# An fMRI-based brain marker of individual differences in delay discounting

Leonie Koban, Sangil Lee, Daniela Schelski, Marie-Christine Simon, Caryn Lerman, Bernd Weber, Joseph Kable, Hilke Plassmann

► To cite this version:

Leonie Koban, Sangil Lee, Daniela Schelski, Marie-Christine Simon, Caryn Lerman, et al. An fMRI-based brain marker of individual differences in delay discounting. Journal of Neuroscience, 2023, 43 (9), pp.1600-1613. 10.1523/JNEUROSCI.1343-22.2022. hal-03957745

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# An fMRI-based brain marker of individual differences in delay discounting

Leonie Koban<sup>1,2,3,*</sup>, Sangil Lee<sup>4</sup>, Daniela S. Schelski<sup>5,6</sup>, Marie-Christine Simon<sup>7</sup>,
Caryn Lerman<sup>8</sup>, Bernd Weber<sup>5,6</sup>, Joseph W. Kable<sup>4</sup>, & Hilke Plassmann<sup>1,2</sup>

<sup>1</sup>Marketing Area, INSEAD, Fontainebleau, France

<sup>2</sup>Control-Interoception-Attention Team, Paris Brain Institute (ICM), INSERM U 1127, CNRS UMR 7225, Sorbonne University, Paris, France

<sup>3</sup>Université Claude Bernard Lyon 1, CNRS, INSERM, Centre de Recherche en Neurosciences de Lyon CRNL U1028 UMR5292, Bron, France

<sup>4</sup>Department of Psychology, University of Pennsylvania, Philadelphia, PA, USA

<sup>5</sup>Center for Economics and Neuroscience, University of Bonn, Bonn, Germany

<sup>6</sup>Institute of Experimental Epileptology and Cognition Research, University of Bonn Medical Center, Bonn, Germany

<sup>7</sup>Institute for Nutrition and Food Science, Nutrition and Microbiota, University of Bonn, Bonn, Germany

<sup>8</sup>Norris Comprehensive Cancer Center, University of Southern California, Los Angeles, CA, USA

\*Correspondence to: leonie.koban@cnrs.fr

Abbreviated title: A BRAIN SIGNATURE OF DELAY DISCOUNTING

## Financial interests or conflict of interest

The authors declare no financial interests or conflict of interests.

## Acknowledgments

We received funding from the ANR (Tremplin-ERC grant "Brain Gut Decision" to HP), Campus France (Marie-Sklodowska-Curie co-fund fellowship PRESTIGE-2018-2-0023 to LK), French federal funding (program 'Investissements d'avenir', ANR-10-IAIHU-06), the Federal Ministry of Education and Research Germany (Diet-Body-Brain grant 01EA1809B to BW and 01EA1707 to MCS), the National Cancer Institute (R35CA197461 [CL] and R01CA170297 [JK and CL]), and the AE Foundation (to JK). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. We thank P. Trautner for help with the programming of the task (Study 1); A. Simonetti, M. Boerth, J. Tholen, A.-A. Ortner, A. Koehlmoos, S. Winkler, L. Bernardo, A. M. Burke, M. K. Caulfield, N. Cooper, G. Donnay, M. Falcone, J. Jorgensen, R. Kazinka, J. Luery, M. McConnell, R. Miglin, D. Mukherjee, T. Parthasarathi, S. Price, M. Schlussel, R. Sharp, H. J. Sohn, D. Spence, and K. Terilli for help with data acquisition; and T. D. Wager for the Canlab toolbox and helpful discussion.
Abstract

Individual differences in delay discounting—how much we discount future compared to immediate rewards—are associated with general life outcomes, psychopathology, and obesity. Here, we use machine learning on fMRI activity during an intertemporal choice task to develop a functional brain marker of these individual differences in human adults. Training and cross-validating the marker in one data set (Study 1, N = 110 male adults) resulted in a significant prediction-outcome correlation (r = 0.49), generalized to predict individual differences in a completely independent data set (Study 2, N = 145 male and female adults, r = 0.45), and predicted discounting several weeks later. Out-of-sample responses of the functional brain marker, but not discounting behavior itself, differed significantly between overweight and lean individuals in both studies, and predicted fasting state blood levels of insulin, c-peptide, and leptin in Study 1. Significant predictive weights of the marker were found in cingulate, insula, and frontoparietal areas, among others, suggesting an interplay among regions associated with valuation, conflict processing, and cognitive control. This new functional brain marker is a step towards a generalizable brain model of individual differences in delay discounting.

Future studies can evaluate it as a potential transdiagnostic marker of altered decision-making in different clinical and developmental populations.
**Significance statement**

People differ substantially in how much they prefer smaller sooner or larger later rewards such as spending money now versus saving it for retirement. These individual differences are generally stable over time and have been related to differences in mental and bodily health. What is their neurobiological basis? We applied machine-learning to brain imaging data to identify a novel brain activity pattern that accurately predicts how much people prefer sooner versus later rewards, and which can be used as a new brain-based measure of intertemporal decision-making in future studies. The resulting functional brain marker also predicts overweight and metabolism-related blood markers, providing new insight into the possible links between metabolism and the cognitive and brain processes involved in intertemporal decision-making.
Introduction

Many decisions in life have consequences at different points in time. For example,
most people need to decide whether to put part of their paycheck towards a retirement
fund or spend it on something fun, like a short vacation. These trade-offs between options
that are immediately rewarding and those that will be more rewarding in the long run are
hard, and people differ substantially in *delay discounting*—the degree to which they
discount future compared to immediate rewards (Kirby and Herrnstein, 1995). Greater
delay discounting (i.e., greater impatience or higher preference for sooner rewards) is
associated with obesity, addiction, and many psychiatric conditions (Bickel et al., 1999;
MacKillop et al., 2011; Mole et al., 2015; Amlung et al., 2016). It has therefore been
proposed as a potential transdiagnostic marker of psychopathology (Amlung et al., 2019;
Lempert et al., 2019) and as a risk factor for short-sighted behaviors such as unhealthy
diet, smoking, and excessive alcohol and drug use (Audrain-McGovern et al., 2009; Fernie
et al., 2013). The goal of the present study is to identify and validate an fMRI-based brain
marker of individual differences in delay discounting.

Previous findings regarding the structural and functional brain bases of individual
differences in delay discounting offer a mixed picture. Several studies suggest a role for
areas involved in reward processing and valuation (Bartra et al., 2013; Cooper et al.,
2013), and for areas central to cognitive control (Hare et al., 2014). Brain areas associated
with memory and prospection have also been found to contribute to individual differences
in delay discounting (Benoit et al., 2011; Peters and Büchel, 2011; Lebreton et al., 2013).
Studies using structural and functional connectivity measures suggested a role for fronto-
striatal and striatal-subcortical connections (van den Bos et al., 2014). The structure of
midbrain dopaminergic nuclei and the ventral striatum has been associated with self-
reported trait impulsivity (MacNiven et al., 2020).
Individual differences in delay discounting may also emerge from the combined activity across multiple brain regions or functional networks. However, only a few studies (Berman et al., 2013; Li et al., 2013; Pehlivanova et al., 2018) have investigated the distributed patterns associated with individual differences in delay discounting. Further, most previous studies used relatively small sample sizes to explore these individual differences, increasing the risk of both false-positive and false-negative results (Poldrack et al., 2017). Given the use of standard correlation or regression analyses that are typically not cross-validated on independent data samples, previous results are difficult to compare with each other and do not provide any formal model that could predict delay discounting in completely independent studies.

Here, we address these limitations by using a machine-learning-based 'brain model' approach (Woo et al., 2017; Kragel et al., 2018). Brain models are trained to predict a mental process or individual variable (here, delay discounting) and can be applied to independent data (Kragel et al., 2018; Scheinost et al., 2019). As such, brain models go beyond reporting peak coordinates by identifying specific large-scale patterns of brain activity that can be replicated, validated, or falsified in a quantifiable way. This approach has been successfully applied to brain-based prediction of pain (Wager et al., 2013), working memory (Rosenberg et al., 2020), and affective states (Yu et al., 2020), among others. The importance of independent validation and model generalizability has also been recognized for brain-based prediction of trait-like individual differences (Gabrieli et al., 2015; Rosenberg et al., 2018; Rosenberg and Finn, 2022).

Here, we build on this approach to predict individual differences in delay discounting. If there is a consistent activity pattern associated with individual differences in delay discounting during intertemporal choices, then this pattern should be able to predict delay discounting in new data (hold-out subjects) and even completely independent data sets. Comparing the resulting pattern to meta-analysis-based masks
allows us to assess the contribution of brain areas associated with valuation, cognitive control, and prospection.

## Materials and methods

### Overview

We used an established machine-learning algorithm, LASSO-PCR (Tibshirani, 1996; Wager et al., 2011) and fMRI data from two independent studies, from different scanners, labs, and countries. Study 1 (N=110) was used for training and cross-validation of a predictive model of individual differences in delay discounting. Study 2 (existing data set from previously published study, see Kable et al., 2017, N=145) was used as an independent test data set to assess the validity and replicability of the predictive model.

### Participants

For Study 1, participants were recruited in the context of a seven-week dietary intervention study at the University of Bonn in Germany (https://osf.io/rj8sw/?view_only=af9cba7f84064e61b29757f768a8d3bf). Due to the nature of this longitudinal intervention study, we recruited only male participants who further fulfilled the following inclusion criteria: age between 20 and 60 years, right-handedness, non-smoker, no excessive drug or alcohol use in the past year, no psychiatric or neurological disease, body mass index (BMI) between 20 and 34, no other chronic illness or medication, following a typical Western diet without dietary restrictions, and no MRI exclusion criteria (large tattoos, non-removable piercings, metal in the body, claustrophobia, etc.). N=116 male participants performed the intertemporal choice task in Study 1. Here, we focus on behavioral and fMRI data collected during a baseline session before the group assignment and dietary intervention (to be reported elsewhere) and use post-intervention behavioral data only for demonstrating the temporal stability of
interindividual differences in delay discounting. The data of six participants had to be excluded for analysis due to the following reasons: technical problems with the scanner (1), with the synchronization between stimulation software and scanner (3), and with the response box (1), and strong motion artifacts (>5mm) and participant quitting the task mid-scan (1). Therefore, 110 participants (mean age=31.7; 52 lean, 48 overweight, and 10 obese; BMIs ranging from 20.6 to 33.7) were included in the final analysis of Study 1. There were no significant differences between lean and overweight-to-obese participants in age, education, or total brain volume (see Table 1). Data from 109 participants were available for the seven-week follow-up measurements (i.e., one participant did not return for the second session).

Study 2 was conducted in the context of a large cognitive training study at the University of Pennsylvania in the United States (Kable et al., 2017). The goal was to examine whether commercial cognitive training software leads to significant changes in decision-making behaviors, including delay discounting. Participants completed two sessions of scans 10 weeks apart. As with Study 1, we focus on the baseline (pre-intervention) behavioral and fMRI data, and report post-intervention behavioral data only to assess the temporal (10-week) stability of interindividual differences in delay discounting. Of the 160 non-pilot participants who completed session 1, we excluded those with missing runs (N=6), frequent or significant head movement (any run with >5% of mean image displacements greater than 0.5mm; N=3), more than 3 missing trials per run for two or more runs (N=2), or lack of participant blinding (N=1, one subject expressed awareness of their experimental condition, i.e. cognitive training vs. control). Of the remaining 148, we excluded three more participants whose choice was entirely one-sided (i.e., choosing only immediate reward or delayed reward), resulting in a final sample of N=145 participants for Study 2 (88 male, 57 female, mean age=24.4; 81 lean, 39 overweight, and 25 obese; BMIs ranging from 16.5 to 40.9). There were no significant
differences between lean and overweight-to-obese participants in sex, age, education, or total brain volume (see Table 1). Due to drop-out, data from 102 participants was available for the 10-week post-intervention measurement of log(k).

The study protocols were approved by the institutional review boards of Bonn University's Medical School (Study 1) and the University of Pennsylvania (Study 2). All participants provided written informed consent, and were paid for their time and participation in the study. The research reported here complies with all relevant ethical regulations.

## Stimuli and task

In Study 1, participants performed 108 choices (trials) between varying amounts of smaller sooner (SS) and larger later (LL) options, presented on the left or right of the screen (position randomized; see Figure 1a). Participants were instructed that one of their choices might be paid out at the end of the experiment. Thus, participants' choices were non-hypothetical and incentive-compatible. During each trial, the two options were presented for 4s, during which participants could make their choice (left or right) by pressing the corresponding response key with their left or right index finger, respectively. Once the choice had been made, a yellow frame highlighted the chosen option and remained on the screen for the remainder of the 4s. Intertrial intervals were jittered using an approximately geometric distribution (2–11s).

SS options varied among €5, €10, and €20, and always had zero delay ('today'). LL options varied between €5 and €96.80 and had delays between 2 days and 8 months (~240 days, choice combinations are presented in Figure 1-1). Amounts and delays were chosen to allow fine-grained estimation of individual k's between 0 and 0.256. Trials were presented in randomized order.
The intertemporal choice task in Study 2 consisted of 120 trials, again with the same choice sets for all participants (see Figure 1-2). In contrast to Study 1, the SS amount was fixed at US$20. Thus, participants were presented with the LL option (with amount ranging from US$22 to US$85 and delays from 19 days to 180 days) and were instructed to press one of two keys to either accept and receive this LL offer, or to reject the LL offer and receive the SS offer ($20 today) instead. Participants were informed that one trial would be randomly chosen at the end of the experiment and their choices implemented (i.e., the chosen amount would be paid via wire transfer at the indicated time delay), resulting in incentive-compatible and mutually independent choices in each trial (as in Study 1).

## Blood measures and body fat measures

In Study 1, blood samples in a fasted state were collected from participants' non-dominant arm before they received a standardized breakfast. HOMA-IR (a marker of insulin resistance) was calculated as the product of fasting insulin and glucose levels, divided by 405 (Lozano et al., 2012). Body weight and proportion of body fat were measured using a bioimpedance scale (Tanita Europe BV, Amsterdam, the Netherlands). For technical reasons, this body fat measure was available for only 103 participants.

## Experimental design and statistical analyses

**Behavioral measures.** For each participant, we calculated the proportion of SS choices (with respect to total number of non-misses) and the model-based discounting parameter k. Individual k's were log-transformed in both studies to obtain less skewed distributions of discounting parameters. This log(k)-parameter describes the steepness of discounting as modeled by the hyperbolic discounting function (Kirby and Herrnstein, 1995). Higher log(k) parameters reflect steeper discounting and thus greater impatience;
smaller (more negative) values reflect less steep discounting and thus more patient
decision-making.

In Study 1 we computed k by calculating the proportion of SS choices for all target
k's (i.e., the k-value for which SS and LL options of any given choice trial should
theoretically be chosen at 50% each). We then used linear interpolation to identify the
individual indifference point at which the proportion of SS and LL choices was equal (50%
each).

In Study 2, we fit a logit utility model on choice data via maximum likelihood
estimation. The logit of the probability of choosing the delayed reward was modeled as
follows:

$$
\text{logit}(p(Y_t = \text{delayed})) = \sigma\left(\frac{LL_t}{1 + kD_t} - 20\right)
$$

Where LLt is the LL amount in trial t and Dt is the delay in trial t. σ was included as
a scaling parameter that controls the relationship between utility difference scale and
choice.

**MRI data acquisition.** Functional and structural brain imaging data for Study 1 were acquired using a Siemens Trio 3T scanner (Erlangen, Germany) at the Life & Brain Institute, Bonn University Hospital, Germany. Functional images used a T2\* weighted EPI-GRAPPA sequence (TR=2.5s, TE=30ms, flip angle=90°, FOV=192mm, acceleration factor R=2, average of 400 volumes) and covered the whole brain in 37 slices (voxel size of 2 x 2 x 3mm, 10% interslice distance). Structural images were acquired using a T1 weighted MPRAGE sequence (1mm isomorphic voxels).

For Study 2, the functional and structural imaging data were acquired with a
Siemens 3T Trio scanner with a 32-channel head coil. High-resolution T1-weighted
anatomical images were acquired using an MPRAGE sequence (T1=1100ms; 160 axial
slices, 0.9375 x 0.9375 x 1.000mm; 192 x 256 matrix). T2*-weighted functional images were acquired using an EPI sequence with 3mm isotropic voxels, 64 x 64 matrix, TR=3s, TE=25ms, 53 axial slices (no interslice gaps), 104 volumes. B0 fieldmap images were collected for distortion correction (TR=1270ms, TE=5 and 7.46ms).

**Preprocessing and basic statistical analyses of fMRI data.** Preprocessing for Study 1 was performed in SPM12 and used a standard pipeline of motion correction, slice time correction, spatial normalization to MNI space, and spatial smoothing of images using an 8mm FWHM Gaussian kernel. Preprocessing for Study 2 was performed in FSL according to the original preprocessing pipeline (Kable et al., 2017). This involved the standard pipeline of motion correction, b0 map unwarping, interleaved slice time correction, spatial smoothing with FWHM 9mm Gaussian kernel, and high-pass filtering (cutoff=104s).

For Study 1, we used SPM12 to fit a general linear model (GLM) for each participant's imaging data, with choice screen onset modeled as a stick function (0s duration) as the main regressor and mean-centered parametric modulators for delay, relative LL amount (LL amount divided by SS amount), SS amount, and reaction time. Six nuisance regressors were added to control for movement artifacts. For Study 2, FSL was used to fit an otherwise similar statistical model with a choice screen onset as main regressor and mean-centered parametric modulators for delay, LL amount, and reaction time. As in Study 1, six movement regressors were added to control for head movement.

Individual contrast images were calculated for the following three regressors of interest that were available for both studies: 1) choice screen onset versus implicit baseline (hereafter referred to as “Choice contrast”), 2) parametric modulation by (relative) LL amount (“LL Amount”), and 3) parametric modulation by delay (“Delay”). Contrast images were gray matter-masked to remove voxels that were unlikely to contain
meaningful BOLD signal and individually z-scored to remove differences in scale across
images (and thereby make results transferable across studies and data sets).

Training and cross-validation.

Training and cross-validation were performed on data from Study 1 only (see
Figure 1b). Individual differences in delay discounting may result from how participants
respond to intertemporal choices overall, from how they process future rewards, and from
how they process time delays. Thus, to capture a combination of functional processes that
together determine delay discounting, we concatenated the contrast images for Choice,
LL Amount, and Delay for each participant, resulting in a feature space that was triple the
size of a single brain image. We then used LASSO-PCR (least absolute shrinkage and
selection operator-principal component regression) (Tibshirani, 1996)—a machine
learning-based regression algorithm—to train a classifier to predict log(k) across all voxel
weights of the concatenated contrast images. LASSO-PCR first performs data reduction
using principal component regression, thus identifying brain regions and networks that are
highly correlated with each other. It then performs the LASSO algorithm, which shrinks
regression weights towards zero, thus reducing the contribution of less important and
more unstable components. LASSO-PCR has been shown to be advantageous for brain
images for several reasons (see Wager et al., 2011; Wager et al., 2013): it is adequate for
predictions based on thousands of voxels, it takes into account multicollinearity between
voxels and brain regions, and it yields interpretable results by allowing reconstruction of
voxel weight maps based on PCR results.

To assess the predictive accuracy of the classifier in new subjects, we used 10-
fold cross-validation. Thus, the training data was split up in 10 stratified combinations of
training (90%) and test sets (10%), such that every subject's data was used for the training
of the classifier in nine folds and held out in the remaining fold to independently assess
the prediction-outcome correlation. Tenfold cross-validation was chosen a priori as a good compromise between maximizing the sample size in each training set and being within the range of recommended folds (between 5 and 10) (Scheinost et al., 2019; Poldrack et al., 2020). A priori set default regularization parameters were used for all machine-learning analysis to avoid biasing the model parameters to the data and thereby generating over-optimistic accuracy scores. Permutation tests (5,000 iterations of randomly permuting the log(k) values) were used to generate null distributions and to assess the statistical significance of the prediction-outcome correlation and the mean absolute error. Out-of-sample predictions of log(k) were used for all correlational analysis (e.g., with BMI, age, blood markers).

**Bootstrapping and thresholding.** To identify the brain areas contributing the most reliable positive or negative weights, we performed a bootstrap analysis; 5,000 samples with replacements were taken from the paired brain and outcome data, and the LASSO-PCR was repeated for each bootstrap sample. Two-tailed, uncorrected p-values were calculated for each voxel based on the proportion of weights above or below zero (Wager et al., 2011; Wager et al., 2013). False discovery rate (FDR) correction was applied to p-values to correct for multiple comparisons across the whole feature space (three combined brain maps).

**Independent test set.** Study 2 was used as an independent test set to assess the validity and generalizability of the brain pattern classifier developed based on Study 1 (i.e., the k-marker). For this purpose of testing its validity in an independent data set (and for all future use of this brain-based model), the k-marker was trained on the data of all participants of Study 1. To assess the response of the predictive marker in Study 2, we calculated the matrix dot product between the k-marker and the concatenated contrast
images (Choice screen onset, LL Amount, and Delay) from each participant. The dot product reflects the pattern similarity between the classifier and each participant's set of contrast images and, in sum with the classifier's intercepts, provides a predicted value of log(k). Predictive accuracy of the marker was quantified by correlating the predicted value of log(k) with the actual log(k)'s of each participant and by calculating the mean absolute error for each prediction.

**Other statistical analyses.** All statistical tests were performed in Matlab, were two-tailed, and used a significance criterion of p=0.05. Statistical power calculations confirmed that the sample sizes in both studies were sufficiently powered (>80%) to detect correlations of r > 0.3 at a significance level of p=0.05 (two-sided tests).

## Results

### Individual differences in delay discounting

In Study 1 (Bonn University, N=110), participants chose the SS option in an average of 43.7% of all trials (median=48.1%) and had a fitted mean log(k) parameter of -5.70 (median log(k)=-5.28, corresponding to a k of 0.0051). Choice behavior was characterized by substantial individual differences, with %SS choices ranging from 5.6% to 88.8%, and log(k) ranging from -9.90 to -1.36 (see Figure 1c). Individual differences were very stable over a 7-week period (see Methods), with a test-retest reliability (correlation between baseline log(k)'s and second session) of r=0.86 (p<0.001, 95%-confidence interval [CI]=[0.80, 0.90], Figure 1c).

On average, participants in Study 2 chose the SS option in 57.4% of trials (median=60.0%) and had an fitted log(k) of -4.08 (median log(k)=-3.95, corresponding to a k of 0.0193). Again, individuals varied substantially in their intertemporal preferences, with %SS ranging from 0.8% to 99.2%, and log(k) ranging from -7.08 to -2.12 (see Figure
1c). As in Study 1, these individual differences were stable over time, with a test-retest reliability between baseline and post-intervention (10 weeks later) measures of log(k) of r=0.74 (Pearson correlation, p<0.001, 95%-CI=[0.63, 0.82], see Figure 1c). Thus, our data confirm both the substantial variability in delay discounting known from previous work (Kable and Glimcher, 2007; Pehlivanova et al., 2018) and the stability of these individual differences over time (Kirby, 2009; Anokhin et al., 2015; Lempert and Phelps, 2016), allowing us to investigate the neurofunctional bases of these individual differences.

## Significant cross-validated prediction of delay discounting based on fMRI

Training (using LASSO-PCR) and cross-validating (10-fold) the predictive marker (termed k-marker, see Figure 2a) in Study 1 resulted in a cross-validated prediction-outcome correlation (i.e., correlation between predicted and actual log(k)) of r=0.49 (permutation test: p<0.001), a mean squared error of 2.84 (permutation test: p<0.001), and a mean absolute error for predicted log(k) of 1.32 (permutation test: p<0.001; see Figure 2b-c for additional results and random cross-validation folds). The explained variance of the prediction compared to a hypothetical mean model (prediction R²) was R²=0.23. Individual differences in head motion (mean absolute framewise displacement) were neither related to log(k) (Pearson correlation: r=-0.05, p=0.58) nor predicted log(k) (Pearson correlation: r=0.01, p=0.92). Statistically controlling for age, education, head motion, and total brain volume (using partial correlations), did not substantially change the relationships between actual log(k) and predicted log(k) (Partial correlation: r=0.54, p<0.001). Out-of-sample k-marker responses also predicted percentage of SS choices (Pearson correlation: r=0.50, p<0.001) and log(k) calculated based on the method of Study 2 (Pearson correlation: r=0.45, p<0.001).

## Validation of the k-marker in an independent test data set (Study 2)
Brain markers of individual differences become more meaningful if they can be validated in different and completely independent data (Kragel et al., 2018). The validity of the marker should not depend on study-specific parameters such as the type of scanner used for data acquisition, preprocessing software, or other aspects of the data (Woo et al., 2017; Kragel et al., 2018; Scheinost et al., 2019).

We therefore tested whether the k-marker—developed and cross-validated entirely on Study 1—could predict discounting in a completely independent data set. The validation data set (Study 2) was acquired on a different scanner, in a different lab and country, and using a different participant sample and different task characteristics, and was preprocessed and analyzed using different MRI analysis software. Evaluating the performance of the k-marker in Study 2 is therefore an even stronger test than cross-validation in Study 1 alone.

For this purpose, we computed the pattern expression of the k-marker using the matrix dot product for each participant's data (contrast images for Choice, parametric modulation for LL Amount, and Delay) in Study 2. The resulting predicted log(k) values were significantly correlated with actual log(k) values (Figure 2c), Pearson correlation: r=0.45, p<0.001, 95%-CI=[0.31, 0.57], mean absolute error of 1.68) demonstrating the replicability of the k-marker in a completely independent data set. For the transfer test to Study 2, prediction R² was -3.2, indicating that, while the k-marker was very accurate in identifying the rankings among individuals, the absolute prediction values were less accurate than a hypothetical mean model.

The training and cross-validation data set (Study 1) consisted of male participants only, which might limit the validity of the k-marker in females. We therefore assessed the accuracy of the k-marker in Study 2 separately in male and female participants (see Figure 2c). In male participants (N=88), the prediction-outcome correlation was r=0.40 (Pearson correlation: p<0.001, 95%-CI=[0.21, 0.56]). In females (N=57), the prediction-outcome
correlation was r=0.55 (Pearson correlation: p<0.001, 95%-CI=[0.34, 0.71]) and thus comparable, if not superior, to the predictive accuracy in males. This demonstrates that the k-marker (despite being trained on male participants' data only) predicts delay discounting well for both male and female participants. As in Study 1, individual differences in head motion in Study 2 were neither related to log(k) (Pearson correlation: r=0.12, p=0.14) nor predicted log(k) (Pearson correlation: r=0.04, p=0.59). Statistically controlling for age, sex, education, head motion, and total brain volume did not change the relationship between predicted and actual log(k) (Partial correlation: r=0.44, p<0.001, 95%-CI=[0.30, 0.56]).

**Brain-based prediction of future discounting**

We next assessed whether responses of the k-marker were predictive of individual
differences in delay discounting as measured several weeks later. Responses of the k-
marker at baseline significantly predicted (out-of-sample) discounting behavior seven
weeks later in Study 1 (Pearson correlation: r=0.38, p<0.001, 95%-CI=[0.20, 0.53]) and
10 weeks later in Study 2 (Pearson correlation: r=0.36, p=0.002, 95%-CI=[0.17, 0.51]; see
Figure 2d). This shows that variability in k-marker responses is driven largely by stable
individual differences and their underlying neurophysiological processes.

Response of the k-marker differs between lean and overweight participants

Given previous findings of higher delay discounting in overweight and obese
people (Jarmolowicz et al., 2014; Amlung et al., 2016), we next tested whether individual
differences in k-marker response were associated with individual differences in body mass
and overweight (as measured by the body mass index [BMI] > 25). In contrast to previous
reports (MacKillop et al., 2011; Amlung et al., 2016) that have studied this relationship
more systematically, actual log(k) was not significantly correlated with BMI in either of the
two samples (Pearson correlations: Study 1: r=0.07, p=0.48, 95%-CI=[-0.12, 0.25]; Study 2: r=-0.04, p=0.69, 95%-CI=[-0.20, 0.12]). However, in Study 1, response of the k-marker significantly correlated with both BMI (Pearson correlation: r=0.26, p=0.005, 95%-CI=[0.08, 0.43]; see Figure 3a) and percentage of body fat (Pearson correlation: r=0.28, p=0.004, 95%-CI=[0.09, 0.45]). The k-marker response in Study 1 also differed between lean (BMI <= 25) and overweight-to-obese (BMI > 25) participants (two-sample t-test: t(108)=2.85, p=0.005, Cohen's d=0.55, 95%-CI=[0.12, 0.69]; see Figure 3b). Further, k-marker response in Study 1 significantly predicted metabolic blood markers that are associated with some of the negative health consequences of obesity, namely fasting-state insulin levels (Pearson correlation: r=0.22, p=0.020, 95%-CI=[0.04, 0.39]), measures related to insulin—HOMA-IR, a marker of insulin resistance (Pearson correlation: r=0.24, p=0.015, 95%-CI=[0.05, 0.41], and C-peptide levels (Pearson correlation: r=0.23, p=0.018, 95%-CI=[0.04, 0.40])—and fasting-state leptin levels (Pearson correlation: r=0.34, p=0.001, 95%-CI=[0.16, 0.49]); see Figure 3c). All these associations remained significant when statistically controlling for age, education, total brain volume, and average head motion.

In Study 2, the correlation between predicted log(k) and BMI was positive but not significant (Pearson correlation: r=0.09, p=0.28, 95%-CI=[-0.07, 0.25]). However, paralleling the findings in Study 1, overweight-to-obese participants had a significantly higher k-marker response (higher predicted discounting) compared to lean participants (two-sample t-test: t(143)=2.11, p=0.037, Cohen's d=0.35, 95%-CI=[0.02, 0.57]; see Figure 3b).

## Thresholded activation patterns of the k-marker

Activation patterns across the whole brain gray matter and across all three contrasts are used for prediction and cross-validation. To identify the areas that
contributed the most strongly with positive or negative weights, we used a bootstrapping procedure (5,000 samples). Bootstrapped weights were thresholded at q=0.05 FDR corrected across the whole weight map of the combined feature space (see Figure 2a and Figures 2-1, 2-2, and 2-3).

Our results revealed a distributed network of areas that jointly contributed to individual differences in delay discounting, including the vmPFC, ventral striatum, anterior midcingulate cortex (aMCC), hippocampus, frontoparietal, and visual areas (see Figure 2). Predictive activity patterns differed for the processes captured by the three different contrast images. Of note, some regions showed negative weights (i.e., predicted less discounting) for one contrast but positive weights (i.e., predicted more discounting) for another. For the Choice (versus implicit baseline) contrast, activity in the striatum, the anterior insula, and lateral prefrontal areas contributed positive weights for more discounting, whereas activity in visual, premotor, and motor areas contributed negative weights. For the parametric modulation by LL Amount, activity in vmPFC, aMCC, posterior cingulate cortex (PCC), precuneus, and frontoparietal areas contributed positive weights for greater discounting, whereas visual areas and premotor areas contributed mainly negative weights. For the parametric modulation by Delay, we observed positive weights in the most ventral part of the vmPFC, premotor areas, and visual cortex and negative weights in frontoparietal areas and brainstem regions.

To further assess the stability of weights, we tested whether developing the predictive model on the data of Study 2 and testing on Study 1 would yield comparable results. Training and cross-validating the model on the data of Study 2 resulted in similar prediction and transfer accuracy (Figure 4) and qualitatively similar weight maps (see Figure 4). At FDR-corrected level, voxels with significant weights in both directions (conjunction null, Nichols et al., 2005) for the LL Amount contrast were found in aMCC, bilateral anterior insula (AI), vmPFC, vLPFC, dLPFC, intraparietal sulcus (IPS), visual
cortex, and cerebellum. For the Delay contrast, significant weights in both directions were found in aMCC, dIPFC, parietal cortex, and AI. No voxels survived FDR correction in both directions for the Choice contrast.

Training predictive patterns on the three contrasts separately resulted in lower predictive accuracies (see Figure 5).

## Similarity of k-marker brain patterns to meta-analytic maps

We next compared the predictive maps of the k-marker with term-based meta-analytic images (Yarkoni et al., 2011) for processes that may contribute to intertemporal decision-making. We computed the spatial correlation (Pearson's r) between the k-marker and meta-analytic maps for 1) affective- and value-related, 2) conflict- and cognitive control-related, and 3) memory-related terms (see Figure 6). While these spatial correlations are descriptive (c.f., Koban et al., 2019), they can inform us quantitatively whether and in which direction (positive or negative) previously identified functional networks contribute to individual differences in delay discounting.

Value- and affect-related maps (especially 'affect' and 'emotion') showed consistent positive correlations ($r$'s > 0.05) with the Choice-related pattern of the k-marker, in line with the idea that more affect-related activity during intertemporal choices leads to more impatient decisions. However, stronger engagement of affective and especially 'reward'- and 'value'-related activity for increasing LL Amount (and, to a lesser extent, for increasing delays) was associated with less discounting. This suggests that lower discounting is associated with greater sensitivity of valuation-related signals to the amount of LL rewards.

In contrast to our initial hypothesis, more activity in cognitive control-related areas was not associated with lower discounting. Instead, there were positive correlations ($r$'s from 0.05 to 0.19) of the Choice pattern with meta-analytic maps for 'attention', 'cognitive
control', 'conflict', and 'executive' (i.e., more positive weights predicting greater discounting). Further, stronger activation of control-related maps by greater LL Amount was associated with greater discounting, whereas stronger activation of control-related activity for longer delays was associated with less discounting.

Finally, we assessed the contribution of brain systems related to memory and prospection. While the term 'memory' (which also includes working-memory studies) showed a similar pattern as control-related maps, more specific terms such as 'episodic memory', 'imagery', and 'planning' were not substantially positively or negatively correlated with any of the k-marker patterns (r's around 0.05 and smaller).

Parallel findings were obtained when testing whether activity in non-overlapping meta-analytic maps (Yarkoni et al., 2011) (for value-related, cognitive control-related, or episodic memory-related activity) could separately predict log(k) (see Figure 7). Whereas areas associated with 'cognitive control' showed significant prediction in Study 1 and transfer to Study 2, areas associated with 'value' predicted discounting in Study 1 but no significant transfer to Study 2. Areas associated with 'episodic memory' showed only marginal prediction in Study 1 and no significant transfer to Study 2.

## Local prediction of log(k)

Finally, we assessed whether activity patterns in smaller, more local brain areas could predict out-of-sample log(k) in Study 1 and whether such predictions would accurately transfer to Study 2. For this purpose, we used an established multi-modal cortical parcellation (Glasser et al., 2016) in combination with several other, subcortical parcellations, resulting in a total of 485 regions (publicly available at https://github.com/canlab/Neuroimaging_Pattern_Masks/tree/master/Atlases_and_parcel lations/2018_Wagerantlas). We trained and cross-validated a separate classifier for each region (combining functional activity across all three contrasts). For
each region we then tested whether the pattern trained on Study 1 data was predictive of
individual differences in Study 2. Activity patterns that consistently predicted delay
discounting in both studies were found in mid- and posterior cingulate cortex, right insula,
and lateral frontal and parietal areas (see Figure 8 and Table 2), in line with the
contributions of these areas in the whole-brain predictive pattern. In addition, activity
patterns in amygdala, hippocampus, basal ganglia and brainstem areas (periaqueductal
gray) also predicted individual differences in delay discounting in both studies.

Discussion

A major goal of neuroscience and psychiatry is to identify neuromarkers of
transdiagnostic processes that are altered across different diseases or predispose
individuals to such diseases (Insel and Cuthbert, 2015). Delay discounting—how much
people prefer sooner compared to future rewards—has been proposed as such a
transdiagnostic process across obesity and various forms of psychopathology, especially
addiction and eating disorders (Bickel et al., 2014; Amlung et al., 2019; Lempert et al.,
2019). In this paper, we advanced our understanding of the brain processes that drive
variability in decision-making by identifying a distributed pattern of functional brain activity
that predicts individual differences in delay discounting. We first used a cross-validation
procedure to develop a novel functional brain marker of delay discounting (k-marker)
based on whole-brain, gray matter-masked fMRI data (N₁=110). We then validated the k-
marker (trained on Study 1 data only) in an independent second fMRI data set (N₂=145),
sampled in a cohort with different socio-demographic characteristics, on a different fMRI
scanner, and employing a different delay discounting task. Prediction-outcome
correlations were 0.49 (Study 1) and 0.45 (Study 2), as large or larger than prediction of
individual differences in other domains reported in previous studies (Rosenberg et al.,
2016; Beaty et al., 2018; Han et al., 2021). In both studies, individual differences in
discounting were stable over time, and k-marker responses measured at baseline
significantly predicted behavior several weeks later.

Recent findings have questioned the utility of brain imaging in predicting individual
differences, especially for structural and resting-state fMRI data and for univariate,
voxelwise-associations (Marek et al., 2022). An important advance of the present study is
that it overcomes many of the limitations of previous studies by providing an independently
cross-validated and multivariate ‘brain model’ (Kragel et al., 2018) of stable individual
differences in impatient decision-making, in line with recent recommendations on studying
brain-based prediction of individual differences (Rosenberg and Finn, 2022). As such, this
brain model can be directly tested, validated, or refined in other existing or future fMRI
data sets acquired during an intertemporal choice task. Its predictive performance can
also be tested in clinical populations, such as patients with severe obesity, eating or
substance use disorders, and other types of psychopathology.

Our results also inform the debate regarding the contributions of specific brain
regions and functional networks to individual differences in delay discounting. Among the
brain areas that contributed with positive and/or negative weights were the vmPFC,
striatum, and other regions associated with valuation and reward (Levy and Glimcher,
2011; Bartra et al., 2013; Clithero and Rangel, 2014). This finding is in line with previous,
univariate findings (Cooper et al., 2013; Pehlivanova et al., 2018; MacNiven et al., 2020).
The present results add to this emergent picture by showing that greater sensitivity of
reward- and value-related areas to the amount of the LL reward is linked to more patient
decision-making.

Significant weights were found most consistently in the frontoparietal areas,
midcingulate cortex, and anterior insula. Activity in these areas also allowed for significant
prediction based on local activity alone (see Figure 8, ROI analysis). The dorsolateral
prefrontal cortex has been theorized to implement self-control and far-sighted decision-
making (McClure et al., 2004; Hare et al., 2014). Yet the present results are surprising as they draw a more complex picture of these areas' contribution to delay discounting, with modulation of these areas by greater LL rewards being positively associated with discounting and modulation by delay being negatively associated with discounting. Thus, areas meta-analytically associated with cognitive control were more recruited for long delays and small LL amounts for low discounters, and for shorter delays and larger LL amounts for high discounters. These are the cases in which decisions are most difficult (closer to the indifference point) and therefore require resolution of response conflict (Botvinick et al., 2001; Kool et al., 2013; Shenhav et al., 2013; Hutcherson et al., 2020), or integration of expected value and risk of future rewards (Tobler et al., 2009).

These findings have implications for models of delay discounting and self-control in cognitive neuroscience. First, they speak against the idea of a simple dual process account of intertemporal choice and self-control (McClure et al., 2004), joining previous work that has suggested more complex neural processes at play (Kable and Glimcher, 2007; Ballard and Knutson, 2009; Hare et al., 2014; Berkman et al., 2017). Second, it also speaks against the idea that more frontoparietal activity is related to higher individual levels of self-control. Instead, it suggests that for which choice options control-related areas are activated is more informative than their overall level of activation. This finding is in line with value-based choice models of self-control (Berkman et al., 2017) and with recent evidence that high and low discounters differ in how much attention they allocate to amount versus delay information (Amasino et al., 2019). It also fits with the idea that low discounters may not need 'control' to discount less (Lempert et al., 2019), and that high discounters may employ cognitive control for different types of decisions.

In line with the importance of prospection and self-projection in intertemporal decision-making, the hippocampus and adjacent midtemporal areas have been associated with individual differences in discounting (Benoit et al., 2011; Peters and
Büchel, 2011; Lebreton et al., 2013). The k-marker has significant weights in parahippocampal areas and in occipital areas, but the weight maps were not strongly associated with broader meta-analysis-based activation maps of episodic memory or prospection, possibly because those masks also include many areas that are involved in processes other than memory and prospection. In agreement with the k-marker results and the literature described above, our ROI-based results showed significant local prediction of individual differences in delay discounting in hippocampus, amygdala and the memory-related anteromedial thalamus.

Our findings highlight the importance of investigating distributed brain activity patterns, confirming the notion that delay discounting depends on the interactions among different functional processes and networks in the brain. In addition to frontoparietal areas, midcingulate, and hippocampus, several other cortical and subcortical areas also allowed for cross-validated local prediction of individual differences in delay discounting, across both data sets. Consistent with the whole-brain results, these included several areas in the mid and posterior insula, which is involved in interoception (Craig, 2009), salience (Bartra et al., 2013), and exploration (Zhen et al., 2022)—processes which may all be involved in delay discounting. Local prediction was also found in subcortical areas associated with affect and visceromotor control, including the amygdala and the periaqueductal gray.

Previous work has related individual differences in delay discounting with obesity, substance use disorders, and psychiatric diseases (Peters and Büchel, 2011; Amlung et al., 2019; Lempert et al., 2019). In the two samples presented here, log(k) values based on participants' choices themselves were not significantly associated with BMI or overweight. However, the two studies were not designed to include a large range of BMI or many obese participants, and obesity-related alterations in discounting might be more pronounced for food than monetary rewards. While in Study 1 participants' height and
weight were measured by the experimenters, these values were self-reported in Study 2, which might explain the lower associations with BMI in Study 2.

In contrast to discounting behavior, responses to the k-marker did significantly differ between lean and overweight participants and predicted out-of-sample blood markers related to glucose and fat metabolism. These findings suggest that this functional brain marker reflects variance in neurophysiology that is related to stable long-term patterns in decision-making and health. The k-marker even seemed more sensitive to individual differences than the behavioral measures it was trained on, potentially because it is a closer reflection of the neurophysiological underpinnings that drive both discounting behavior and more distal health outcomes, in line with previous evidence that brain-based can outperform behavior-based prediction (Genevsky et al., 2017). Of note, our approach is cross-sectional and remains agnostic regarding potential causal links among brain function, behavior, and body weight. While higher discounting is typically considered a causal or predisposing factor for weight gain, an alternative hypothesis is that overweight and changes in metabolism lead to changes in brain physiology and subsequent behavioral outcomes (Cornil et al., 2021; Schmidt et al., 2021). Future work can test the k-marker in larger numbers of participants with obesity and other health conditions.

In conclusion, the k-marker—a novel fMRI-based brain signature—predicts individual differences in intertemporal decision-making in neurotypical, healthy adults across different populations, scanners, and analysis pipelines. It can be quantitatively tested in any other fMRI study on delay discounting for which contrast images for Choice, LL Amount, and Delay can be computed, including in other delay discounting paradigms, such as those that involve non-monetary rewards such as food or social discounting tasks (Jones and Rachlin, 2006; Strombach et al., 2015). Future work could test the generalizability of the k-marker in children, adolescents, the elderly, or clinical populations. Most importantly, future work will show whether the k-marker prospectively predicts clinical
status and health outcomes in conditions related to abnormal discounting, such as eating
disorders, substance use, and other psychiatric disorders.

Data and code availability statement

Data from Study 2 is available in an online public repository (doi:
10.18112/openneuro ds002843.v1.0.0). Deidentified data from Study 1 will be made
available upon publication. The resulting classifier patterns (k-marker) and code to apply
it to other datasets is available at: https://github.com/ldmk/k-marker. Code for analyses is
available at https://github.com/canlab and upon request to the first author.
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Zhen S, Yaple ZA, Eickhoff SB, Yu R (2022) To learn or to gain: neural signatures of exploration in human decision-making. Brain Struct Funct 227:63-76.
Tables

<table><caption>**Table 1. Person-level characteristics of lean (BMI <= 25) and overweight-to-obese (BMI > 25) participants in Study 1 and Study 2. Except for body mass (by definition) and k-marker responses, none of the variables differed significantly between the two groups.**</caption><thead><tr><th rowspan="2"></th><th colspan="2">BMI <= 25</th><th colspan="3">two-sample t-test</th></tr><tr><th>M(STD)</th><th>M(STD)</th><th>t(df)</th><th>p-value</th><th>CI</th></tr></thead><tbody><tr><td>Study 1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>N</td><td>52</td><td>58</td><td></td><td></td><td></td></tr><tr><td>BMI</td><td>23.0 (1.3)</td><td>27.8 (2.2)</td><td>-13.8 (108)</td><td>&lt;0.001*</td><td>[-5.51, -4.13]</td></tr><tr><td>Log(k)</td><td>-5.71 (1.83)</td><td>-5.70 (2.04)</td><td>-0.04 (108)</td><td>0.96</td><td>[-0.75, 0.72]</td></tr><tr><td>k-marker</td><td>-5.87 (0.76)</td><td>-5.46 (0.74)</td><td>-2.85 (108)</td><td>0.005*</td><td>[-0.69, -0.12]</td></tr><tr><td>Age (y)</td><td>30.8 (10.4)</td><td>32.4 (9.8)</td><td>-0.85 (108)</td><td>0.40</td><td>[-5.43, 2.17]</td></tr><tr><td>Education (ordinal scale)</td><td>5.09 (2.71)</td><td>5.05 (2.89)</td><td>0.08 (108)</td><td>0.93</td><td>[-1.02, 1.11]</td></tr><tr><td>Total brain volume (l)</td><td>1.17 (0.09)</td><td>1.18 (0.09)</td><td>-0.62 (108)</td><td>0.53</td><td>[-0.04, 0.02]</td></tr></tbody></table>

<table><thead><tr><th rowspan="2"></th><th colspan="2">BMI <= 25</th><th colspan="3">two-sample t-test</th></tr><tr><th>M(STD)</th><th>M(STD)</th><th>t(df)</th><th>p-value</th><th>CI</th></tr></thead><tbody><tr><td>Study 2</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>N</td><td>81</td><td>64</td><td></td><td></td><td></td></tr><tr><td>BMI</td><td>22.2 (1.8)</td><td>29.4 (3.9)</td><td>-14.9 (143)</td><td>&lt;0.001*</td><td>[-8.18, -6.27]</td></tr><tr><td>Log(k)</td><td>-4.09 (1.00)</td><td>-4.08 (0.83)</td><td>-0.08 (143)</td><td>0.94</td><td>[-0.32, 0.30]</td></tr><tr><td>k-marker</td><td>-5.86 (0.90)</td><td>-5.57 (0.74)</td><td>-2.1 (143)</td><td>0.037*</td><td>[-0.57, -0.02]</td></tr><tr><td>Age</td><td>24.2 (4.5)</td><td>24.6 (4.5)</td><td>-0.57 (143)</td><td>0.57</td><td>[-1.93, 1.07]</td></tr><tr><td>Education</td><td>3.31 (0.93)</td><td>3.39 (0.81)</td><td>-0.56 (143)</td><td>0.58</td><td>[-0.37, 0.21]</td></tr><tr><td>Total brain volume (l)</td><td>1.26 (0.12)</td><td>1.26 (0.12)</td><td>-0.11 (143)</td><td>0.91</td><td>[-0.04, 0.04]</td></tr></tbody></table>

chi²-test
<table><thead><tr><th>Sex</th><th></th><th></th><th>chi²</th><th>p-value</th></tr></thead><tbody><tr><td>-Male (N)</td><td>46</td><td>42</td><td>1.17 (1)</td><td>0.28</td></tr><tr><td>-Female (N)</td><td>35</td><td>22</td><td></td><td></td></tr></tbody></table>
**Table 2. ROI-based prediction of individual differences in log(k).** This analysis used an existing atlas of the brain, including 485 regions based on several different previous parcellations (Diedrichsen et al., 2009; Shen et al., 2013; Bär et al., 2016; Glasser et al., 2016; Pauli et al., 2016) available at: https://github.com/canlab/Neuroimaging_Pattern_Masks/tree/master/Atlases_and_parcels/2018_Wagerantlas). Predictive patterns were trained and cross-validated on Study 1 data only (using the same procedures as for the global classifier) and then tested in Study 2. The table below shows only brain parcels that had significant prediction in both data sets (p-values are uncorrected for multiple comparisons). Note that each parcel contains many voxels, each of which may contribute with positive and/or negative weights to delay discounting for each of the three contrast images.

<table><thead><tr><th rowspan="2">Area name</th><th rowspan="2">Area description</th><th rowspan="2">Hemisphere</th><th colspan="2">Study 1 (training and cross-validation)</th><th colspan="2">Study 2 (test)</th></tr><tr><th>Prediction-outcome r</th><th>p-value</th><th>Prediction-outcome r</th><th>p-value</th></tr></thead><tbody><tr><td>RSC</td><td>RetroSplenial Complex</td><td>L</td><td>0.30</td><td>0.010</td><td>0.21</td><td>0.010</td></tr><tr><td>RSC</td><td>RetroSplenial Complex</td><td>R</td><td>0.23</td><td>0.049</td><td>0.21</td><td>0.013</td></tr><tr><td>23d</td><td>Area dorsal 23</td><td>L</td><td>0.23</td><td>0.042</td><td>0.17</td><td>0.043</td></tr><tr><td>7Am</td><td>Medial Area 7a</td><td>L</td><td>0.23</td><td>0.045</td><td>0.22</td><td>0.007</td></tr><tr><td>7Am</td><td>Medial Area 7a</td><td>R</td><td>0.30</td><td>0.009</td><td>0.28</td><td>0.001</td></tr><tr><td>7PC</td><td>Area 7PC</td><td>R</td><td>0.28</td><td>0.016</td><td>0.20</td><td>0.014</td></tr><tr><td>Area1</td><td>Area 1</td><td>L</td><td>0.23</td><td>0.037</td><td>0.18</td><td>0.035</td></tr><tr><td>p24pr</td><td>Area posterior 24 prime</td><td>L</td><td>0.30</td><td>0.014</td><td>0.21</td><td>0.011</td></tr></tbody></table>
<table>
  <tr>
    <td>a24pr</td>
    <td>Area anterior 24 prime</td>
    <td>L</td>
    <td>0.38</td>
    <td>0.001</td>
    <td>0.21</td>
    <td>0.013</td>
  </tr>
  <tr>
    <td>a24pr</td>
    <td>Area anterior 24 prime</td>
    <td>R</td>
    <td>0.37</td>
    <td>0.001</td>
    <td>0.21</td>
    <td>0.010</td>
  </tr>
  <tr>
    <td>p32pr</td>
    <td>Area posterior 32 prime</td>
    <td>L</td>
    <td>0.43</td>
    <td>0.000</td>
    <td>0.20</td>
    <td>0.016</td>
  </tr>
  <tr>
    <td>d32</td>
    <td>Area dorsal 32</td>
    <td>L</td>
    <td>0.36</td>
    <td>0.002</td>
    <td>0.24</td>
    <td>0.004</td>
  </tr>
  <tr>
    <td>d32</td>
    <td>Area dorsal 32</td>
    <td>R</td>
    <td>0.28</td>
    <td>0.016</td>
    <td>0.34</td>
    <td>0.000</td>
  </tr>
  <tr>
    <td>8BM</td>
    <td>Area 8BM</td>
    <td>L</td>
    <td>0.25</td>
    <td>0.033</td>
    <td>0.29</td>
    <td>0.000</td>
  </tr>
  <tr>
    <td>8BM</td>
    <td>Area 8BM</td>
    <td>R</td>
    <td>0.30</td>
    <td>0.012</td>
    <td>0.26</td>
    <td>0.001</td>
  </tr>
  <tr>
    <td>13l</td>
    <td>Area 13I</td>
    <td>R</td>
    <td>0.25</td>
    <td>0.025</td>
    <td>-0.16</td>
    <td>0.048</td>
  </tr>
  <tr>
    <td>6a</td>
    <td>Area 6 anterior</td>
    <td>R</td>
    <td>0.40</td>
    <td>0.001</td>
    <td>0.30</td>
    <td>0.000</td>
  </tr>
  <tr>
    <td>PoI2</td>
    <td>Posterior Insular Area 2</td>
    <td>R</td>
    <td>0.35</td>
    <td>0.004</td>
    <td>0.21</td>
    <td>0.009</td>
  </tr>
  <tr>
    <td>MI</td>
    <td>Middle Insular Area</td>
    <td>R</td>
    <td>0.23</td>
    <td>0.040</td>
    <td>0.39</td>
    <td>0.000</td>
  </tr>
  <tr>
    <td>AVI</td>
    <td>Anterior Ventral Insular Area</td>
    <td>R</td>
    <td>0.30</td>
    <td>0.009</td>
    <td>0.43</td>
    <td>0.000</td>
  </tr>
  <tr>
    <td>TPOJ3</td>
    <td>Temporoparietooccipital Junction 3</td>
    <td>R</td>
    <td>0.28</td>
    <td>0.017</td>
    <td>0.20</td>
    <td>0.018</td>
  </tr>
  <tr>
    <td>IP1</td>
    <td>Area IntraParietal11</td>
    <td>R</td>
    <td>0.29</td>
    <td>0.013</td>
    <td>0.23</td>
    <td>0.006</td>
  </tr>
  <tr>
    <td>PFm</td>
    <td>Area PFm Complex</td>
    <td>R</td>
    <td>0.25</td>
    <td>0.028</td>
    <td>0.24</td>
    <td>0.003</td>
  </tr>
  <tr>
    <td>PoI1</td>
    <td>Posterior Insular Area 1</td>
    <td>R</td>
    <td>0.24</td>
    <td>0.041</td>
    <td>0.27</td>
    <td>0.001</td>
  </tr>
  <tr>
    <td>FOP5</td>
    <td>Area Frontal Opercular 5</td>
    <td>R</td>
    <td>0.27</td>
    <td>0.022</td>
    <td>0.36</td>
    <td>0.000</td>
  </tr>
  <tr>
    <td>GPi</td>
    <td>Internal globus pallidus Anteromedial thalamic</td>
    <td>R</td>
    <td>0.23</td>
    <td>0.046</td>
    <td>0.23</td>
    <td>0.005</td>
  </tr>
  <tr>
    <td>Thal_AM</td>
    <td>nucleus</td>
    <td>L</td>
    <td>0.27</td>
    <td>0.024</td>
    <td>0.19</td>
    <td>0.020</td>
  </tr>
</table>
<table><tr><td>Bstem Midbd</td><td>Brainstem midbrain</td><td>L</td><td>0.23</td><td>0.047</td><td>0.22</td><td>0.008</td></tr><tr><td></td><td>Brainstem periaqueductal</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Bstem PAG</td><td>gray</td><td>R&L</td><td>0.39</td><td>0.001</td><td>0.19</td><td>0.023</td></tr><tr><td>CA2</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hippocampus</td><td>Hippocampus area CA2</td><td>R&L</td><td>0.22</td><td>0.040</td><td>0.20</td><td>0.015</td></tr><tr><td>Amygdala CM</td><td>Centromedial amygdala</td><td>R&L</td><td>0.22</td><td>0.038</td><td>0.17</td><td>0.042</td></tr></table>
Figure Legends

<figure><img src="image_1.png" /><figcaption>**b Analytic approach**</figcaption></figure>

<figure><img src="image_2.png" /><figcaption>**c Distribution and temporal stability of individual log(k) parameters**</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Figure 1. Experimental design, analytical approach, and discounting behavior.** **a)**</figcaption></figure>

Visual presentation of the intertemporal choice tasks and their timing in Study 1 and Study 2. All combinations of amounts and delays can be found in Extended Data tables Figure 1-1 (for Study 1) and Figure 1-2 (for Study 2).

**b) Analytic approach.** Contrast
images for brain activity in response to the onset of the Choice screen and its parametric
modulation by LL Amount and Delay were computed for each participant and
concatenated. Data from Study 1 was used for training and 10-fold cross-validation. In
each fold, the classifier was trained on 90% of the data using LASSO-PCR and tested on
the remaining 10% hold-out data to evaluate its predictive accuracy. The predictive
classifier obtained from Study 1 was then tested on Study 2 data, acquired on a different
scanner, in a different lab and country, assessing its validity in a completely independent
data set. c) Distribution and temporal stability of individual log-transformed k-parameters
by study. Scatterplots show high correlations between individual differences in discounting
at baseline and several weeks later (Study 1: N=110, r=0.86, p=0.001, 95% CI=[0.80,
0.90], Study 2: N=145, r=0.74, p=0.001, 95%-CI=[0.63, 0.82]).
<figure><img src="image_4.png" /><figcaption>b) Permutation test results (Study 1)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>c) Prediction-outcome correlations</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>d) Prediction of future discounting</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 2. Weight maps and predictive accuracy of the classifier ('k-marker'). a)</figcaption></figure>

Classifier weights for the three contrast images (Choice screen onset, parametric modulation by LL Amount and Delay), thresholded for illustration at q=0.05 FDR corrected across the combined feature space (three concatenated maps). See Extended Data Figure 2-1, Figure 2-2, and Figure 2-3 for coordinate tables. Note that unthresholded maps are used for prediction and that the combined weights across maps are contributing to the prediction. Pop-out maps show the unthresholded patterns for selected regions of interest (transversal slices for vmPFC, coronal for dlPFC, and sagittal for hippocampus), in order to illustrate the heterogeneity of voxel weights (e.g., positive versus negative) within each
region and across the three interdependent weight maps. **b)** Results of the permutation tests (Study 1). Log(k) values were randomly permuted, and the prediction algorithm was repeated on the permuted brain-outcome data 5000 times to generate null distributions (in gray) for standard accuracy metrics (from left to right): mean squared error (MSE), root mean squared error (RMSE), mean absolute error (mean abs error), and prediction-outcome correlation (all *p*-values < 0.0002). In addition, observed metrics in 5000 random cross-validation folds are shown in blue bars. **c)** For interpretability and comparability across both studies, prediction-outcome correlations are shown as scatterplots, for Study 1 (N=110, r=0.49, p<0.001, permutation test) and Study 2 (independent validation data set, parametric prediction-outcome correlation, N=145, r=0.45, p<0.001, 95%-CI=[0.31, 0.57]). Correlations between predicted and observed log(k) were significant in both male and female participants (Study 2). **d)** Prediction of future discounting. Responses of the k-marker responses at baseline significantly predict individual differences in log(k) seven weeks later in Study 1 (left panel, N=109, r=0.38, p=0.001, 95%-CI=[0.20, 0.53]) and ten weeks later in Study 2 (right panel, N=102, r=0.36, p=0.002, 95%-CI=[0.17, 0.51]).
a

Study 1

<figure><img src="image_8.png" /></figure>

Study 2

<figure><img src="image_9.png" /></figure>

b

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

c

Study 1

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

**Figure 3. Association of k-marker response with BMI, overweight, and metabolic blood markers.**

a) The k-marker response was positively and significantly correlated with BMI in Study 1 (N=110, r=0.26, p=0.005, 95%-CI=[0.08, 0.43]), but not significantly in Study 2 (N=145, r=0.09, p=0.28, 95%-CI=[-0.07, 0.25]).

b) In both studies, k-marker response was significantly greater (predicting more delay discounting) in overweight (BMI > 25) compared to lean participants (Study 1: t(108)=2.85, p=0.005, Cohen's d=0.55, 95%-CI=[0.12, 0.69]; Study 2: t(143)=2.11, p=0.037, Cohen's d=0.35, 95%-CI=[0.02, 0.57]). Lean and overweight participants did not differ on any demographic variables in both studies (see Table 1).

c) Individual differences in out-of-sample k-marker response
in Study 1 were positively and significantly correlated with serum insulin (N=110, r=0.22, p=0.020, 95%-CI=[0.04, 0.39]), C-peptide (N=110, r=0.23, p=0.018, 95%-CI=[0.04, 0.40]), insulin resistance (as measured by the HOMA-IR index, N=105, r=0.24, p=0.015, 95%-CI=[0.05, 0.41]), and leptin (N=102, r=0.34, p=0.001, 95%-CI=[0.16, 0.49]).
<figure><img src="image_16.png" /><figcaption>Figure 4. Results for an alternative model trained on the data of Study 2 and comparison of weight maps (control analysis). a) Training and cross-validating an alternative predictive model on the data of Study 2 (N=145) resulted in a prediction-outcome correlation of r=0.50 (comparable to the original predictive model) and a</figcaption></figure>
prediction R²=0.25. Testing this model on the data of Study 1 (N=110, as an independent test set) resulted in a prediction-outcome correlation of r=0.47 and a prediction R²=-0.61.

The contrast-wise unthresholded weight maps of the two different predictive models are displayed in panels **b**) (for the Choice contrast), **c**) (LL-Amount), and **d**) (Delay). Yellow indicates positive and blue indicates negative voxel weights, with lower transparencies indicating stronger absolute weights. Black outlines reflect the conjunction of significant feature weights in both models (at P < 0.05 corrected for multiple comparisons in each model). The correlation between feature weights correlated of the two models was r=0.09 (across all three maps). Correlations for the LL-Amount (r=0.10) and Delay contrast (r=0.11) were numerically higher than for the Choice screen contrast (r=0.05).

<figure><img src="image_17.png" /><figcaption>**Figure 5.** Results (prediction-outcome correlations) for training separate predictive models for each of the three contrasts (control analysis). To assess their distinct</figcaption></figure>
contributions, we trained three separate predictive models on each of the three contrast
maps of Study 1 and tested them on the corresponding contrast maps of Study 2 (using
the same algorithm and cross-validation procedure as before). The results showed modest
predictive accuracy for the model trained on the Choice screen contrast only (top row),
with a prediction-outcome correlation of r = 0.19 in Study 1 (training and cross-validation
set, p = 0.10 based on permutation test, 5000 iterations) and of r = 0.15 in Study 2
(p = 0.07). Training a model based on the LL-Amount contrast had a significant prediction-
outcome correlation of r = 0.38 in Study 1 (p < 0.001, permutation test) and of r = 0.34
(p < 0.001) in Study 2. Similarly, training a model on the Delay contrast resulted in a
significant prediction-outcome correlation of r = 0.34 in Study 1 (p = 0.014, permutation
test) and of r = 0.25 (p = 0.002) in Study 2. Thus, none of the separate models achieved
similarly high predictive performance as the combined model (three concatenated
contrasts), especially regarding transfer to Study 2.
<figure><img src="image_18.png" /><figcaption>**Figure 6.** Spatial similarity of the k-marker with meta-analytic maps. In order to quantitatively compare the classifier patterns with theoretically relevant functional networks, we computed the spatial correlation of the unthresholded k-marker patterns with thresholded Neurosynth meta-analytic maps (Yarkoni et al., 2011) associated with a) value, reward and affect, b) conflict and control, and c) memory, imagery, and planning. Meta-analytic maps from each group of terms are overlaid on the left (outline colors matching the outlines of the terms on the right) and can be inspected in greater detail online (www.Neurosynth.org). Note that spatial correlations are purely descriptive, indicating whether activity in any of the shown functional maps is positively (r > 0) or</figcaption></figure>
negatively ($r < 0$) associated with discounting for each component map of the k-marker
(Choice, LL Amount, Delay).
<figure><img src="image_19.png" /><figcaption>Figure 7. Results for training separate predictive models in three different meta-analytic maps. Term-based meta-analytic maps for a) ‘value’, b) ‘cognitive control’, and c) ‘episodic memory’ were downloaded from Neurosynth (Yarkoni et al., 2011). To obtain</figcaption></figure>
non-overlapping maps (displayed in orange), we masked by excluding voxels that were part of any of the other two maps. We then trained and cross-validated predictive patterns of individual differences in log(k) in the data of Study 1 (blue scatter plots) and further tested the performance of these patterns in Study 2 (green scatter plots). While activity in 'cognitive-control'-related areas led to significant cross-validated prediction in Study 1 and significant transfer to Study 2, such effects were weaker for value or episodic-memory related areas.

<figure><img src="image_20.png" /><figcaption>**Figure 8.** Region of interest (ROI)-based prediction of individual differences in discounting. An established cortical parcellation (Glasser et al., 2016) together with a combination of subcortical parcellations (see atlas available on Github:</figcaption></figure>

https://github.com/canlab/Neuroimaging_Pattern_Masks/tree/master/Atlases_and_parcettations/2018_WagerantCombinedAtlas) was used to test whether functional activity across all three contrasts (Choice, LL -Amount, and Delay) in local brain areas could predict individual log(k)'s. ROIs that resulted in significant cross-validated prediction in Study 1 and significant transfer to Study 2 are shown in yellow (*p*=0.01 uncorrected for multiple comparisons in both studies) and orange (*p*=0.05 uncorrected in both studies). They included areas in the mid- and posterior cingulate, dorsomedial prefrontal cortex, several
regions in the right insula, lateral frontoparietal regions, hippocampus, amygdala, thalamus, and brainstem areas.
**Extended Data Legends**

**Figure 1-1.** Combination of SS, LL amounts, and delays used in Study 1. Indifference k denotes the discounting rate at which the SS and LL options should be chosen at equal proportions.

**Figure 1-2.** Combination of SS, LL amounts, and delays used in Study 2. Indifference k denotes the discounting rate at which the SS and LL options should be chosen at equal proportions.

**Figure 2-1.** Significant positive and negative weights contributing to the k-marker during Choice screen onset (FDR corrected q < 0.05 across the whole feature space, i.e., three concatenated gray-matter-masked whole-brain maps, and at least three contingent voxels). In the column ‘Atlas label’, cortical regions (Ctx) are labeled based on the multimodal cortical parcellation by Glasser et al. (2016), basal ganglia regions based on Pauli et al. (2016), cerebellar regions based on Diedrichsen et al. (2009), and brain stem regions based on a combination of studies (Shen et al., 2013; Bär et al., 2016). The entire combined anatomical atlas is available on Github:

https://github.com/canlab/Neuroimaging_Pattern_Masks/tree/master/Atlases_and_parcels/2018_Wagerzeile组合atlas. This repository includes multiple atlases and other meta-analytic and multivariate maps. Tools for manipulating and analyzing this and other atlases are in the CANlab Core Tools repository: https://github.com/canlab/CanlabCore.

**Figure 2-2.** Significant positive and negative weights contributing to the k-marker for the parametric modulation by LL-Amount (FDR corrected q < 0.05 across the whole feature
space, i.e., three concatenated gray-matter-masked whole-brain maps, at least three contingent voxels).

**Figure 2-3.** Significant positive and negative weights contributing to the k-marker for the parametric modulation by Delay (FDR corrected q < 0.05 across the whole feature space, i.e., three concatenated gray-matter-masked whole-brain maps, at least three contingent voxels).
<table><caption>Figure 1-1</caption><thead><tr><th>LL delay<br>(in days)</th><th>Display of<br>LL delay</th><th>SS amount<br>(in Euro)</th><th>LL amount<br>(in Euro)</th><th>Indifference k</th></tr></thead><tbody><tr><td>2</td><td>In 2 days</td><td>5</td><td>7.6</td><td>0.256</td></tr><tr><td>7</td><td>In 7 days</td><td>5</td><td>9.5</td><td>0.128</td></tr><tr><td>7</td><td>In 7 days</td><td>5</td><td>14.0</td><td>0.256</td></tr><tr><td>14</td><td>In 14 days</td><td>5</td><td>9.5</td><td>0.064</td></tr><tr><td>14</td><td>In 14 days</td><td>5</td><td>14.0</td><td>0.128</td></tr><tr><td>14</td><td>In 14 days</td><td>5</td><td>22.9</td><td>0.256</td></tr><tr><td>30</td><td>In 1 month</td><td>5</td><td>6.1</td><td>0.008</td></tr><tr><td>30</td><td>In 1 month</td><td>5</td><td>7.2</td><td>0.016</td></tr><tr><td>30</td><td>In 1 month</td><td>5</td><td>9.5</td><td>0.032</td></tr><tr><td>30</td><td>In 1 month</td><td>5</td><td>14.0</td><td>0.064</td></tr><tr><td>30</td><td>In 1 month</td><td>5</td><td>22.9</td><td>0.128</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>5.0</td><td>0</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>5.1</td><td>0.00025</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>5.2</td><td>0.0005</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>5.3</td><td>0.001</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>5.6</td><td>0.002</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>6.2</td><td>0.004</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>7.4</td><td>0.008</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>9.8</td><td>0.016</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>14.6</td><td>0.032</td></tr><tr><td>60</td><td>In 2 months</td><td>5</td><td>24.2</td><td>0.064</td></tr><tr><td>120</td><td>In 4 months</td><td>5</td><td>5.0</td><td>0</td></tr><tr><td>120</td><td>In 4 months</td><td>5</td><td>5.2</td><td>0.00025</td></tr><tr><td>120</td><td>In 4 months</td><td>5</td><td>5.3</td><td>0.0005</td></tr><tr><td>120</td><td>In 4 months</td><td>5</td><td>5.6</td><td>0.001</td></tr><tr><td>120</td><td>In 4 months</td><td>5</td><td>6.2</td><td>0.002</td></tr><tr><td>120</td><td>In 4 months</td><td>5</td><td>7.4</td><td>0.004</td></tr></tbody></table>
<table>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>5</td>
    <td>9.8</td>
    <td>0.008</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>5</td>
    <td>14.6</td>
    <td>0.016</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>5</td>
    <td>24.2</td>
    <td>0.032</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>5</td>
    <td>5.0</td>
    <td>0</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>5</td>
    <td>5.3</td>
    <td>0.00025</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>5</td>
    <td>5.6</td>
    <td>0.0005</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>5</td>
    <td>6.2</td>
    <td>0.001</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>5</td>
    <td>7.4</td>
    <td>0.002</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>5</td>
    <td>9.8</td>
    <td>0.004</td>
  </tr>
  <tr>
    <td>2</td>
    <td>In 2 days</td>
    <td>10</td>
    <td>15.1</td>
    <td>0.256</td>
  </tr>
  <tr>
    <td>7</td>
    <td>In 7 days</td>
    <td>10</td>
    <td>19.0</td>
    <td>0.128</td>
  </tr>
  <tr>
    <td>7</td>
    <td>In 7 days</td>
    <td>10</td>
    <td>27.9</td>
    <td>0.256</td>
  </tr>
  <tr>
    <td>14</td>
    <td>In 14 days</td>
    <td>10</td>
    <td>19.0</td>
    <td>0.064</td>
  </tr>
  <tr>
    <td>14</td>
    <td>In 14 days</td>
    <td>10</td>
    <td>27.9</td>
    <td>0.128</td>
  </tr>
  <tr>
    <td>14</td>
    <td>In 14 days</td>
    <td>10</td>
    <td>45.8</td>
    <td>0.256</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>10</td>
    <td>12.2</td>
    <td>0.008</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>10</td>
    <td>14.5</td>
    <td>0.016</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>10</td>
    <td>19.0</td>
    <td>0.032</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>10</td>
    <td>27.9</td>
    <td>0.064</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>10</td>
    <td>45.8</td>
    <td>0.128</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>10.0</td>
    <td>0</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>10.2</td>
    <td>0.00025</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>10.3</td>
    <td>0.0005</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>10.6</td>
    <td>0.001</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>11.2</td>
    <td>0.002</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>12.4</td>
    <td>0.004</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>14.8</td>
    <td>0.008</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>19.6</td>
    <td>0.016</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>29.2</td>
    <td>0.032</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>10</td>
    <td>48.4</td>
    <td>0.064</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>10</td>
    <td>10.0</td>
    <td>0</td>
  </tr>
</table>
<table>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>10</td>
    <td>10.3</td>
    <td>0.00025</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>10</td>
    <td>10.6</td>
    <td>0.0005</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>10</td>
    <td>11.2</td>
    <td>0.001</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>10</td>
    <td>12.4</td>
    <td>0.002</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>10</td>
    <td>14.8</td>
    <td>0.004</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>10</td>
    <td>19.6</td>
    <td>0.008</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>10</td>
    <td>29.2</td>
    <td>0.016</td>
  </tr>
  <tr>
    <td>120</td>
    <td>In 4 months</td>
    <td>10</td>
    <td>48.4</td>
    <td>0.032</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>10</td>
    <td>10.0</td>
    <td>0</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>10</td>
    <td>10.6</td>
    <td>0.00025</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>10</td>
    <td>11.2</td>
    <td>0.0005</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>10</td>
    <td>12.4</td>
    <td>0.001</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>10</td>
    <td>14.8</td>
    <td>0.002</td>
  </tr>
  <tr>
    <td>240</td>
    <td>In 8 months</td>
    <td>10</td>
    <td>19.6</td>
    <td>0.004</td>
  </tr>
  <tr>
    <td>2</td>
    <td>In 2 days</td>
    <td>20</td>
    <td>30.2</td>
    <td>0.256</td>
  </tr>
  <tr>
    <td>7</td>
    <td>In 7 days</td>
    <td>20</td>
    <td>37.9</td>
    <td>0.128</td>
  </tr>
  <tr>
    <td>7</td>
    <td>In 7 days</td>
    <td>20</td>
    <td>55.8</td>
    <td>0.256</td>
  </tr>
  <tr>
    <td>14</td>
    <td>In 14 days</td>
    <td>20</td>
    <td>37.9</td>
    <td>0.064</td>
  </tr>
  <tr>
    <td>14</td>
    <td>In 14 days</td>
    <td>20</td>
    <td>55.8</td>
    <td>0.128</td>
  </tr>
  <tr>
    <td>14</td>
    <td>In 14 days</td>
    <td>20</td>
    <td>91.7</td>
    <td>0.256</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>20</td>
    <td>24.5</td>
    <td>0.008</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>20</td>
    <td>29.0</td>
    <td>0.016</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>20</td>
    <td>37.9</td>
    <td>0.032</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>20</td>
    <td>55.8</td>
    <td>0.064</td>
  </tr>
  <tr>
    <td>30</td>
    <td>In 1 month</td>
    <td>20</td>
    <td>91.7</td>
    <td>0.128</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>20</td>
    <td>20.0</td>
    <td>0</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>20</td>
    <td>20.3</td>
    <td>0.00025</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>20</td>
    <td>20.6</td>
    <td>0.0005</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>20</td>
    <td>21.2</td>
    <td>0.001</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>20</td>
    <td>22.4</td>
    <td>0.002</td>
  </tr>
  <tr>
    <td>60</td>
    <td>In 2 months</td>
    <td>20</td>
    <td>24.8</td>
    <td>0.004</td>
  </tr>
</table>
<table><tr><td>60</td><td>In 2 months</td><td>20</td><td>29.6</td><td>0.008</td></tr><tr><td>60</td><td>In 2 months</td><td>20</td><td>39.2</td><td>0.016</td></tr><tr><td>60</td><td>In 2 months</td><td>20</td><td>58.4</td><td>0.032</td></tr><tr><td>60</td><td>In 2 months</td><td>20</td><td>96.8</td><td>0.064</td></tr><tr><td>120</td><td>In 4 months</td><td>20</td><td>20.0</td><td>0</td></tr><tr><td>120</td><td>In 4 months</td><td>20</td><td>20.6</td><td>0.00025</td></tr><tr><td>120</td><td>In 4 months</td><td>20</td><td>21.2</td><td>0.0005</td></tr><tr><td>120</td><td>In 4 months</td><td>20</td><td>22.4</td><td>0.001</td></tr><tr><td>120</td><td>In 4 months</td><td>20</td><td>24.8</td><td>0.002</td></tr><tr><td>120</td><td>In 4 months</td><td>20</td><td>29.6</td><td>0.004</td></tr><tr><td>120</td><td>In 4 months</td><td>20</td><td>39.2</td><td>0.008</td></tr><tr><td>120</td><td>In 4 months</td><td>20</td><td>58.4</td><td>0.016</td></tr><tr><td>120</td><td>In 4 months</td><td>20</td><td>96.8</td><td>0.032</td></tr><tr><td>240</td><td>In 8 months</td><td>20</td><td>20.0</td><td>0</td></tr><tr><td>240</td><td>In 8 months</td><td>20</td><td>21.2</td><td>0.00025</td></tr><tr><td>240</td><td>In 8 months</td><td>20</td><td>22.4</td><td>0.0005</td></tr><tr><td>240</td><td>In 8 months</td><td>20</td><td>24.8</td><td>0.001</td></tr><tr><td>240</td><td>In 8 months</td><td>20</td><td>29.6</td><td>0.002</td></tr><tr><td>240</td><td>In 8 months</td><td>20</td><td>39.2</td><td>0.004</td></tr></table>
<table><caption>Figure 1-2</caption><thead><tr><th>LL delay<br>(in days)</th><th>Display of<br>LL delay</th><th>SS amount<br>(in Dollars)</th><th>LL amount<br>(in Dollars)</th><th>Indifference k</th></tr></thead><tbody><tr><td>19</td><td>19 days</td><td>20</td><td>43</td><td>0.0605</td></tr><tr><td>21</td><td>21 days</td><td>20</td><td>22</td><td>0.0048</td></tr><tr><td>22</td><td>22 days</td><td>20</td><td>54</td><td>0.0773</td></tr><tr><td>23</td><td>23 days</td><td>20</td><td>30</td><td>0.0217</td></tr><tr><td>23</td><td>23 days</td><td>20</td><td>54</td><td>0.0739</td></tr><tr><td>23</td><td>23 days</td><td>20</td><td>67</td><td>0.1022</td></tr><tr><td>24</td><td>24 days</td><td>20</td><td>77</td><td>0.1188</td></tr><tr><td>26</td><td>26 days</td><td>20</td><td>45</td><td>0.0481</td></tr><tr><td>27</td><td>27 days</td><td>20</td><td>41</td><td>0.0389</td></tr><tr><td>27</td><td>27 days</td><td>20</td><td>22</td><td>0.0037</td></tr><tr><td>36</td><td>36 days</td><td>20</td><td>30</td><td>0.0139</td></tr><tr><td>36</td><td>36 days</td><td>20</td><td>58</td><td>0.0528</td></tr><tr><td>37</td><td>37 days</td><td>20</td><td>63</td><td>0.0581</td></tr><tr><td>38</td><td>38 days</td><td>20</td><td>43</td><td>0.0303</td></tr><tr><td>38</td><td>38 days</td><td>20</td><td>24</td><td>0.0053</td></tr><tr><td>39</td><td>39 days</td><td>20</td><td>80</td><td>0.0769</td></tr><tr><td>41</td><td>41 days</td><td>20</td><td>75</td><td>0.0671</td></tr><tr><td>41</td><td>41 days</td><td>20</td><td>50</td><td>0.0366</td></tr><tr><td>41</td><td>41 days</td><td>20</td><td>67</td><td>0.0573</td></tr><tr><td>42</td><td>42 days</td><td>20</td><td>23</td><td>0.0036</td></tr><tr><td>43</td><td>43 days</td><td>20</td><td>34</td><td>0.0163</td></tr><tr><td>44</td><td>44 days</td><td>20</td><td>73</td><td>0.0602</td></tr><tr><td>44</td><td>44 days</td><td>20</td><td>29</td><td>0.0102</td></tr><tr><td>52</td><td>52 days</td><td>20</td><td>74</td><td>0.0519</td></tr><tr><td>53</td><td>53 days</td><td>20</td><td>58</td><td>0.0358</td></tr><tr><td>55</td><td>55 days</td><td>20</td><td>58</td><td>0.0345</td></tr><tr><td>55</td><td>55 days</td><td>20</td><td>41</td><td>0.0191</td></tr></tbody></table>
<table>
  <tr>
    <td>57</td>
    <td>57 days</td>
    <td>20</td>
    <td>32</td>
    <td>0.0105</td>
  </tr>
  <tr>
    <td>58</td>
    <td>58 days</td>
    <td>20</td>
    <td>81</td>
    <td>0.0526</td>
  </tr>
  <tr>
    <td>58</td>
    <td>58 days</td>
    <td>20</td>
    <td>29</td>
    <td>0.0078</td>
  </tr>
  <tr>
    <td>58</td>
    <td>58 days</td>
    <td>20</td>
    <td>66</td>
    <td>0.0397</td>
  </tr>
  <tr>
    <td>59</td>
    <td>59 days</td>
    <td>20</td>
    <td>50</td>
    <td>0.0254</td>
  </tr>
  <tr>
    <td>59</td>
    <td>59 days</td>
    <td>20</td>
    <td>28</td>
    <td>0.0068</td>
  </tr>
  <tr>
    <td>60</td>
    <td>60 days</td>
    <td>20</td>
    <td>75</td>
    <td>0.0458</td>
  </tr>
  <tr>
    <td>61</td>
    <td>61 days</td>
    <td>20</td>
    <td>23</td>
    <td>0.0025</td>
  </tr>
  <tr>
    <td>70</td>
    <td>70 days</td>
    <td>20</td>
    <td>25</td>
    <td>0.0036</td>
  </tr>
  <tr>
    <td>71</td>
    <td>71 days</td>
    <td>20</td>
    <td>66</td>
    <td>0.0324</td>
  </tr>
  <tr>
    <td>72</td>
    <td>72 days</td>
    <td>20</td>
    <td>58</td>
    <td>0.0264</td>
  </tr>
  <tr>
    <td>72</td>
    <td>72 days</td>
    <td>20</td>
    <td>45</td>
    <td>0.0174</td>
  </tr>
  <tr>
    <td>73</td>
    <td>73 days</td>
    <td>20</td>
    <td>58</td>
    <td>0.0260</td>
  </tr>
  <tr>
    <td>74</td>
    <td>74 days</td>
    <td>20</td>
    <td>67</td>
    <td>0.0318</td>
  </tr>
  <tr>
    <td>74</td>
    <td>74 days</td>
    <td>20</td>
    <td>25</td>
    <td>0.0034</td>
  </tr>
  <tr>
    <td>74</td>
    <td>74 days</td>
    <td>20</td>
    <td>82</td>
    <td>0.0419</td>
  </tr>
  <tr>
    <td>74</td>
    <td>74 days</td>
    <td>20</td>
    <td>32</td>
    <td>0.0081</td>
  </tr>
  <tr>
    <td>74</td>
    <td>74 days</td>
    <td>20</td>
    <td>31</td>
    <td>0.0074</td>
  </tr>
  <tr>
    <td>75</td>
    <td>75 days</td>
    <td>20</td>
    <td>29</td>
    <td>0.0060</td>
  </tr>
  <tr>
    <td>76</td>
    <td>76 days</td>
    <td>20</td>
    <td>31</td>
    <td>0.0072</td>
  </tr>
  <tr>
    <td>76</td>
    <td>76 days</td>
    <td>20</td>
    <td>71</td>
    <td>0.0336</td>
  </tr>
  <tr>
    <td>77</td>
    <td>77 days</td>
    <td>20</td>
    <td>23</td>
    <td>0.0019</td>
  </tr>
  <tr>
    <td>78</td>
    <td>78 days</td>
    <td>20</td>
    <td>33</td>
    <td>0.0083</td>
  </tr>
  <tr>
    <td>87</td>
    <td>87 days</td>
    <td>20</td>
    <td>24</td>
    <td>0.0023</td>
  </tr>
  <tr>
    <td>88</td>
    <td>88 days</td>
    <td>20</td>
    <td>71</td>
    <td>0.0290</td>
  </tr>
  <tr>
    <td>89</td>
    <td>89 days</td>
    <td>20</td>
    <td>57</td>
    <td>0.0208</td>
  </tr>
  <tr>
    <td>89</td>
    <td>89 days</td>
    <td>20</td>
    <td>24</td>
    <td>0.0022</td>
  </tr>
  <tr>
    <td>89</td>
    <td>89 days</td>
    <td>20</td>
    <td>64</td>
    <td>0.0247</td>
  </tr>
  <tr>
    <td>91</td>
    <td>91 days</td>
    <td>20</td>
    <td>27</td>
    <td>0.0038</td>
  </tr>
  <tr>
    <td>92</td>
    <td>92 days</td>
    <td>20</td>
    <td>79</td>
    <td>0.0321</td>
  </tr>
  <tr>
    <td>92</td>
    <td>92 days</td>
    <td>20</td>
    <td>44</td>
    <td>0.0130</td>
  </tr>
</table>
<table>
  <tr>
    <td>93</td>
    <td>93 days</td>
    <td>20</td>
    <td>56</td>
    <td>0.0194</td>
  </tr>
  <tr>
    <td>95</td>
    <td>95 days</td>
    <td>20</td>
    <td>72</td>
    <td>0.0274</td>
  </tr>
  <tr>
    <td>95</td>
    <td>95 days</td>
    <td>20</td>
    <td>39</td>
    <td>0.0100</td>
  </tr>
  <tr>
    <td>103</td>
    <td>103 days</td>
    <td>20</td>
    <td>33</td>
    <td>0.0063</td>
  </tr>
  <tr>
    <td>103</td>
    <td>103 days</td>
    <td>20</td>
    <td>67</td>
    <td>0.0228</td>
  </tr>
  <tr>
    <td>104</td>
    <td>104 days</td>
    <td>20</td>
    <td>39</td>
    <td>0.0091</td>
  </tr>
  <tr>
    <td>105</td>
    <td>105 days</td>
    <td>20</td>
    <td>83</td>
    <td>0.0300</td>
  </tr>
  <tr>
    <td>107</td>
    <td>107 days</td>
    <td>20</td>
    <td>45</td>
    <td>0.0117</td>
  </tr>
  <tr>
    <td>107</td>
    <td>107 days</td>
    <td>20</td>
    <td>55</td>
    <td>0.0164</td>
  </tr>
  <tr>
    <td>108</td>
    <td>108 days</td>
    <td>20</td>
    <td>25</td>
    <td>0.0023</td>
  </tr>
  <tr>
    <td>108</td>
    <td>108 days</td>
    <td>20</td>
    <td>78</td>
    <td>0.0269</td>
  </tr>
  <tr>
    <td>108</td>
    <td>108 days</td>
    <td>20</td>
    <td>70</td>
    <td>0.0231</td>
  </tr>
  <tr>
    <td>110</td>
    <td>110 days</td>
    <td>20</td>
    <td>23</td>
    <td>0.0014</td>
  </tr>
  <tr>
    <td>111</td>
    <td>111 days</td>
    <td>20</td>
    <td>32</td>
    <td>0.0054</td>
  </tr>
  <tr>
    <td>114</td>
    <td>114 days</td>
    <td>20</td>
    <td>36</td>
    <td>0.0070</td>
  </tr>
  <tr>
    <td>120</td>
    <td>120 days</td>
    <td>20</td>
    <td>43</td>
    <td>0.0096</td>
  </tr>
  <tr>
    <td>121</td>
    <td>121 days</td>
    <td>20</td>
    <td>74</td>
    <td>0.0223</td>
  </tr>
  <tr>
    <td>123</td>
    <td>123 days</td>
    <td>20</td>
    <td>28</td>
    <td>0.0033</td>
  </tr>
  <tr>
    <td>124</td>
    <td>124 days</td>
    <td>20</td>
    <td>60</td>
    <td>0.0161</td>
  </tr>
  <tr>
    <td>125</td>
    <td>125 days</td>
    <td>20</td>
    <td>24</td>
    <td>0.0016</td>
  </tr>
  <tr>
    <td>126</td>
    <td>126 days</td>
    <td>20</td>
    <td>54</td>
    <td>0.0135</td>
  </tr>
  <tr>
    <td>128</td>
    <td>128 days</td>
    <td>20</td>
    <td>48</td>
    <td>0.0109</td>
  </tr>
  <tr>
    <td>129</td>
    <td>129 days</td>
    <td>20</td>
    <td>50</td>
    <td>0.0116</td>
  </tr>
  <tr>
    <td>129</td>
    <td>129 days</td>
    <td>20</td>
    <td>85</td>
    <td>0.0252</td>
  </tr>
  <tr>
    <td>129</td>
    <td>129 days</td>
    <td>20</td>
    <td>78</td>
    <td>0.0225</td>
  </tr>
  <tr>
    <td>129</td>
    <td>129 days</td>
    <td>20</td>
    <td>41</td>
    <td>0.0081</td>
  </tr>
  <tr>
    <td>130</td>
    <td>130 days</td>
    <td>20</td>
    <td>27</td>
    <td>0.0027</td>
  </tr>
  <tr>
    <td>132</td>
    <td>132 days</td>
    <td>20</td>
    <td>28</td>
    <td>0.0030</td>
  </tr>
  <tr>
    <td>134</td>
    <td>134 days</td>
    <td>20</td>
    <td>23</td>
    <td>0.0011</td>
  </tr>
  <tr>
    <td>137</td>
    <td>137 days</td>
    <td>20</td>
    <td>65</td>
    <td>0.0164</td>
  </tr>
  <tr>
    <td>139</td>
    <td>139 days</td>
    <td>20</td>
    <td>24</td>
    <td>0.0014</td>
  </tr>
</table>
<table>
  <tr>
    <td>139</td>
    <td>139 days</td>
    <td>20</td>
    <td>52</td>
    <td>0.0115</td>
  </tr>
  <tr>
    <td>140</td>
    <td>140 days</td>
    <td>20</td>
    <td>36</td>
    <td>0.0057</td>
  </tr>
  <tr>
    <td>140</td>
    <td>140 days</td>
    <td>20</td>
    <td>49</td>
    <td>0.0104</td>
  </tr>
  <tr>
    <td>141</td>
    <td>141 days</td>
    <td>20</td>
    <td>25</td>
    <td>0.0018</td>
  </tr>
  <tr>
    <td>141</td>
    <td>141 days</td>
    <td>20</td>
    <td>61</td>
    <td>0.0145</td>
  </tr>
  <tr>
    <td>142</td>
    <td>142 days</td>
    <td>20</td>
    <td>77</td>
    <td>0.0201</td>
  </tr>
  <tr>
    <td>142</td>
    <td>142 days</td>
    <td>20</td>
    <td>27</td>
    <td>0.0025</td>
  </tr>
  <tr>
    <td>143</td>
    <td>143 days</td>
    <td>20</td>
    <td>44</td>
    <td>0.0084</td>
  </tr>
  <tr>
    <td>145</td>
    <td>145 days</td>
    <td>20</td>
    <td>66</td>
    <td>0.0159</td>
  </tr>
  <tr>
    <td>145</td>
    <td>145 days</td>
    <td>20</td>
    <td>80</td>
    <td>0.0207</td>
  </tr>
  <tr>
    <td>145</td>
    <td>145 days</td>
    <td>20</td>
    <td>42</td>
    <td>0.0076</td>
  </tr>
  <tr>
    <td>156</td>
    <td>156 days</td>
    <td>20</td>
    <td>65</td>
    <td>0.0144</td>
  </tr>
  <tr>
    <td>157</td>
    <td>157 days</td>
    <td>20</td>
    <td>45</td>
    <td>0.0080</td>
  </tr>
  <tr>
    <td>159</td>
    <td>159 days</td>
    <td>20</td>
    <td>40</td>
    <td>0.0063</td>
  </tr>
  <tr>
    <td>159</td>
    <td>159 days</td>
    <td>20</td>
    <td>65</td>
    <td>0.0142</td>
  </tr>
  <tr>
    <td>161</td>
    <td>161 days</td>
    <td>20</td>
    <td>77</td>
    <td>0.0177</td>
  </tr>
  <tr>
    <td>161</td>
    <td>161 days</td>
    <td>20</td>
    <td>76</td>
    <td>0.0174</td>
  </tr>
  <tr>
    <td>161</td>
    <td>161 days</td>
    <td>20</td>
    <td>39</td>
    <td>0.0059</td>
  </tr>
  <tr>
    <td>163</td>
    <td>163 days</td>
    <td>20</td>
    <td>55</td>
    <td>0.0107</td>
  </tr>
  <tr>
    <td>163</td>
    <td>163 days</td>
    <td>20</td>
    <td>28</td>
    <td>0.0025</td>
  </tr>
  <tr>
    <td>163</td>
    <td>163 days</td>
    <td>20</td>
    <td>33</td>
    <td>0.0040</td>
  </tr>
  <tr>
    <td>171</td>
    <td>171 days</td>
    <td>20</td>
    <td>35</td>
    <td>0.0044</td>
  </tr>
  <tr>
    <td>172</td>
    <td>172 days</td>
    <td>20</td>
    <td>49</td>
    <td>0.0084</td>
  </tr>
  <tr>
    <td>172</td>
    <td>172 days</td>
    <td>20</td>
    <td>69</td>
    <td>0.0142</td>
  </tr>
  <tr>
    <td>172</td>
    <td>172 days</td>
    <td>20</td>
    <td>56</td>
    <td>0.0105</td>
  </tr>
  <tr>
    <td>174</td>
    <td>174 days</td>
    <td>20</td>
    <td>41</td>
    <td>0.0060</td>
  </tr>
  <tr>
    <td>176</td>
    <td>176 days</td>
    <td>20</td>
    <td>71</td>
    <td>0.0145</td>
  </tr>
  <tr>
    <td>176</td>
    <td>176 days</td>
    <td>20</td>
    <td>34</td>
    <td>0.0040</td>
  </tr>
  <tr>
    <td>176</td>
    <td>176 days</td>
    <td>20</td>
    <td>23</td>
    <td>0.0009</td>
  </tr>
  <tr>
    <td>176</td>
    <td>176 days</td>
    <td>20</td>
    <td>25</td>
    <td>0.0014</td>
  </tr>
  <tr>
    <td>180</td>
    <td>180 days</td>
    <td>20</td>
    <td>62</td>
    <td>0.0117</td>
  </tr>
</table>
<figure><img src="image_21.png" /></figure>
<table><caption>Figure 2-1</caption><thead><tr><th rowspan="2">Positive weights</th><th rowspan="2">Atlas label</th><th rowspan="2">Volume<br>(voxels)</th><th colspan="4">MNI Coordinates</th></tr><tr><th>X</th><th>Y</th><th>Z</th><th>max(z)</th></tr></thead><tbody><tr><td>Orbitofrontal cortex</td><td>Ctx_a47r_L</td><td>29</td><td>-34</td><td>40</td><td>-12</td><td>4.49</td></tr><tr><td>Anterior insula</td><td>Ctx_FOP5_R</td><td>114</td><td>32</td><td>24</td><td>4</td><td>4.45</td></tr><tr><td>Midtemporal gyrus</td><td>Ctx_PHT_R</td><td>18</td><td>68</td><td>-48</td><td>4</td><td>4.43</td></tr><tr><td>Frontal pole/vmpFC</td><td>Ctx_10pp_L</td><td>29</td><td>-8</td><td>60</td><td>-12</td><td>4.42</td></tr><tr><td>Midtemporal gyrus</td><td>Ctx_TE1a_R</td><td>6</td><td>66</td><td>-4</td><td>-24</td><td>4.24</td></tr><tr><td>Temporal operculum</td><td>Ctx_LBelt_L</td><td>32</td><td>-42</td><td>-28</td><td>2</td><td>4.21</td></tr><tr><td>Other</td><td>No_label</td><td>9</td><td>-2</td><td>-28</td><td>14</td><td>4.13</td></tr><tr><td>Visual cortex</td><td>Ctx_V2_R</td><td>18</td><td>20</td><td>-100</td><td>0</td><td>4.04</td></tr><tr><td>Orbitofrontal cortex</td><td>Ctx_a47r_L</td><td>11</td><td>-44</td><td>38</td><td>-12</td><td>4.03</td></tr><tr><td>Ventrolateral prefrontal cortex</td><td>Ctx_45_L</td><td>72</td><td>-50</td><td>28</td><td>-2</td><td>4.03</td></tr><tr><td>Striatum</td><td>V_Striatum_R</td><td>38</td><td>18</td><td>26</td><td>0</td><td>3.99</td></tr><tr><td>Striatum</td><td>V_Striatum_L</td><td>22</td><td>0</td><td>4</td><td>-2</td><td>3.96</td></tr><tr><td>Orbitofrontal cortex</td><td>Ctx_111_L</td><td>13</td><td>-18</td><td>42</td><td>-14</td><td>3.95</td></tr><tr><td>Retrosplenial cortex</td><td>Ctx_RSC_R</td><td>15</td><td>2</td><td>-46</td><td>8</td><td>3.94</td></tr><tr><td>Temporal operculum</td><td>Ctx_PoI1_L</td><td>20</td><td>-38</td><td>-4</td><td>-16</td><td>3.89</td></tr><tr><td>Visual cortex</td><td>Ctx_V4_R</td><td>3</td><td>30</td><td>-92</td><td>22</td><td>3.86</td></tr><tr><td>Other</td><td>No_label</td><td>3</td><td>66</td><td>-54</td><td>8</td><td>3.84</td></tr><tr><td>Visual cortex</td><td>Ctx_V3_L</td><td>3</td><td>-22</td><td>-94</td><td>24</td><td>3.82</td></tr><tr><td>Midtemporal gyrus</td><td>Ctx_TE1a_L</td><td>14</td><td>-64</td><td>-10</td><td>-14</td><td>3.79</td></tr><tr><td>Amygdala</td><td>Ctx_PeEc_R</td><td>5</td><td>20</td><td>6</td><td>-26</td><td>3.75</td></tr><tr><td>Caudate</td><td>Cau_L</td><td>3</td><td>-26</td><td>-32</td><td>20</td><td>3.72</td></tr><tr><td>Precentral gyrus</td><td>Ctx_4_L</td><td>9</td><td>-12</td><td>-26</td><td>70</td><td>3.71</td></tr><tr><td>Temporal pole/amygdala</td><td>Ctx_TGd_R</td><td>7</td><td>34</td><td>12</td><td>-24</td><td>3.65</td></tr><tr><td>Visual cortex</td><td>Ctx_V2_L</td><td>4</td><td>-14</td><td>-102</td><td>14</td><td>3.62</td></tr><tr><td>Midtemporal gyrus</td><td>Ctx_TGd_R</td><td>4</td><td>52</td><td>4</td><td>-26</td><td>3.59</td></tr><tr><td>Orbitofrontal cortex</td><td>Ctx_131_L</td><td>4</td><td>-28</td><td>28</td><td>-14</td><td>3.48</td></tr></tbody></table>
<table><thead><tr><th rowspan="2">Negative weights</th><th rowspan="2">Atlas label</th><th colspan="5">Volume</th></tr><tr><th>(voxels)</th><th>X</th><th>Y</th><th>Z</th><th>max(z)</th></tr></thead><tbody><tr><td>Midcingulate cortex</td><td>Ctx_24dv_R</td><td>58</td><td>8</td><td>0</td><td>36</td><td>-5.03</td></tr><tr><td>Cerebellum</td><td>Cblm_CrusII_L</td><td>130</td><td>-24</td><td>-76</td><td>-40</td><td>-4.87</td></tr><tr><td>Superior frontal gyrus</td><td>Ctx_SFL_L</td><td>106</td><td>-8</td><td>10</td><td>70</td><td>-4.83</td></tr><tr><td>Visual cortex</td><td>Ctx_ProS_R</td><td>79</td><td>24</td><td>-52</td><td>4</td><td>-4.81</td></tr><tr><td>Inferior parietal lobule</td><td>Ctx_PF_L</td><td>338</td><td>-54</td><td>-30</td><td>42</td><td>-4.75</td></tr><tr><td>Precuneus</td><td>Ctx_7Am_L</td><td>67</td><td>-2</td><td>-56</td><td>60</td><td>-4.63</td></tr><tr><td>Posterior cingulate cortex</td><td>Ctx_23c_R</td><td>51</td><td>8</td><td>-24</td><td>40</td><td>-4.35</td></tr><tr><td>Parietal cortex</td><td>Ctx_PGs_R</td><td>17</td><td>38</td><td>-70</td><td>52</td><td>-4.28</td></tr><tr><td>Parahippocampal cortex</td><td>Ctx_VMV2_L</td><td>7</td><td>-32</td><td>-50</td><td>-6</td><td>-4.06</td></tr><tr><td>Midcingulate cortex</td><td>Ctx_p24pr_L</td><td>20</td><td>-6</td><td>2</td><td>36</td><td>-4.00</td></tr><tr><td>Parahippocampal cortex</td><td>Ctx_ProS_L</td><td>13</td><td>-20</td><td>-48</td><td>-2</td><td>-3.99</td></tr><tr><td>Intraparietal sulcus</td><td>Ctx_7PC_L</td><td>11</td><td>-44</td><td>-42</td><td>60</td><td>-3.94</td></tr><tr><td>Cerebellum</td><td>Cblm_CrusI_R</td><td>6</td><td>50</td><td>-48</td><td>-28</td><td>-3.88</td></tr><tr><td>vmPFC</td><td>Ctx_9m_L</td><td>8</td><td>-8</td><td>50</td><td>16</td><td>-3.87</td></tr><tr><td>Cerebellum</td><td>Cblm_CrusI_L</td><td>6</td><td>-46</td><td>-64</td><td>-42</td><td>-3.87</td></tr><tr><td>Midcingulate cortex</td><td>Ctx_33pr_L</td><td>6</td><td>-2</td><td>22</td><td>20</td><td>-3.84</td></tr><tr><td>Inferior parietal lobule</td><td>Ctx_PF_R</td><td>13</td><td>54</td><td>-34</td><td>46</td><td>-3.83</td></tr><tr><td>Inferior frontal cortex</td><td>Ctx_6r_L</td><td>3</td><td>-54</td><td>4</td><td>16</td><td>-3.80</td></tr><tr><td>Dorsolateral prefrontal cortex</td><td>Ctx_9_46d_R</td><td>4</td><td>20</td><td>48</td><td>26</td><td>-3.68</td></tr></tbody></table>
<table><caption>Figure 2-2</caption><thead><tr><th rowspan="2">Positive weights</th><th rowspan="2">Atlas label</th><th rowspan="2">Volume<br>(voxels)</th><th colspan="4">MNI Coordinates</th></tr><tr><th>X</th><th>Y</th><th>Z</th><th>max(z)</th></tr></thead><tbody><tr><td>Medial frontal gyrus</td><td>Ctx_8BM_R</td><td>386</td><td>-2</td><td>26</td><td>36</td><td>5.86</td></tr><tr><td>Dorsolateral prefrontal cortex</td><td>Ctx_6a_R</td><td>199</td><td>26</td><td>8</td><td>52</td><td>5.80</td></tr><tr><td>Intraparietal Sulcus</td><td>Ctx_PFm_R</td><td>288</td><td>48</td><td>-36</td><td>52</td><td>5.72</td></tr><tr><td>Orbitofrontal cortex</td><td>Ctx_111_R</td><td>50</td><td>16</td><td>30</td><td>-24</td><td>5.55</td></tr><tr><td>Inferior parietal lobule</td><td>Ctx_PGs_R</td><td>298</td><td>38</td><td>-74</td><td>36</td><td>5.40</td></tr><tr><td>Dorsolateral prefrontal cortex</td><td>Ctx_SCEF_L</td><td>131</td><td>-14</td><td>14</td><td>52</td><td>5.12</td></tr><tr><td>Precuneus</td><td>Ctx_POS2_R</td><td>177</td><td>12</td><td>-66</td><td>38</td><td>5.12</td></tr><tr><td>Cingulate cortex</td><td>Ctx_d32_R</td><td>114</td><td>10</td><td>34</td><td>22</td><td>4.93</td></tr><tr><td>Inferior frontal cortex</td><td>Ctx_IFJa_L</td><td>134</td><td>-44</td><td>8</td><td>26</td><td>4.88</td></tr><tr><td>Ventromedial prefrontal cortex</td><td>Ctx_p32_L</td><td>24</td><td>-12</td><td>44</td><td>4</td><td>4.80</td></tr><tr><td>Cerebellum</td><td>Cblm_IX_R</td><td>18</td><td>4</td><td>-50</td><td>-34</td><td>4.75</td></tr><tr><td>Orbitofrontal cortex</td><td>Ctx_111_L</td><td>37</td><td>-24</td><td>44</td><td>-18</td><td>4.66</td></tr><tr><td>Dorsolateral prefrontal cortex</td><td>Ctx_p9_46v_L</td><td>67</td><td>-46</td><td>28</td><td>22</td><td>4.66</td></tr><tr><td>Visual cortex</td><td>Ctx_V1_R</td><td>29</td><td>18</td><td>-76</td><td>12</td><td>4.66</td></tr><tr><td>Intraparietal Sulcus</td><td>Ctx_AIP_L</td><td>24</td><td>-38</td><td>-44</td><td>42</td><td>4.61</td></tr><tr><td>Inferior parietal lobule</td><td>Ctx_IP1_L</td><td>58</td><td>-32</td><td>-72</td><td>32</td><td>4.57</td></tr><tr><td>Posterior cingulate cortex</td><td>Ctx_23d_R</td><td>56</td><td>-2</td><td>-28</td><td>36</td><td>4.56</td></tr><tr><td>Anterior insula</td><td>Ctx_AVI_L</td><td>58</td><td>-32</td><td>20</td><td>2</td><td>4.55</td></tr><tr><td>Ventrolateral prefrontal cortex</td><td>Ctx_a9_46v_R</td><td>66</td><td>42</td><td>46</td><td>10</td><td>4.47</td></tr><tr><td>Ventrolateral prefrontal cortex</td><td>Ctx_a9_46v_L</td><td>35</td><td>-36</td><td>44</td><td>6</td><td>4.40</td></tr><tr><td>Ventromedial prefrontal cortex</td><td>Ctx_p32_R</td><td>47</td><td>8</td><td>42</td><td>0</td><td>4.27</td></tr><tr><td>Anterior insula</td><td>Ctx_AVI_R</td><td>16</td><td>32</td><td>20</td><td>2</td><td>4.19</td></tr><tr><td>Posterior cingulate cortex</td><td>Ctx_RSC_R</td><td>7</td><td>6</td><td>-16</td><td>32</td><td>4.06</td></tr><tr><td>Ventromedial prefrontal cortex</td><td>Ctx_10r_L</td><td>13</td><td>-12</td><td>38</td><td>-8</td><td>4.05</td></tr><tr><td>Parahippocampal cortex</td><td>CtxPeEc_R</td><td>5</td><td>26</td><td>-22</td><td>-30</td><td>4.04</td></tr><tr><td>Cerebellum</td><td>Cblm_VI_R</td><td>11</td><td>34</td><td>-50</td><td>-28</td><td>4.02</td></tr><tr><td>Thalamus/Pulvinar</td><td>Thal_Pulv</td><td>10</td><td>-12</td><td>-32</td><td>0</td><td>4.00</td></tr></tbody></table>
<table><tr><td>Medial temporal cortex</td><td>Ctx_Pres_R</td><td>11</td><td>14</td><td>-36</td><td>0</td><td>3.99</td></tr><tr><td>Cerebellum</td><td>Cblm_CrusI_R</td><td>10</td><td>40</td><td>-40</td><td>-38</td><td>3.99</td></tr><tr><td>Orbitofrontal cortex</td><td>Ctx_OFC_L</td><td>3</td><td>-8</td><td>50</td><td>-24</td><td>3.98</td></tr><tr><td>Dorsolateral prefrontal cortex</td><td>Ctx_p9_46v_R</td><td>9</td><td>46</td><td>34</td><td>24</td><td>3.72</td></tr><tr><td>Precuneus</td><td>Ctx_POS2_R</td><td>8</td><td>14</td><td>-60</td><td>24</td><td>3.70</td></tr><tr><td>Ventrolateral thalamus</td><td>Thal_VL</td><td>7</td><td>-12</td><td>-12</td><td>14</td><td>3.65</td></tr><tr><td>Cerebellum</td><td>Cblm_VI_L</td><td>6</td><td>-34</td><td>-56</td><td>-26</td><td>3.61</td></tr><tr><td>Precuneus</td><td>Ctx_POS2_L</td><td>3</td><td>-12</td><td>-68</td><td>36</td><td>3.55</td></tr></table>

<table><thead><tr><th colspan="7">Negative weights</th></tr><tr><th>Name</th><th>Atlas label</th><th>Volume<br>(voxels)</th><th>X</th><th>Y</th><th>Z</th><th>max(z)</th></tr></thead><tbody><tr><td>Visual cortex</td><td>Ctx_V2_L</td><td>142</td><td>-8</td><td>-80</td><td>-10</td><td>-5.51</td></tr><tr><td>Visual cortex</td><td>Ctx_V4t_L</td><td>70</td><td>-42</td><td>-82</td><td>0</td><td>-4.99</td></tr><tr><td>Cerebellum</td><td>Cblm_CrusI_L</td><td>148</td><td>-28</td><td>-80</td><td>-30</td><td>-4.93</td></tr><tr><td>Cerebellum</td><td>Cblm_CrusI_R</td><td>64</td><td>24</td><td>-84</td><td>-30</td><td>-4.85</td></tr><tr><td>Superior frontal cortex</td><td>Ctx_SFL_R</td><td>47</td><td>4</td><td>6</td><td>68</td><td>-4.85</td></tr><tr><td>Paracentral lobule</td><td>Ctx_4_R</td><td>37</td><td>6</td><td>-30</td><td>60</td><td>-4.83</td></tr><tr><td>Superior parietal lobule</td><td>Ctx_7AL_L</td><td>158</td><td>-20</td><td>-40</td><td>64</td><td>-4.63</td></tr><tr><td>Parahippocampal cortex</td><td>Ctx_VMV1_R</td><td>59</td><td>20</td><td>-44</td><td>-10</td><td>-4.60</td></tr><tr><td>Visual cortex</td><td>Ctx_V3A_L</td><td>94</td><td>-12</td><td>-86</td><td>24</td><td>-4.51</td></tr><tr><td>Superior temporal sulcus</td><td>Ctx_STSdp_L</td><td>78</td><td>-50</td><td>-32</td><td>-6</td><td>-4.49</td></tr><tr><td>Cerebellum</td><td>Cblm_V_L</td><td>16</td><td>-22</td><td>-34</td><td>-30</td><td>-4.49</td></tr><tr><td>Midcingulate cortex</td><td>Ctx_24dv_L</td><td>21</td><td>-8</td><td>-2</td><td>40</td><td>-4.40</td></tr><tr><td>Parahippocampal cortex</td><td>Ctx_VMV1_L</td><td>32</td><td>-18</td><td>-60</td><td>-8</td><td>-4.36</td></tr><tr><td>Superior frontal cortex</td><td>Ctx_8BL_R</td><td>35</td><td>2</td><td>50</td><td>46</td><td>-4.28</td></tr><tr><td>Visual cortex</td><td>Ctx_V4t_R</td><td>48</td><td>44</td><td>-78</td><td>-2</td><td>-4.23</td></tr><tr><td>Visual cortex</td><td>Ctx_V3_R</td><td>41</td><td>16</td><td>-72</td><td>-8</td><td>-4.22</td></tr><tr><td>Superior frontal cortex</td><td>Ctx_8BL_R</td><td>15</td><td>4</td><td>30</td><td>62</td><td>-4.20</td></tr><tr><td>Superior parietal lobule</td><td>Ctx_7AL_R</td><td>14</td><td>18</td><td>-44</td><td>70</td><td>-4.13</td></tr><tr><td>Putamen</td><td>Putamen_Pp_R</td><td>3</td><td>28</td><td>-12</td><td>10</td><td>-4.10</td></tr></tbody></table>
<table><tr><td>Putamen</td><td>Putamen_Pp_L</td><td>10</td><td>-30</td><td>-22</td><td>10</td><td>-4.06</td></tr><tr><td>Superior frontal cortex</td><td>Ctx_9a_L</td><td>24</td><td>-10</td><td>62</td><td>26</td><td>-4.05</td></tr><tr><td>Paracentral lobule</td><td>Ctx_SCEF_L</td><td>11</td><td>-8</td><td>-6</td><td>66</td><td>-4.05</td></tr><tr><td>Visual cortex</td><td>Ctx_V3A_R</td><td>31</td><td>20</td><td>-90</td><td>18</td><td>-4.00</td></tr><tr><td>Frontal pole</td><td>Ctx_10d_R</td><td>7</td><td>12</td><td>68</td><td>16</td><td>-3.90</td></tr><tr><td>Temporal pole</td><td>CtxPeEc_L</td><td>4</td><td>-28</td><td>-4</td><td>-34</td><td>-3.87</td></tr><tr><td>Visual cortex</td><td>Ctx_MT_R</td><td>9</td><td>48</td><td>-68</td><td>4</td><td>-3.83</td></tr><tr><td>Superior temporal gyrus</td><td>Ctx_PSL_L</td><td>17</td><td>-56</td><td>-36</td><td>16</td><td>-3.80</td></tr><tr><td>Precuneus</td><td>Ctx_5L_R</td><td>6</td><td>12</td><td>-48</td><td>66</td><td>-3.80</td></tr><tr><td>Visual cortex</td><td>Ctx_V4_R</td><td>8</td><td>32</td><td>-78</td><td>-10</td><td>-3.79</td></tr><tr><td>Superior temporal gyrus</td><td>Ctx_A4_L</td><td>4</td><td>-60</td><td>-30</td><td>10</td><td>-3.70</td></tr><tr><td>Temporal pole</td><td>Ctx_TE1a_L</td><td>4</td><td>-52</td><td>-6</td><td>-32</td><td>-3.70</td></tr><tr><td>Superior temporal sulcus</td><td>Ctx_STV_R</td><td>6</td><td>50</td><td>-42</td><td>10</td><td>-3.68</td></tr><tr><td>Superior temporal gyrus</td><td>Ctx_PSL_R</td><td>5</td><td>54</td><td>-32</td><td>22</td><td>-3.56</td></tr></table>
<table><caption>Figure 2-3</caption><thead><tr><th rowspan="2">Positive weights</th><th rowspan="2">Atlas label</th><th rowspan="2">Volume<br>(voxels)</th><th colspan="4">MNI Coordinates</th></tr><tr><th>X</th><th>Y</th><th>Z</th><th>max(z)</th></tr></thead><tbody><tr><td>Visual cortex</td><td>Ctx_V3A_R</td><td>131</td><td>12</td><td>-86</td><td>20</td><td>5.30</td></tr><tr><td>Ventromedial prefrontal cortex</td><td>Ctx_10v_R</td><td>160</td><td>2</td><td>42</td><td>-20</td><td>5.14</td></tr><tr><td>Precuneus</td><td>Ctx_PCV_L</td><td>102</td><td>-10</td><td>-54</td><td>46</td><td>4.75</td></tr><tr><td>Superior temporal sulcus</td><td>Ctx_STSdp_L</td><td>63</td><td>-54</td><td>-34</td><td>4</td><td>4.71</td></tr><tr><td>Superior temporal gyrus</td><td>Ctx_TA2_R</td><td>59</td><td>52</td><td>-8</td><td>-2</td><td>4.66</td></tr><tr><td>Precentral gyrus</td><td>Ctx_3b_L</td><td>214</td><td>-34</td><td>-26</td><td>62</td><td>4.62</td></tr><tr><td>Angular gyrus</td><td>Ctx_PGi_R</td><td>27</td><td>40</td><td>-60</td><td>22</td><td>4.61</td></tr><tr><td>Ventromedial prefrontal cortex</td><td>Ctx_9m_R</td><td>37</td><td>16</td><td>48</td><td>6</td><td>4.58</td></tr><tr><td>Putamen</td><td>Putamen_Pp_L</td><td>35</td><td>-32</td><td>-14</td><td>2</td><td>4.43</td></tr><tr><td>Caudate</td><td>Cau_L</td><td>36</td><td>-22</td><td>22</td><td>2</td><td>4.35</td></tr><tr><td>Superior temporal gyrus</td><td>Ctx_TPOJ1_R</td><td>29</td><td>50</td><td>-30</td><td>8</td><td>4.34</td></tr><tr><td>Angular gyrus</td><td>Ctx_PGi_L</td><td>43</td><td>-48</td><td>-54</td><td>22</td><td>4.34</td></tr><tr><td>Precentral gyrus</td><td>Ctx_4_L</td><td>5</td><td>-32</td><td>-16</td><td>44</td><td>4.33</td></tr><tr><td>Cingulate sulcus</td><td>Ctx_24dd_L</td><td>49</td><td>-6</td><td>-10</td><td>48</td><td>4.29</td></tr><tr><td>Subgenual cingulate cortex</td><td>Ctx_s32_L</td><td>17</td><td>-10</td><td>26</td><td>-12</td><td>4.24</td></tr><tr><td>Paracentral lobule</td><td>Ctx_5L_R</td><td>28</td><td>10</td><td>-40</td><td>62</td><td>4.16</td></tr><tr><td>Midcingulate cortex</td><td>Ctx_24dv_R</td><td>9</td><td>10</td><td>-4</td><td>44</td><td>4.15</td></tr><tr><td>Cerebellum</td><td>Cblm_CrusII_L</td><td>3</td><td>-12</td><td>-84</td><td>-44</td><td>4.04</td></tr><tr><td>Caudate</td><td>Cau_R</td><td>7</td><td>6</td><td>26</td><td>-4</td><td>3.99</td></tr><tr><td>Superior frontal gyrus</td><td>Ctx_9m_R</td><td>21</td><td>4</td><td>56</td><td>38</td><td>3.97</td></tr><tr><td>Midtemporal gyrus</td><td>Ctx_MT_R</td><td>9</td><td>46</td><td>-68</td><td>12</td><td>3.96</td></tr><tr><td>Visual cortex</td><td>Ctx_V1_L</td><td>14</td><td>-14</td><td>-82</td><td>-4</td><td>3.94</td></tr><tr><td>Cerebellum</td><td>Cblm_CrusII_R</td><td>7</td><td>28</td><td>-84</td><td>-44</td><td>3.93</td></tr><tr><td>Posterior insula/temporal operculum</td><td>Ctx_52_R</td><td>16</td><td>40</td><td>-22</td><td>-2</td><td>3.91</td></tr><tr><td>Superior temporal sulcus</td><td>Ctx_A5_L</td><td>8</td><td>-58</td><td>2</td><td>-10</td><td>3.90</td></tr><tr><td>Paracentral lobule</td><td>Ctx_5mv_R</td><td>4</td><td>18</td><td>-32</td><td>44</td><td>3.83</td></tr><tr><td>Cerebellum</td><td>Cblm_CrusI_R</td><td>10</td><td>40</td><td>-74</td><td>-34</td><td>3.82</td></tr></tbody></table>
<table><tr><td>Midtemporal gyrus</td><td>Ctx_A5_L</td><td>4</td><td>-62</td><td>-12</td><td>-10</td><td>3.80</td></tr><tr><td>Superior parietal lobule</td><td>No_label</td><td>4</td><td>-22</td><td>-44</td><td>50</td><td>3.78</td></tr><tr><td>Paracentral lobule</td><td>Ctx_5m_L</td><td>11</td><td>-10</td><td>-44</td><td>64</td><td>3.77</td></tr><tr><td>Paracentral lobule</td><td>Ctx_5mv_R</td><td>7</td><td>16</td><td>-24</td><td>44</td><td>3.72</td></tr><tr><td>Inferior frontal cortex</td><td>Ctx_45_L</td><td>5</td><td>-54</td><td>26</td><td>14</td><td>3.72</td></tr><tr><td>Precentral gyrus</td><td>Ctx_6d_L</td><td>3</td><td>-26</td><td>-18</td><td>62</td><td>3.72</td></tr><tr><td>Superior parietal lobule</td><td>Ctx_7Am_L</td><td>5</td><td>-4</td><td>-66</td><td>62</td><td>3.70</td></tr><tr><td>Visual cortex</td><td>Ctx_V2_L</td><td>8</td><td>-6</td><td>-86</td><td>18</td><td>3.69</td></tr><tr><td>Visual cortex</td><td>Ctx_IP0_R</td><td>6</td><td>30</td><td>-70</td><td>22</td><td>3.68</td></tr><tr><td>Caudate</td><td>Cau_L</td><td>4</td><td>-18</td><td>8</td><td>18</td><td>3.68</td></tr><tr><td>Posterior cingulate cortex</td><td>Ctx_24dd_R</td><td>7</td><td>10</td><td>-20</td><td>44</td><td>3.66</td></tr><tr><td>Superior parietal lobule</td><td>Ctx_2_L</td><td>3</td><td>-18</td><td>-38</td><td>60</td><td>3.63</td></tr><tr><td>Superior temporal sulcus</td><td>Ctx_STV_R</td><td>3</td><td>58</td><td>-34</td><td>8</td><td>3.57</td></tr></table>

<table><thead><tr><th colspan="8">Negative weights</th></tr><tr><th>Name</th><th>Atlas label</th><th>Volume<br>(voxels)</th><th>X</th><th>Y</th><th>Z</th><th>max(z)</th></tr></thead><tbody><tr><td>Dorsolateral prefrontal cortex</td><td>Ctx_a9_46v_L</td><td>76</td><td>-40</td><td>50</td><td>14</td><td>-5.20</td></tr><tr><td>Brain stem</td><td>Bstem_Ponscd</td><td>54</td><td>2</td><td>-28</td><td>-36</td><td>-4.78</td></tr><tr><td>Intraparietal sulcus</td><td>Ctx_7PC_L</td><td>34</td><td>-40</td><td>-46</td><td>48</td><td>-4.70</td></tr><tr><td>Dorsolateral prefrontal cortex</td><td>Ctx_8C_R</td><td>26</td><td>40</td><td>12</td><td>30</td><td>-4.57</td></tr><tr><td>Brain stem</td><td>Bstem_Ponscd_L</td><td>69</td><td>-12</td><td>-38</td><td>-36</td><td>-4.54</td></tr><tr><td>Paracentral lobule</td><td>Ctx_4_R</td><td>12</td><td>6</td><td>-30</td><td>78</td><td>-4.41</td></tr><tr><td>Inferior parietal lobule</td><td>Ctx_PFm_R</td><td>23</td><td>54</td><td>-44</td><td>52</td><td>-4.39</td></tr><tr><td>Cerebellum</td><td>Cblm_Dentate_R</td><td>39</td><td>18</td><td>-42</td><td>-36</td><td>-4.25</td></tr><tr><td>Cerebellum</td><td>Cblm_IX_L</td><td>51</td><td>-6</td><td>-54</td><td>-36</td><td>-4.23</td></tr><tr><td>Medial frontal gyrus</td><td>Ctx_8BM_R</td><td>45</td><td>0</td><td>22</td><td>42</td><td>-4.17</td></tr><tr><td>Orbitofrontal cortex</td><td>Ctx_a10p_R</td><td>5</td><td>22</td><td>58</td><td>-10</td><td>-4.16</td></tr><tr><td>Visual cortex</td><td>Ctx_V4_R</td><td>19</td><td>30</td><td>-86</td><td>-10</td><td>-4.11</td></tr><tr><td>Paracentral lobule</td><td>Ctx_SFL_R</td><td>10</td><td>4</td><td>-2</td><td>76</td><td>-4.10</td></tr><tr><td>Thalamus</td><td>Thal_Pulv</td><td>13</td><td>-4</td><td>-30</td><td>4</td><td>-4.08</td></tr><tr><td>Orbitofrontal cortex</td><td>Ctx_111_R</td><td>17</td><td>22</td><td>32</td><td>-18</td><td>-4.07</td></tr></tbody></table>
<table>
  <tr>
    <td>Visual cortex</td>
    <td>Ctx_LO2_L</td>
    <td>3</td>
    <td>-46</td>
    <td>-82</td>
    <td>-6</td>
    <td>-4.07</td>
  </tr>
  <tr>
    <td>Anterior insula/frontal operculum</td>
    <td>Ctx_AVI_R</td>
    <td>3</td>
    <td>36</td>
    <td>26</td>
    <td>-4</td>
    <td>-4.06</td>
  </tr>
  <tr>
    <td>Dorsolateral prefrontal cortex</td>
    <td>Ctx_p9_46v_R</td>
    <td>52</td>
    <td>44</td>
    <td>36</td>
    <td>16</td>
    <td>-3.99</td>
  </tr>
  <tr>
    <td>Cerebellum</td>
    <td>Cblm_CrusII_R</td>
    <td>3</td>
    <td>8</td>
    <td>-86</td>
    <td>-28</td>
    <td>-3.92</td>
  </tr>
  <tr>
    <td>Frontal pole</td>
    <td>Ctx_a10p_R</td>
    <td>9</td>
    <td>28</td>
    <td>66</td>
    <td>-6</td>
    <td>-3.85</td>
  </tr>
  <tr>
    <td>Thalamus</td>
    <td>Thal_Pulv</td>
    <td>19</td>
    <td>6</td>
    <td>-26</td>
    <td>8</td>
    <td>-3.85</td>
  </tr>
  <tr>
    <td>Orbitofrontal cortex</td>
    <td>Ctx_pOFC_R</td>
    <td>8</td>
    <td>16</td>
    <td>10</td>
    <td>-16</td>
    <td>-3.84</td>
  </tr>
  <tr>
    <td>Midcingulate cortex</td>
    <td>Ctx_a32pr_L</td>
    <td>4</td>
    <td>-8</td>
    <td>34</td>
    <td>24</td>
    <td>-3.84</td>
  </tr>
  <tr>
    <td>Visual cortex</td>
    <td>Ctx_V4_L</td>
    <td>10</td>
    <td>-34</td>
    <td>-90</td>
    <td>-6</td>
    <td>-3.80</td>
  </tr>
  <tr>
    <td>Frontal pole</td>
    <td>Ctx_a10p_L</td>
    <td>3</td>
    <td>-20</td>
    <td>60</td>
    <td>-10</td>
    <td>-3.80</td>
  </tr>
  <tr>
    <td>Visual cortex</td>
    <td>Ctx_V3CD_L</td>
    <td>9</td>
    <td>-44</td>
    <td>-86</td>
    <td>12</td>
    <td>-3.79</td>
  </tr>
  <tr>
    <td>Superior parietal lobule</td>
    <td>No_label</td>
    <td>3</td>
    <td>28</td>
    <td>-38</td>
    <td>76</td>
    <td>-3.79</td>
  </tr>
  <tr>
    <td>Posterior cingulate cortex</td>
    <td>Ctx_31a_L</td>
    <td>9</td>
    <td>0</td>
    <td>-32</td>
    <td>44</td>
    <td>-3.74</td>
  </tr>
  <tr>
    <td>Inferior parietal lobule</td>
    <td>Ctx_PFm_L</td>
    <td>4</td>
    <td>-50</td>
    <td>-48</td>
    <td>52</td>
    <td>-3.69</td>
  </tr>
  <tr>
    <td>Frontal pole</td>
    <td>Ctx_p10p_L</td>
    <td>3</td>
    <td>-30</td>
    <td>66</td>
    <td>0</td>
    <td>-3.65</td>
  </tr>
  <tr>
    <td>Visual cortex</td>
    <td>Ctx_VVC_R</td>
    <td>4</td>
    <td>30</td>
    <td>-62</td>
    <td>-14</td>
    <td>-3.63</td>
  </tr>
  <tr>
    <td>Nucleus accumbens</td>
    <td>NAC_L</td>
    <td>6</td>
    <td>-10</td>
    <td>4</td>
    <td>-18</td>
    <td>-3.57</td>
  </tr>
  <tr>
    <td>Nucleus accumbens</td>
    <td>NAC_L</td>
    <td>3</td>
    <td>-8</td>
    <td>12</td>
    <td>-10</td>
    <td>-3.52</td>
  </tr>
</table>