and more antisocial behavior, such as the inter-network dynamic FCs between the high-level control networks and other functional systems. In particular, three high-order cognitive function-related networks showed to be associated with ASB, especially the impaired controllability as reflected by the reduced dFCs among the control networks. Our study demonstrates that the temporal FC variation measured by the dFC-ALFF method could be a promising tool for ASB assessment, treatment, and prevention.

ACKNOWLEDGMENT
This work was supported in part by NIH grants (EB022880, AG041721, and EB006733) and HSCME grant (19YJAZH035).