Validation of Soft Multipin Dry EEG Electrodes

Current developments towards multipin, dry electrodes in electroencephalography (EEG) are promising for applications in non-laboratory environments. Dry electrodes do not require the application of conductive gel, which mostly confines the use of gel EEG systems to the laboratory environment. The aim of this study is to validate soft, multipin, dry EEG electrodes by comparing their performance to conventional gel EEG electrodes. Fifteen healthy volunteers performed three tasks, with a 32-channel gel EEG system and a 32-channel dry EEG system: the 40 Hz Auditory Steady-State Response (ASSR), the checkerboard paradigm, and an eyes open/closed task. Within-subject analyses were performed to compare the signal quality in the time, frequency, and spatial domains. The results showed strong similarities between the two systems in the time and frequency domains, with strong correlations of the visual (ρ = 0.89) and auditory evoked potential (ρ = 0.81), and moderate to strong correlations for the alpha band during eye closure (ρ = 0.81–0.86) and the 40 Hz-ASSR power (ρ = 0.66–0.72), respectively. However, delta and theta band power was significantly increased, and the signal-to-noise ratio was significantly decreased for the dry EEG system. Topographical distributions were comparable for both systems. Moreover, the application time of the dry EEG system was significantly shorter (8 min). It can be concluded that the soft, multipin dry EEG system can be used in brain activity research with similar accuracy as conventional gel electrodes.

Introduction
Electroencephalography (EEG) is an electrophysiological measurement technique that records the electrical activity of the cerebral cortex with a high temporal resolution, using non-invasive scalp electrodes [1]. In research, it is a widely used technique to investigate visual, auditory, and cognitive functioning, as well as to gain insights, for instance, into the cortical pathways and impairments involved in neurological (movement) disorders [2], such as Parkinson's disease [3] or stroke [4]. More recently, EEG has become an important tool in research on brain-computer interfaces [5,6]. In addition to its utility in research, EEG is used clinically as a diagnostic tool for diseases such as epilepsy or sleep disorders [7,8]. It is likely that the applicability of EEG systems will be extended in the future because of current developments towards mobile EEG systems and developments in the design of the electrodes.
The gold standard in EEG sensors is the use of conventional gel electrodes. These electrodes require the application of conductive gel, which serves as a conductive medium to bridge the gap between the subject's head and the electrodes, thereby reducing the electrode-skin impedance [1]. Gel EEG systems are known for their high signal quality and their good comfort. However, as frequently reported, the need for conductive gel yields

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The checkerboard paradigm (CHECK) is used to compare systems in the time and spatial domains. The checkerboard paradigm evokes the pattern-reversal visual evoked potential (VEP). This VEP is known for its low variability within and between subjects [23,24] and can be used to evaluate visual functioning in a variety of diseases (reviewed in [23]).

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The 40 Hz auditory steady-state response (ASSR)-task is used to compare systems in the time, frequency, and spatial domains. The ASSR is an auditory evoked potential (AEP), which can be used to evaluate hearing thresholds [25,26], and is a potential biomarker for psychiatric disorders such as schizophrenia [27]. Amplitude modulated tones evoke a synchronous activity in the auditory pathways, which can be observed as a large peak at the modulation frequency in the power spectral density (PSD) [25,28].

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The eyes open/eyes closed (EOEC)-task is used to compare systems in the frequency and spatial domains. The EOEC-task is frequently used in studies that validate newly developed EEG electrodes [10][11][12][13][14]18]. When closing the eyes, an increase in alphaband activity can be observed (i.e., Berger effect [29]), which then reduces immediately when opening the eyes.
Compared to previous studies using multipin electrodes, it is hypothesized that application time will be reduced, and experienced comfort will be improved for the soft multipin dry EEG system. Moreover, it is expected that similar patterns will be observed for EEG analyzed in the time, frequency, and spatial domains, with slightly increased noise levels for the soft, multipin dry EEG electrodes compared to the gel electrodes.

Participants
Fifteen healthy subjects (8 males, 7 females) participated in the study. They had an average age of 22.7 ± 2.2 years (mean ± SD), and an average head circumference of 56.3 ± 1.9 cm (mean ± SD). Subjects were included if they were between 18 and 30 years old. They were excluded from participation if they suffered from a skin disease affecting the skin on the head, used drugs affecting the central nervous system (e.g., antidepressant, antipsychotics), had brain surgery in the past, suffered from epilepsy, suffered from a psychiatric or neurological disease in the past year, or if they had a history of substance abuse in the past year. All subjects provided written informed consent prior to the experiment.

Data Acquisition
The gel EEG system (waveguard original; ANT Neuro b.v., Hengelo, The Netherlands) consisted of 32 silver/silver-chloride (Ag/AgCl) electrodes positioned according to the 10-10 international system. Two integrated electrodes at AFz and CPz were used as the ground and reference, respectively. Electrode-skin impedance levels of the electrodes were aimed to be below 20 kΩ by using conductive gel. The average impedance level of the gel electrodes (with the exception of the ground and reference) was 6.8 ± 5.6 kΩ (mean ± SD; standard deviation). The dry EEG system (waveguard touch; ANT Neuro b.v., Hengelo, The Netherlands) consisted of 32 soft, multipin electrodes positioned according to the 10-10 international system. The electrodes were made of a polyurethane (PU) substrate. All electrodes were coated using a silver-chloride (AgCl) electroless plating technique [11]. Electrodes had a Sensors 2021, 21, 6827 4 of 18 diameter of 1.5 cm and comprised 30 pins. The length of the pins was variable in accordance with the head region ( Figure 1). Therefore, short pin lengths (1.5 mm) were used for the prefrontal area, medium pin lengths (3 mm) for the frontal-temporal and anterior areas, and long pin lengths (6 mm) for the frontal-central, central, temporal, parietal, and occipital areas. In contrast to previous studies using electrodes with a homogeneous shore hardness of A98 [11,12], the present study used electrodes with flexibility selected specifically for each electrode pin length and head region ( Figure 1). The electrodes with short pins comprised a substrate of Shore A 40. Electrodes with medium pins were based on substrates of Shore A 60. The electrodes comprising long pins had a shore hardness of A 80. Two external self-adhesive hydrogel AgCl disc electrodes at the left and right mastoid were used as ground and reference, respectively. The impedance of the ground and reference were aimed to be below 20 kΩ by cleaning the skin with alcohol and using a tiny drop of conductive gel on the ring electrodes. A specialized dry EEG software module (eego TM software v1.9.1; ANT Neuro b.v., Hengelo, The Netherlands) was used to observe and improve the signal quality of the dry electrodes. This module assesses the signal quality of each electrode separately by a peak-to-peak amplitude threshold of 400 µV in a 1 s sliding window. A channel reliability of at least 80% was aimed for. The average impedance level of the dry electrodes (with the exception of the ground and reference) was 601.5 ± 400.8 kΩ (mean ± SD).
6.8 ± 5.6 kΩ (mean ± SD; standard deviation). The dry EEG system (waveguard touch; ANT Neuro b.v., Hengelo, The Netherlands) consisted of 32 soft, multipin electrodes positioned according to the 10-10 international system. The electrodes were made of a polyurethane (PU) substrate. All electrodes were coated using a silver-chloride (AgCl) electroless plating technique [11]. Electrodes had a diameter of 1.5 cm and comprised 30 pins. The length of the pins was variable in accordance with the head region ( Figure 1). Therefore, short pin lengths (1.5 mm) were used for the prefrontal area, medium pin lengths (3 mm) for the frontal-temporal and anterior areas, and long pin lengths (6 mm) for the frontal-central, central, temporal, parietal, and occipital areas. In contrast to previous studies using electrodes with a homogeneous shore hardness of A98 [11,12], the present study used electrodes with flexibility selected specifically for each electrode pin length and head region ( Figure 1). The electrodes with short pins comprised a substrate of Shore A 40. Electrodes with medium pins were based on substrates of Shore A 60. The electrodes comprising long pins had a shore hardness of A 80. Two external self-adhesive hydrogel AgCl disc electrodes at the left and right mastoid were used as ground and reference, respectively. The impedance of the ground and reference were aimed to be below 20 kΩ by cleaning the skin with alcohol and using a tiny drop of conductive gel on the ring electrodes. A specialized dry EEG software module (eego TM software v1.9.1; ANT Neuro b.v., Hengelo, The Netherlands) was used to observe and improve the signal quality of the dry electrodes. This module assesses the signal quality of each electrode separately by a peakto-peak amplitude threshold of 400 μV in a 1 s sliding window. A channel reliability of at least 80% was aimed for. The average impedance level of the dry electrodes (with the exception of the ground and reference) was 601.5 ± 400.8 kΩ (mean ± SD).
For both EEG systems, data was collected using the eego TM amplifier (EE-225; ANT Neuro b.v., Hengelo, The Netherlands), with a sampling frequency of 1024 Hz. Figure 1. The 32-channel layout of the soft, multipin, dry EEG system, indicating the location and shore hardness of short pins (green), medium pins (blue), and long pins (orange).

Experimental Protocol
All subjects performed two experimental sessions at the Radboud University, Nijmegen, in a room with dimmed lights. The two sessions occurred on separate days but at the same part of the day. During the sessions, either the dry EEG system or the gel EEG Figure 1. The 32-channel layout of the soft, multipin, dry EEG system, indicating the location and shore hardness of short pins (green), medium pins (blue), and long pins (orange).
For both EEG systems, data was collected using the eego TM amplifier (EE-225; ANT Neuro b.v., Hengelo, The Netherlands), with a sampling frequency of 1024 Hz.

Experimental Protocol
All subjects performed two experimental sessions at the Radboud University, Nijmegen, in a room with dimmed lights. The two sessions occurred on separate days but at the same part of the day. During the sessions, either the dry EEG system or the gel EEG system was tested in a pseudorandomized order between subjects. In both sessions, subjects performed three tasks: the checkerboard paradigm, the auditory steady-state response, and the eyes-open/eyes-closed task. The order of the tasks was similar for both experimental sessions within a subject but randomized between subjects. The MATLAB toolbox, Psychtoolbox-3 [30], was used for the presentation of visual stimuli and sound stimuli via a standard laptop. Sound stimuli and instructions were presented via insert earphones (Etymotic ER1). Volume levels and display settings were set equally between sessions and subjects.

Checkerboard Paradigm (CHECK)
During the checkerboard paradigm, the subject was asked to focus on a red dot in the middle of the screen. A 24-by-18 checkerboard pattern was presented with black and white checks (visual angle of 1 • , distance to screen 65 cm). Every 0.45 s, the checkerboard reversed (i.e., black checks became white and vice versa). After a 10 s baseline, one block of 300 trials (i.e., checkerboard reversals) was obtained per subject. The pattern-reversal VEP, as evoked by the checkerboard paradigm, was used to compare both systems in the time and spatial domains.

Auditory Steady-State Response (ASSR)
During the ASSR-task, 12 s audio segments were presented, with a jittered intertrial interval of 2 to 3 s. The subject was asked to focus on a red fixation point on the wall. The audio segments consisted of tones with a 500 Hz carrier frequency and a 40 Hz modulation frequency. In total, 75 trials of 12 s were obtained per subject, unequally divided over 3 blocks. Each block started with a 10 s baseline. The auditory evoked potential (AEP), occurring in the first second of each 12 s trial, was used to compare both systems in the time and spatial domains. Furthermore, the 40 Hz power (caused by the modulation component of the audio stimulus) was used to compare both systems in the frequency domain.

Questionnaires
Before and after performing the tasks, subjects completed two short questionnaires. First, subjects indicated their level of sleepiness by the Karolinska Sleepiness Scale (KSS; 1 = extremely alert; 10 = extremely sleepy, cannot keep awake [31,32]). Second, they indicated their experienced comfort of the EEG cap with a 10-point Likert scale (1 = extremely comfortable; 10 = maximum imaginable pain).

Data Processing and Analysis
Pre-processing and analysis of the data were performed in MATLAB using eeglab (an open-source toolbox [33]). Electrodes that were not contained in both systems were removed from further analysis. Therefore, M1 and POz were removed for the gel EEG system, and AFz, FT9, and FT10 were removed for the dry EEG system. The 29 overlapping electrodes remained for further analyses. The data was filtered using a zero-phase, 2ndorder Butterworth bandpass filter (cut-off frequencies 1-48 Hz) and a zero-phase 2nd-order Butterworth bandstop filter (cut-off frequencies 48-52 Hz) to remove 50 Hz line noise. Bad channels with an average amplitude below 1 µV (flat line) or above 50 µV were removed from further analyses. The independent component analysis was applied to remove eye blink artifacts. The eye blink component was selected based on the following properties [34]: (1) the topographical distribution of the independent component shows activity in the frontal electrodes only, (2) the characteristic pattern of eye blinks can be observed in the independent component over time, and (3) the eyeblink component is present over the entire course of the experiment and is not linked to a specific task. Moreover, the reference was set equal for both EEG systems. Therefore, the data of the gel EEG system was rereferenced to the right mastoid (M2), similarly as for the dry EEG system. Subsequently, the data of each task was extracted, including an additional 5 s before and after the start and end of the task, respectively. For each of the tasks separately, bad channels were removed based on three criteria: (1) if the channel's average amplitude within the specific task was below 1 µV or above 50 µV, (2) if the channel's average amplitude within the specific task exceeded the mean + 2xSD over all channels within the task, or (3) if the channel's average power within the specific task exceeded the mean + 2xSD over all channels within the task in at least 2 out of 5 frequency bands (delta [1][2][3][4], theta [4][5][6][7][8], alpha [8][9][10][11][12][13][14], beta [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], gamma [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]). For the third criterium, the average power over the task-specific trials was calculated using a Hann window (window length: VEP 0.5 s; AEP 0.8 s; 40 Hz-ASSR 11 s; EOEC 3 s).

Performance in the Time Domain
The VEP evoked by the checkerboard paradigm and the AEP evoked by the ASSR-task were used to compare the EEG systems in the time domain. Additional pre-processing steps were applied. First, the data were filtered using a zero-phase, 2nd-order Butterworth bandpass filter (cut-off frequencies 1-30 Hz). Second, data were divided into trials of 500 ms for the VEP and 800 ms for the AEP, including a pre-stimulus baseline of −100 ms. Baseline correction was performed by subtracting the channel's average baseline per trial. Lastly, bad trials were removed per channel: (1) if the channel's average amplitude exceeded the threshold (mean + 2xSD over all trials) during the specific trial, or (2) if the channel's average power exceeded the threshold (mean + 2xSD over all trials) in at least 2 out of 4 frequency bands (delta, theta, alpha, beta) during the specific trial.
After pre-processing, the VEP and AEP were averaged over all remaining trials. Moreover, the global field power in the time domain (GFPt) was calculated (Equation (1); [11,35]).
The GFPt is a measure of spatial standard deviation over all electrodes n at a certain point in time t. It takes into account the voltage difference U between all pairs of electrodes i and j. Thus, local activity at a certain time point can be observed by a high GFPt, while broadly spread activity is indicated by lower GFPt values.
To evaluate the similarities in GFPt between the gel and dry EEG system, the Spearman's rank correlation (COR) and the root mean square deviation (RMSD) of the GFPt were calculated per subject [11].

Performance in the Frequency Domain
Besides the AEP, the ASSR-task was used for comparison in the frequency domain by evaluating the 40 Hz peak (caused by the modulation frequency) in the power spectral density (PSD). Some additional pre-processing steps were taken. First, electrodes with a less pronounced or absent 40 Hz-ASSR response were removed. Therefore, T7, T8, P7, P8, O1, O2, and Oz were removed for both caps for all subjects [36]. Second, data were filtered using a zero-phase, 2nd-order Butterworth bandpass filter (cut-off frequencies 30-48 Hz). Third, the first 1 s of all trials was removed, eliminating the AEP. Last, using a nonoverlapping, sliding window of 1 s, bad windows were removed from trials: (1) if the channel's average amplitude exceeded the threshold (mean + 2xSD over all trials) during the specific trial, or (2) if the channel's average power in the gamma band exceeded the threshold (mean + 2xSD over all trials) during the specific trial.
After pre-processing, the PSD was calculated using a 4 s sliding Hann window with 75% overlap to obtain the power between 35 and 45 Hz with a frequency resolution of 0.5 Hz. Moreover, the PSD was standardized by calculating the Z-score. For both the absolute and standardized PSD, the average 40 Hz power and the signal-to-noise ratio (SNR) were obtained. The SNR (Equation (2)) was calculated by dividing the 40 Hz power P (i.e., signal) by the standard deviation of the power in the frequency window 35-39 Hz and 41-45 Hz (i.e., noise).
In addition to the ASSR-task, the EOEC-task was also used for comparison in the frequency domain. Additional pre-processing steps were applied. First, eyes open (EO) and eyes closed (EC) trials were extracted separately. Since the duration of EC trials (3 s) was shorter than the duration of EO trials (5 s), the middle 3 s were taken for the latter condition. Second, using a nonoverlapping sliding window of 1 s, bad windows were removed from trials: (1) if the channel's average amplitude exceeded the threshold (mean + 2xSD over all windows), or (2) if the channel's average power exceeded the threshold (mean + 2xSD over all windows) in at least 2 out of 5 frequency bands (delta, theta, alpha, beta, gamma).
After the additional pre-processing steps, the PSD was calculated using a 1 s sliding Hann window with 50% overlap. The PSD was standardized by calculating the Z-score. The average power per frequency band was calculated for both the absolute and standardized PSD.

Performance in the Spatial Domain
The standardized topographic distribution (Z-score) of the two main components of the VEP and AEP were generated for both systems. Therefore, the peaks of the average GFPt were used as time points to calculate the topographical distribution of the main components of the VEP (i.e., N75 and P100) and the AEP (i.e., N1 and P1). Moreover, the standardized topographic distribution of the average alpha band power (i.e., frequency of main interest in the EOEC-task) was calculated for both systems. Biharmonic spline interpolation was used for the areas in between electrodes.

General Performance
To assess the general performance of both systems, the time needed for the application and preparation of the EEG systems was assessed (i.e., application time). The percentage of data that had been rejected in the pre-processing phase (i.e., bad channel rejection and bad trial/window rejection) was evaluated per channel for both systems. Moreover, the subject indicated the comfort of the cap on a 10-point Likert scale as described previously.

Statistical Analysis
The assumption of a normal distribution of the dependent variable failed, as assessed using the one-sample Kolmogorov-Smirnov test. Therefore, non-parametric statistical tests were performed with a significance level of α = 0.05. For statistical comparison between systems in the time domain, the Wilcoxon signed-rank test was used to examine differences in the COR and RMSD values of the VEP and AEP. For statistical comparison in the frequency domain, the Wilcoxon signed-rank test was used for both the absolute and standardized PSD to evaluate the subject's averages over channels of the 40 Hz-ASSR power, the SNR, and the power per frequency band (EOEC-task). A Bonferroni correction was applied for the EOEC-task to adjust for the number of frequency bands (α = (0.05/5) = 0.01). Moreover, a within-subject correlation between all pairs of electrodes was performed for the 40 Hz-ASSR power, the SNR, and the power per frequency band, using Spearman's rank correlation. For statistical comparison of the general performance, the Wilcoxon signed-rank test was performed to examine differences in the application time and the percentage of rejected data between the two systems. In addition, the nonparametric two-way repeated-measures ANOVA (i.e., Friedman's test) was performed to evaluate differences in experienced comfort and sleepiness before and after the experiment. The topographic distribution (spatial domain) of the main components of the VEP and AEP, and the distribution of the average alpha band power during the EOEC-task, were statistically compared using non-parametric permutation testing, including a pixel-based correction for multiple comparisons [37,38]. Therefore, a permutation distribution (H 0 ) was created for each of the 3409 pixels in 23,768 iterations (2 n , with n = 15 subjects). For each iteration, the condition label (i.e., 'dry EEG' or 'gel EEG') was permuted, and the t-statistic of the paired t-test was calculated (Equation (3)): with X D and S D as the average and standard deviation of the difference between the pairs and n as the number of pairs (n = 15 subjects). Moreover, the minimum and maximum t-value over all pixels were saved for each iteration. Pixel-based correction for multiple comparisons was performed by calculating the statistical thresholds, defined as the 2.5th percentile of the smallest t-values (lower threshold) and the 97.5th percentile of the largest t-values (upper threshold). The observed test statistic (obs) for every pixel, using the real condition labels, was converted to a Z-value (Equation (4); [37]): by subtracting the average value of the H 0 permutation distribution and dividing the result by the standard deviation of the H 0 permutation distribution. A pixel was significantly different between systems if its Z-value was smaller than the lower threshold or higher than the upper threshold.

Performance in the Time Domain
The time signals of the evoked responses, the VEP ( Figure 2a) and AEP (Figure 3a), recorded by the dry EEG system, showed strong similarities to those recorded with the gel EEG system. Moreover, the two peaks resulting from the first and second main components could clearly be observed in the GFPt of the VEP (N75 and P100; Figure 2b) and AEP (N1 and P1; Figure 3b). The average amplitudes and the latencies of these components of the GFPt were highly comparable between both systems (Table 1). Moreover, very strong within-subject correlations and small RMSD values were observed between the two systems for the GFPt of the VEP (ρ = 0.89 ± 0.10; RMSD = 1.33 µV ± 0.77 µV; median ± SD) and the AEP (ρ = 0.81 ± 0.13; RMSD = 2.27 µV ± 1.03 µV; median ± SD).

Performance in the Frequency Domain
The ASSR-task resulted in a clear 40 Hz peak in the recordings of both systems, which can be observed in both the absolute PSD ( Figure 4a) and standardized PSD (Figure 4b).
Both the absolute (Figure 5a) and standardized PSD (Figure 5b) of the EOEC-task clearly showed a peak in the alpha band during the EC condition, while this peak was less pronounced during the EO condition. The absolute power was significantly increased for the dry EEG system in the delta and theta band during EO and EC and in the alpha band during EO ( Table 2). The increase in absolute power for the dry EEG system was most pronounced for the delta band, as supported by a poor and fair correlation during both EO (ρ = 0.27, p < 0.001) and EC (ρ = 0.37, p < 0.001), respectively. However, the absolute power of the alpha band showed a moderate correlation during EO (ρ = 0.69, p < 0.001), and a very strong correlation during EC (ρ = 0.86, p < 0.001).   and eyes closed (right) for the gel EEG system and the dry EEG system. Black lines in the topographic distribution encircle the pixels that were significantly different between systems. Table 2. Descriptive statistics (mean ± SD) of the absolute (µV 2 /Hz) and standardized (Z-score) power spectral density (PSD) per frequency band during the eyes open/eyes closed (EOEC)-task for the dry EEG system and gel EEG system. p-value (p-Val) after Bonferroni correction as a result of the Wilcoxon signed-rank test and Spearman's correlation coefficient (rho) are indicated for each frequency band and condition. For the standardized PSD, the power was significantly decreased for the dry EEG system in the alpha band during EO only (Table 2). In addition, Spearman's rank correlation showed high similarities between the two systems in the standardized PSD. With the exception of the gamma band during EO (ρ = 0.52, p < 0.001), moderate correlations were found for all frequency bands during both EO and EC, with a strong correlation for the alpha band (ρ = 0.81, p < 0.001) during EC.

Performance in the Spatial Domain
The P100 component of the VEP, respectively, 34.8% and 20.1% of the pixels were significantly different between the two systems (Figure 2c). For the N1 and P1 components of the AEP, respectively, only 4.1% and 0.0% of the pixels were significantly different between the systems (Figure 3c).
Moreover, the topographic distribution of the alpha band was highly comparable between both systems (Figure 5c). For EC, only 1.2% of the pixels were significantly different between systems. For the EO, 5.9% of the pixels were significantly different.

General Performance
The application time was significantly reduced by 8 min (p < 0.05; Figure 6a) for the dry EEG system (23 ± 13 min; median ± SD) in comparison to the gel EEG system (31 ± 10 min; median ± 2xSD). However, the percentage of rejected data was significantly increased for the dry EEG system (p < 0.05; Figure 6b). For the dry EEG system, 10.5% ± 5.7% (mean ± SD) of the data was rejected per subject, while for the gel EEG system, 3.9% ± 2.7% (mean ± SD) of the data was rejected per subject.
Sensors 2021, 21, x FOR PEER REVIEW 13 of 19 Figure 6. General performance. (a) Application time (min) for the gel EEG system (blue) and the dry EEG system (red). (b) Percentage of data rejection (%) per channel averaged over subjects for the gel EEG system (left) and the dry EEG system (right). 0% = no data rejected; 100% = all data rejected.
Color bar from 0-50%. (c) Experienced comfort for the gel EEG system (blue) and the dry EEG system (red), rated by the subject before (open) and after the experiment (shaded). 1 = extremely comfortable; 10 = maximum imaginable pain. * p < 0.01.

Discussion
The current study validates the soft, multipin, dry EEG electrode system by comparing its signal quality in the time, frequency, and spatial domains and its general performance with the signal quality and performance of a conventional gel EEG electrode system. The findings indicate similar signal quality in the time, frequency, and spatial domains for the two systems. The soft, dry electrodes measured electrical brain activity with similar accuracy as compared to conventional gel electrodes while maintaining good Figure 6. General performance. (a) Application time (min) for the gel EEG system (blue) and the dry EEG system (red). (b) Percentage of data rejection (%) per channel averaged over subjects for the gel EEG system (left) and the dry EEG system (right). 0% = no data rejected; 100% = all data rejected. Color bar from 0-50%. (c) Experienced comfort for the gel EEG system (blue) and the dry EEG system (red), rated by the subject before (open) and after the experiment (shaded). 1 = extremely comfortable; 10 = maximum imaginable pain. * p < 0.05. Moreover, there were no significant differences in experienced comfort between the two systems ( Figure 6c) when taking time (i.e., the comfort rating before or after the experiment) into account (χ 2 (1) = 3.075, p = 0.08). The experienced comfort before the experiment was rated as 2.0 ± 1.2 and 2.0 ± 1.0 (median ± SD), and after the experiment as 3.0 ± 1.5 and 2.0 ± 1.3 (median ± SD), for the dry and gel EEG system, respectively. The level of sleepiness of the participants did not differ between the experimental sessions with either the dry EEG system or the gel EEG system (χ 2 (1) = 2.020, p = 0.155).

Discussion
The current study validates the soft, multipin, dry EEG electrode system by comparing its signal quality in the time, frequency, and spatial domains and its general performance with the signal quality and performance of a conventional gel EEG electrode system. The findings indicate similar signal quality in the time, frequency, and spatial domains for the two systems. The soft, dry electrodes measured electrical brain activity with similar accuracy as compared to conventional gel electrodes while maintaining good comfort. Therefore, the dry EEG system, consisting of soft, multipin dry electrodes, is a promising technique for use in future out-of-laboratory experiments.

Performance in the Time Domain
The time signals of the evoked responses, the VEP and AEP, recorded by the dry EEG system showed strong similarities to those recorded with the gel EEG system. Both the general evolution over time, assessed by the Spearman's rank correlation (ρ > 0.8), and the absolute amplitudes of the VEP and AEP, assessed by the RMSD (RMSD < 2.3 µV), reveal the good performance of the dry EEG system. These results are in accordance with the previous results of Fiedler et al. [11], who evaluated comparable PU-based multipin dry electrodes with Ag/AgCl coating. They reported an average correlation of 0.8 and an average RMSD of 2.9 µV for the VEP between a dry and gel EEG system. These findings show that the dry EEG system can be used for future investigations on event-related potentials with similar accuracy as compared to a conventional gel EEG system.

Performance in the Frequency Domain
The absolute and standardized PSD of both the dry EEG system and the gel EEG system showed a clear 40 Hz peak induced by the ASSR-task and a clear increase in alpha band activity in response to a period of closed eyes. Standardization is a frequently used method that converts absolute values into a standard score (i.e., Z-score) in order to make a better comparison between channels or between subjects. Therefore, in the current study, both the absolute and standardized PSD were calculated.
The 40 Hz-ASSR power was not significantly different between systems for the absolute PSD, while the standardized 40 Hz-ASSR power was slightly decreased for the dry EEG system. A previous study of Grummett et al. [39] found a similar decrease in the power of the absolute 16 Hz and 23 Hz visual steady-state response for gold-coated multipin dry electrodes in comparison to standard gel electrodes. In addition to the 40 Hz-ASSR power, the ASSR-task was used to compare the SNR of the two systems. Consistent with the previous studies evaluating gold-plated dry electrodes [17,18], a slightly decreased SNR was found for the dry EEG system in both the absolute and standardized PSD. However, Spearman's rank correlation over all possible pairs of electrodes showed moderate correlations for the 40 Hz-ASSR power and SNR in both the absolute and standardized PSD.
The absolute and standardized PSD of both the dry EEG system and the gel EEG system showed a clear increase in the alpha band during a period of closed eyes in comparison to a period of open eyes. High similarities could be observed between the two systems for both the absolute and standardized PSD. However, the absolute power of the delta band was significantly increased for the dry EEG system. This noticeable increase in the delta band for dry electrodes is frequently reported [10,12,14,18,20,39] and might be explained by a less stable skin-electrode contact due to the lack of conductive gel. Therefore, the dry electrodes might be more susceptible to movement artifacts or to changes in hydration of the skin (e.g., sweating), resulting in a low-frequency drift. However, the current results show a strong correlation for the frequency band of interest, i.e., the alpha band, especially during eyes closed (absolute PSD: ρ = 0.86; standardized PSD: ρ = 0.81). This strong correlation for the alpha band during an EOEC-task is reported in the literature as well [10,13,18,20].
In summary, the signals measured with the dry EEG system showed a distinct 40 Hz-ASSR power and a clear increase in the alpha band during EOEC, with slightly increased noise levels. Moreover, the signals of the dry EEG system strongly correlated with the signals of the gel EEG system. Therefore, the dry EEG system can be used properly in future investigations involving similar tasks.

Performance in the Spatial Domain
The topographical distributions of the main ERP components were comparable for the two systems. With the exception of the N75 component of the VEP, the pixels that were significantly different between the two systems were located primarily outside the main regions of interest of the VEP (i.e., the occipital area), and the AEP (i.e., the frontal/central area), similar to previous findings evaluating comparable PU-based multipin electrodes with Ag/AgCl coating [11]. It is remarkable that the percentage of significantly different pixels is increased for the VEP components in comparison to the AEP components. This can be explained by the faster evolution of the VEP over time and the slower and more smooth evolution of the AEP over time. Therefore, the fixed time points set to calculate the topographical distribution might include more variability for the VEP in comparison to the AEP. Another explanation is the low electrode density in the occipital area in comparison to the more densely covered frontal/central area. Larger interpolation areas for the VEP might have induced a higher number of significantly different pixels between the two systems.
Additionally, the topographical distribution of the alpha band was similar for the two systems, with less than 6% of the pixels being significantly different. The significant pixels were mainly located in the frontal-temporal region, outside the main region of interest (i.e., the parietal/occipital area). The significant differences in the topographical distribution might be caused by the interpolation of the frontal-temporal region because of the low density of electrodes and the increased percentage of rejected data within this region.
The number of significantly different pixels for the VEP and alpha band power is slightly increased in comparison to a previous study of Fiedler et al. [11], evaluating comparable multipin dry electrodes. This can be explained by the different spatial resolution due to a lower number of electrodes in the current study (32-channels vs. 97-channels), thereby producing larger interpolation areas and increased impact of channel dropouts.

General Performance
In the current study, the general performance of the dry EEG system was evaluated by the application time, the experienced comfort, and the percentage of rejected data. The application time of the dry EEG system was significantly decreased by 8 min, which is a reduction of 25%. One extreme outlier could be observed for the dry EEG system (Figure 2), with an application time of 55 min. This was caused by technical problems related to the hardware on which the recording software was installed, resulting in a delay of approximately 15 to 20 min. The application time is frequently reported as the main advantage of dry EEG systems. Previous studies evaluating comparable PU-based multipin dry electrodes with an Ag/AgCl coating observed a reduction from 33% (64-channel gel vs. 64-channel dry EEG system [12]) up to 86% (128-channel gel vs. 97-channel dry EEG system [11]) in application time when correcting for the number of electrodes. However, others reported an increased application time for the dry EEG system (64-channel gel vs. 33-channel dry EEG system consisting of (2 pins) spring-loaded sliver electrodes [13]). A confounding factor responsible for the high variability in results might be the prior experience of the experimenter with the application of one of the caps, as discussed by Kam et al. [13]. Therefore, it is worth noting that the experimenter of the current study had no previous experience in the application of either dry or gel EEG systems. Another possible explanation might be the differences in the number of electrodes of the systems used in studies [10]. During the application of a gel EEG system, every single electrode is handled individually to prepare the gel and obtain a good signal quality. In contrast, only the channels without a direct good signal quality are handled individually for the dry EEG system. Therefore, it can be expected that the difference in application time between the two systems is more pronounced with an increasing number of electrodes.
The experienced comfort was not significantly different between the dry and gel EEG system when taking time (i.e., the rating before and after the experiment) into account. As reported by Di Fronso et al. [12], the experienced comfort might be improved further if the experiment involves the subject performing a specific task, which distracts from the sensation of the EEG cap.
Despite the promising general performance regarding application time and comfort, the dry EEG system performed slightly worse compared to the gel EEG system with respect to the percentage of rejected data, consistent with previous studies [11][12][13][14]. This might be caused by a less stable electrode-skin contact, either due to the softness of the electrodes or due to the lack of conductive gel. It is important to point out the remarkably high percentage of data rejection for the FC1 electrode in the dry EEG system. A possible explanation might be the insufficient adduction and skin contact of the electrode. Nevertheless, only 10.5% of the data per subject was rejected for the dry EEG system, compared to 3.9% for the gel EEG system, which results in a difference of 6.6%. It must be expected that the percentage of rejected data for the dry EEG electrodes influenced the SNR. A decrease of the SNR for both the dry and gel EEG systems must be expected if the analyses were performed on the entire dataset (including the respectively rejected data during pre-processing). This aspect highlights bad channel and artifact detection and rejection, which are well established for conventional gel EEG systems [40][41][42][43][44], to be even more important for dry EEG systems [42,43]. It is important to note that our results provided enough data to compare the two systems, including statistical analyses.
In the current study, a threshold (mean + 2xSD) was used to eliminate noisy channels or epochs. Even though this method might have missed some of the noisy epochs in either the dry or gel EEG system, it is more objective than visual inspection of the signals by raters as the same criteria were used for both systems.

Limitations and Recommendations
For the dry EEG system, external self-adhesive drop leads were used as the reference and ground electrodes and were positioned at the mastoids. It is important to note that a tiny drop of conductive gel was applied on the drop leads to improve the impedance. Moreover, only the impedance of the ground and reference electrodes were considered for the dry EEG system. The recording software (eego TM software v1.9.1, ANT Neuro b.v., Hengelo, The Netherlands) provides a 'Dry-EEG module', in which the signal quality, instead of the impedance, can be used to judge the raw signals. Therefore, the current study did not compare the electrode impedances between the two systems [11,12,14].
In the current study, the signal quality was determined by the software based on the raw data, and the raw data was visualized and exported. Although applicability and performance depend on the specific field of application and environmental conditions, algorithms for the automatic detection and correction of artifactual channels [40][41][42][43][44] can be beneficial for measurements outside the laboratory performed by less trained experimenters, or if the subject applies the cap themselves during experiments at home. The dry EEG system, in combination with such algorithms, should ease and speed up the preparation of the EEG system even more, making it applicable for experiments at home.
The experimental protocol included three different tasks to evaluate the performance and signal quality of the dry EEG system. The checkerboard task and the EOEC-task were used in previous validation studies, whereas the ASSR-task has not been used before. Not all subjects showed a prominent 40 Hz peak power, just as not all subjects showed a clear increase in the alpha band activity during a period of eyes closure because of inter-subject variability. However, the ASSR-task is a valuable addition to experimental protocol because of the several advantages. First, the ASSR-task can be used to evaluate multiple aspects of signal quality. The AEP can be used to compare the signal quality in the time and spatial domains, while the 40 Hz-ASSR power can be evaluated in the frequency domain. Additionally, the SNR can be determined quite well because it is explicitly known what the 'signal' (i.e., 40 Hz-ASSR power) should be. Second, the ASSR is a good addition to the frequently used EOEC-task, as it creates the possibility to evaluate the signal quality within multiple frequency bands. Whereas the analysis of the EOEC-task mainly focuses on the lower frequency bands, specifically the alpha band, the ASSR-task can be used to compare the signal quality of systems in the higher gamma frequency band. Moreover, the EOEC-task is used to compare frequency bands, while the ASSR-task can be used to evaluate the sensitivity of the systems to detect the power of one specific peak frequency. Third, the ASSR might be a suitable task for the validation of EEG systems during gait or cycling to evaluate susceptibility to motion artifacts. Although the available literature is limited, Yokota et al. [45] effectively used the ASSR to assess workload during walking. Taken together, the ASSR-task can be a valuable addition to the study protocol of future EEG validation studies.
A limitation of the study is that the VEP and AEP were delayed. In the current study, a delay of approximately 50 ms for the VEP and 100 ms for the AEP could be observed. These latencies are likely caused by a systematic problem in the experimental script regarding the presentation of visual and auditory stimuli or the transfer of event-markers between systems. Since it is a systematic delay, similar for all subjects and experimental sessions, it affected the recordings with both electrode systems equally and therefore did not invalidate the further analysis and interpretation of the data in case of the comparative validation study at hand.
The current study strongly suggests that the dry EEG system can be used in future studies for the measurement of brain activity in stationary tasks. However, further research should be performed to investigate the signal quality of the soft dry electrodes during mobile tasks, such as walking or cycling, to evaluate the effect of motion artifacts. Moreover, it would be interesting to observe the effect of an increased measurement time on the signal quality and the experienced comfort for both systems.

Conclusions
The current study showed that the soft, multipin, dry EEG electrode system could be used for future investigations and studies on electrical brain activity during stationary tasks, with similar accuracy as compared to a conventional gel EEG system. The signal quality in the time, frequency, and spatial domains were comparable for the two systems, with slightly increased noise levels for the dry EEG system. Moreover, the general performance of the system was promising, with a reduced application time and only a slight increase in the percentage of rejected data. Therefore, it can be concluded that the dry EEG system is a promising technique for future out-of-laboratory applications requiring rapid and/or intermittent measurements.  Data Availability Statement: Pre-processed data, processed data, and analysis scripts are available from the Data Sharing Collection of the Donders Repository via the following URL: https://doi.org/ 10.34973/ytxa-qn07. Raw, unprocessed data are stored in the local Data Acquisition Collection and Research Documentation Collection of the Donders Repository and are available upon request to the corresponding author (j.j.a.heijs@utwente.nl).


General Board Game Concepts

Many games often share common ideas or aspects between them, such as their rules, controls, or playing area. However, in the context of General Game Playing (GGP) for board games, this area remains under-explored. We propose to formalise the notion of"game concept", inspired by terms generally used by game players and designers. Through the Ludii General Game System, we describe concepts for several levels of abstraction, such as the game itself, the moves played, or the states reached. This new GGP feature associated with the ludeme representation of games opens many new lines of research. The creation of a hyper-agent selector, the transfer of AI learning between games, or explaining AI techniques using game terms, can all be facilitated by the use of game concepts. Other applications which can benefit from game concepts are also discussed, such as the generation of plausible reconstructed rules for incomplete ancient games, or the implementation of a board game recommender system.

I. INTRODUCTION
Since the foundation of Artificial Intelligence (AI), games have often been used as testbeds for major advancements [1]. This can be explained by their simplicity and popularity, but also because, as humans, we can perceive the problems (game interfaces) and their solutions (strategies). In the field of game AI, two agent types can be distinguished. Dedicated Game AI agents designed for a single game (or a small set of games) and General Game AI agents built to play any arbitrary game.
Game-specific agents have been studied since the beginning of the AI field [2], [3] and are often used as benchmarks of well-known problems. For example, many single-player games, commonly called puzzles, are interesting illustrations of planning problems (e.g. Rubik's Cube [4] or Sokoban [5]) or Constraint Satisfaction Problems [6]. Similarly, multiplayer games are representations of many different AI research areas (Knowledge Representation, Reinforcement Learning, Transfer Learning, etc.) which lead to the development of many game AI agents trying to outperform human players. Nowadays, computer players for classical board games like Chess [7], Go [8], Shogi [9] or Checkers [10], can defeat expert human players. Even for stochastic games like Backgammon [11], games with incomplete information like Poker [12], or video games like Starcraft II [13], computer players have reached an excellent level of play. The success of these dedicated game-playing programs has demonstrated their capacity to outperform humans, marking a milestone in artificial intelligence research [8], [14]. However, they are often highly reliant on game-specific knowledge and expertise, preventing them from playing other games as effectively.
Building general game AI agents that perform well on any board game, rather than being specialised, is the aim of General Game Playing (GGP). These general game AI agents are implemented without knowing the games they will play in advance and consequently, they cannot use specific pre-defined knowledge about them when playing the game. This differs greatly from dedicated game AI agents, as the AIs developed for specific games are often biased by human-developed heuristics. Unfortunately, humans still tend to outperform AI in general board games. This can be explained by the human capacity for understanding common aspects between games and consequently being able to learn new games quicker by detecting common points with previously played games.
This paper introduces board game concepts for GGP through the Ludii general game system. These concepts are expressed in game terms commonly used by game players and designers, making them an interesting mechanism for providing human-understandable explanations of different AI techniques. These concepts can be associated with several levels of abstraction, such as the game itself, a game trial, a game state, or individual moves. This opens many new possibilities for different AI research topics, including agent selection, transfer learning between games, AI explainability, as well as game generation, reconstruction, and recommendation.
The remainder of this paper is organised as follows: Section II describes the field of GGP and the different general game systems proposed so far. Section III describes the Ludii system as well as the ludeme-based language used to describe the games and the reasons behind its use for identifying game concepts. Section IV highlights the notion of game concepts in the context of Ludii, how they are modelled and computed for each game. Section V proposes several GGP research directions which can benefit from our proposed game concepts. Finally, Section VI concludes the paper.

II. BACKGROUND A. General Game Playing
In Artificial Intelligence, the General Game Playing (GGP) challenge [15] is to develop computer players that understand the rules of previously unknown games, and learn to play these games well without human intervention in situations where its knowledge of the games rules, objectives and strategies is limited to the game description. Developing these general agents, and the AI techniques behind them, is vitally important in the development of real-world agents which can deal with unpredictable and novel situations. For this reason, General Game Playing is seen as a necessary step on the way to Artificial General Intelligence (AGI) [16].
Historically, the first GGP model is defined in 1968 by Jacques Pitrat [17] to describe two-player games with complete information and rectangular boards. Then, only from the '90s, other work on General Game systems appeared such as SAL [18], Metagamer [19], Hoyle [20], and Morph-II [21]. After the turn of the millennium, more modern General Game systems started appearing such as Multigame [22] in 2001 and Zillions of Games [23] in 2002.

B. General board Game Languages
Many GGP systems describe their games using a standardised game description language. Different game descriptions are written in different formats and with different levels of abstraction, lending themselves to different kinds of knowledge representation, reasoning, and learning approaches (such as for performance reasons).
1) GDL: Since 2005, the Game Description Language (GDL) [24] and the GGP-Base platform [25] proposed by the Stanford Logic Group 1 has become one of the main standards for academic research in GGP. The purpose of GDL is to provide a generic language for representing any board game [26], including collaborative games and games with simultaneous actions. GDL describes the games in a language inspired by Prolog, using first-order logical clauses. An extension named GDL-II [27] has been developed to handle games with partial observations and stochastic actions, and another extension named GDL-III [28] for epistemic games. This formalism and platform have provided a high-level challenge which has led to important research contributions [29], [30] especially in Monte Carlo tree search (MCTS) enhancements [31], [32], with some original algorithms combining constraint programming, MCTS, and symmetry detection [33]. These techniques have lead to the development of several General Game AI agents that perform well on specific games (e.g. Gamer [34], CadiaPlayer [35], ClunePlayer [36], WoodStock [37], etc.).
Unfortunately, GDL also has some negative points. This includes poor efficiency [38], the fact that each element of the game has to be defined tabula rasa and cannot easily be taken from previously modelled examples, and verbose game descriptions that are not representative of any game-related aspects that human players typically use. The opaque and low-level character of GDL descriptions, without any shared semantics or high-level concepts being explicitly recognisable between games, forms a challenge for tasks such as the creation of mappings between games for transfer learning, or the generation of human-understandable explanations about any aspect of a game. 1 Stanford Logic Group: logic.stanford.edu/ 2) RBG: The Regular Boardgames (RBG) system [39] proposes the idea of encoding piece movement for games using a regular language. This formalism can describe any finite deterministic game with perfect information excluding simultaneous moves. RBG game descriptions are typically much short than their GDL counterparts, making it much easier to model complex board games (e.g. Chess, Go and Arimaa). RBG also runs substantially faster than GDL, averaging over 50 times as many playouts during a recent comparison [38].
3) Ludii: The Ludii system 2 , named after its predecessor LUDI [40], is a complete general board game system, that can model games as a tree of ludemes. The decomposition of games into their conceptual units of game-related information ludemes [41] results in more intuitive games descriptions compared to prior GGP systems. The number and variety of board games that are implemented within Ludii also go far beyond those presented by most prior general game systems [42]. Ludii is capable of modelling the full range of playable GDL games, as well as stacking games, boardless games, and games with hidden information. This, combined with high efficiency compared to other general systems [38], makes Ludii the ideal system for investigating the new game concepts-based research directions discussed in this paper.

C. Related Work
In the context of game AI research, prior work on feature extraction has been predominantly focused on video games. This includes more general frameworks such as the General Video Game AI (GVGAI) system [43], [44], but also specific video games such as Angry Birds [45] and Starcraft [46]. These papers used their extracted features to predict the performance of different agents on unknown games, creating a portfolio or ensemble agent that combines the strengths of multiple AI techniques.
Despite the demonstrated advantages of this approach, little work has been done on feature extraction for general board games. Banerjee and Stone [47] proposed a reinforcement learning game player interacting with the GGP-base system, which can transfer knowledge learned in one game to expedite learning in other games. This work is based on valuefunction transfer [48] where general features are extracted from the state space of a previous game and matched with the different state space of a new game. This work showed good performance for low-level features on small games, but only for a limited set of specific types of source-target pairs where appropriate state space mappings can be automatically detected based on GDL game descriptions [49].
Some of the best General Game Playing players based on GDL have shown the importance of heuristics and game features by using them to improve their performance during GGP competitions. ClunePlayer used heuristic evaluation functions to represent simplified games as abstract models, incorporating the most essential aspects of the original game to construct tailored heuristics [36]. CadiaPlayer used template matching to identify simple board game features, such as square tiling or specific piece types [35]. Each of these agents won the International General Game Competition [50], in 2005 for ClunePlayer and 2007, 2008, and 2012 for CadiaPlayer.

III. LUDII
Ludii 3 uses a class grammar approach [51] to provide a direct link between the keywords in its game descriptions and the underlying Java code that implements them. The core of Ludii is a ludeme library, consisting of several classes, each implementing a specific ludeme. Ludemes are used to define both the form of the game (rules and equipment) and its function (legal moves and outcomes for the end state).
Each game description is composed of three different sections which define the relevant information about the players (number, facing direction, etc.), the equipment (board, pieces, etc.), and the rules of the game. The rules of the game can also be decomposed into four specific sub-sections: • Meta-rules applied to each state (e.g. no repetition). • Starting rules defining the initial state. • Playing rules defining the legal moves for a state s. • Ending rules defining the conditions under which the game's outcome is determined. An important benefit of this representation is that it allows each game description to be expressed in a compact and human-understandable manner by hiding unnecessary implementation details [52]. Figure 1 shows Ludii game descriptions for the board games Amazons 4 and Havannah, 5 alongside the graphical interfaces of playouts run on these games.
Moves in Ludii are represented using an atomic model. At each state s, the ludemes describing the playing rules are evaluated and return a list of k legal moves M: m 1 , . . . , m i , . . . , m k . In Ludii, the transition between two successive states s i and s i+1 is possible thanks to a sequence of atomic actions A i applied on s i . Such a sequence is modelled as a move m: a 1 , . . . , a i , . . . , a n with n the number of actions in A i . Thanks to this representation, it is possible to associate with each move m the concepts triggered by the list of actions defining m. Similarly, concepts can be associated with any state s, by computing the concepts involved at s.

IV. GAME CONCEPTS
A concept is an abstract representation that can be shared between different objects or ideas highlighting common points. Previous work (see Section II-C)) commonly uses the term "game feature" to designate a high-level aspect of games. However, in a board game context but also for the more general purpose of this paper, we are going to use the term "game concept" due to the existing use of the term "feature" by previous work on state-action features for board games [53].
Every game concept in Ludii is defined by its name, its category, its data type (numerical or binary) and its computation type. Each concept's name is selected to be as close as possible to terms used by human players or game designers. Version 1.2.0 of Ludii, used in this paper, currently implements 428 distinct game concepts. To organise these concepts, we propose a taxonomy 6 inspired by the Core Subject Taxonomy for Mathematical Sciences Education outlined by the Mathematical Association of America [54].

A. Categories
The seven main concept categories are: • Implementation: Concepts describing game implementation details. Thanks to this taxonomy, it is possible to focus only on a specific subset of categories depending on the specific application or research field. For example, many game-playing applications would have no use for the visual category, while explainable AI research will likely disregard the implementation category.

B. Data Type
A game concept can be numerical or binary. Binary concepts are used to show the existence of concepts in games, while numerical concepts are used to quantify them.
A binary game concept is activated if a specific ludeme, or a combination of ludemes, is used in the game's description. As an example, the concept STOCHASTIC describes games involving chance elements. It can be activated by multiple ludemes in isolation, such as rolling dice (ROLL) or the use of any random value (VALUE RANDOM 1 5). Contrary to this, the concept HOP CAPTURE will be triggered if the game involves a (MOVE HOP ...) ludeme and a capturing effect within it, such as the ludeme (REMOVE ...).
Rather than being activated or not, numerical game concepts are instead associated with a value. This can be an integer, such as the number of players (NUM PLAYERS) or the number of playable sites (NUM PLAYABLE SITES), or a float, such as the average number of possible directions per site (NUM DIRECTIONS). Some numerical concepts also correspond to the frequency of binary concepts, such as the average number of times a specific terminal state is reached, e.g., in Havannah, the frequency of winning with a loop (LOOP END) compare to connected regions (CONNECTION END), or the average number of times a specific move type was made, e.g. In Amazons, the frequencies of the concepts SLIDE or SHOOT.

C. Computation
Within the Ludii software, game concepts can be obtained in two different ways. One is done near-instantaneously during game compilation (compilation concepts), the other requires running playouts (playout concepts). This distinction is important depending on the intended application. For example, tasks that have to be responsive cannot use the concepts that require playouts, as these take significantly longer to compute.
Compilation concepts are based only on the ludemes used to describe static properties of the game, such as the dimensions of the game board. During the compilation process of Ludii games [51], the existence of specific ludemes or combinations of ludemes trigger each of these concepts. Binary concepts are simply activated by the existence of ludemes while numerical concepts instead have their values set, such as the number of component types (NUM COMPONENT TYPES).
Each atomic action in Ludii can return the concepts triggered by their application to a game state, consequently, game concepts can be associated with each move played instantaneously, due to the atomic-action representation of a move. However, at a higher level such as the game, playout concepts require more time to be computed. All concepts relating to the frequency of specific binary concepts are based on playouts. Each playout corresponds to a sequence of moves called a trial τ : m 1 , . . . , m i , . . . , m ter with m ter the last move played reaching the terminal state s ter . Thanks to the association of each move to a set of binary concepts, each trial τ can compute the frequency of the concepts involved. By running many playouts and consequently obtaining many trials for a single game, the values of the frequency game concepts can be computed by averaging the frequency of the concepts in each trial. Similarly, all the concepts belonging to the Metrics category, such as GAME LENGTH or BRANCHING FACTOR, are also computed using these playouts. For all playout concepts, it is important to note that their values are dependent on the playout type, which can be obtained randomly or with different game-playing agents. Table I shows the values for a subset of concepts on  Figure 1, the concepts are shown at ludii.games/concepts.php?gameId=52 and ludii.games/concepts.php?gameId=372, respectively. We can observe that for Amazons the frequencies of the concepts SLIDE and SHOOT are both 50%, while for Havannah the frequencies of the concepts CONNECTIONEND and LOOPEND are 27% and 73%, respectively.
V. GGP RESEARCH DIRECTIONS Having now described the different game concept categories and data types, as well as how they are computed, we turn to the different possible applications and research directions that can utilise them.

A. Agent Selection
Hyper-heuristic approaches aim to select the best agent, heuristic or strategy for a given task from a pre-defined set of choices [55]. Such approaches, especially for game AI research, typically involve identifying features between games that give an indication of how these different choices will perform [56], [57]. Our proposed game concepts may provide such features, if a correlation between the values for certain concepts and the performance of different agents can be identified.
Although not yet proven, it is highly likely that the existence of certain concepts or concept values would affect the abilities of different game-playing agents. A larger board and more pieces would typically indicate a greater branching factor, which affects the performance of certain AI techniques more than others. Likewise, agents that require full playouts to compare different moves (e.g. Monte Carlo tree search) may perform worse on games that take longer to complete, compared to agents that use defined state evaluation heuristics (e.g. Minimax).
After determining the performance of a set of agents for a given set of games, we can attempt to train models to predict the best agent for a game based on its concepts. If successful, this can provide a portfolio agent which can predict the best agent on a new game using its concept values. A similar approach has been previously presented in [58], which uses the ludemes within the games -rather than their conceptsto predict the performance of different general-game-playing heuristics. It is likely that the game concepts provide additional information which can help give more accurate predictions, thus leading to better portfolio agent performance.

B. Transfer Learning
Transfer learning research in games, and more generally reinforcement learning [59]- [61], focuses on transferring learned objects such as heuristics, value functions, policies, etc. from one or more source domains, to one or more target domains. This may involve transferring trained weights and/or representations -which may be explicit features [53], or learned representations such as those in hidden layers of deep neural networks.
Transfer of heuristics or value functions, which are functions of game states, between any pair of games requires that those games have identical state spaces, or compatible state representations such that we can create mappings between their state spaces. Similarly, transfer of policies, which are functions of game states and actions, also requires identical action spaces or compatible action representations that enable mappings between action spaces. There has been some research towards transferring value functions in GGP based on general features of the shape of a lookahead search tree [47], as well as value function transfer in a limited set of specific types of sourcetarget pairs where appropriate state space mappings can be automatically detected based on GDL game descriptions [49].
Ludii's object-oriented, game-independent state and action representations [52] has already been demonstrated to facilitate straightforward mappings between state and action spaces of different games, allowing for effective transfer of deep neural networks with both policy and value heads between many different pairs of games [62]. However, even when such mappings are possible, transfer learning is sometimes still ineffective (or even detrimental, a phenomenon known as negative transfer [63]) due to significant differences in the goals or optimal strategies between games. For example, the state and action representations of Hex and Misère Hex -which is Hex with an inverted win condition -are very similar, but neither policy nor value functions work well when transferred directly (although learned features, or hidden representations, can still be useful).
Game concepts may be viewed as "summarising" a problem or task description for a game, and hence also used to analyse in which aspects any pair of games is similar or different. This can be used to predict whether or not transfer may be successful, or more specifically to predict which aspectsonly policies, or only value functions, or only features/learned representations, etc. -may successfully transfer [64], [65].

C. Explainability
Explainable AI (XAI) is an emerging field in Artificial Intelligence that has become increasingly important in recent years [66]. XAI attempts to bring transparency to how AI agents perform, by providing human-understandable explanations for the decisions they make. For many AI agents, the strategies played are generally obscure and difficult to decipher. For example, Deep Reinforcement Learning based agents such as AlphaGo [67] outperforming the best Go players, are playing strategies that are still analysed by Go experts [68] years after its victory on Lee Sedol [69]. It can be similarly difficult to understand the strategies followed by agents that do not explicitly use understandable domain knowledge, such as general game agents or puzzle solvers.
Correlations between concepts associated with played moves, and concepts associated with the states in which moves are played, may provide human-understandable insights -expressed in "game terms" -of agents' strategies. For example, identifying specific concepts triggered by moves played only from states always corresponding to the same set of concepts can explain the strategy followed by an AI agent.
For General Game agents, the good or bad performance of AI techniques/agents on games could be explained by the concepts shared between games. This explanation could be provided at a game agent level but also for the different parameters or guiding search techniques to some subsets of games but not others. For example, agents based on MCTS techniques or an Alpha-Beta search without any pre-defined knowledge, are generally achieving different performances based on the rules of the games requiring more or less time to be computing at each state (e.g. Chess-like games are generally in favour of Alpha-Beta agents because of the checkmate rule).

D. Move Evaluation
Concepts associated with moves can be used as a means of classifying them based on high-level categories, such as distinguishing capture moves from moves that do not capture. This may provide basic evaluations of the usefulness of different moves, and hence used to guide search algorithms. For example, such concepts could be used for move ordering in minimax-based agents, or to bias move selection in playouts using techniques such as FAST [32]. Such guidance will typically be fairly basic due to the high-level nature of concepts, but also highly efficient because the concepts can be extracted directly from moves generated by Ludii. This process does not require any additional computation, as would be required for features of a successor state.

E. Game Generation
Board game generation through the use of an evolutionary algorithm has been shown to provide interesting new games [40], [70]. One improvement to this work might be to generate games that result in some particular combination of game concepts that a specific player might find appealing. Game concepts could also be an important aspect of fitness functions for evaluating generated games, particularly for search-based approaches in the same vein as previous work on puzzle generation [71]. Concepts can also help to direct the selection of specific ludemes within a generated games description, by favouring ludemes that are associated with desirable concepts.
The use of game concepts to generate games can also provide new challenges. For example, the generation of games that use some novel combination of concepts that have not been previously created, perhaps leading to new and exciting gameplay properties. Similarly, the simplification of games by removing a particular concept from its rules could provide games that help teach specific rules to beginners. It has been shown in prior work [72] that agents learn faster when independently trained on separate simpler versions of a large game. This is useful in cases where training time is limited, for example in AI competitions [42], [50].

F. Game Reconstruction
As described by the Digital Ludeme Project (DLP) [73], there are a large number of historical games for which the rules are unknown or incomplete. A process similar to that of game generation could be used to reconstruct the rules of an incomplete game. By looking at the concepts used in known nearby games, we can use these to predict which concepts our incomplete game might have. In essence, for each game concept, we can calculate a probability that it was included in an incomplete game, based on the concepts present in other similar games.

G. Game Recommender Systems
Concepts can also be used to recommend new games to human players based on their preferences. If a player favours games with certain concepts, such as asymmetric games with hidden information, but dislike others, such as games with capture moves, then we can find and suggest other games in Ludii that also contain these desired combinations. Our concepts could also be combined with other board game recommendation systems, such as those developed for the online board game geek database [74]- [77], to create an even more extensive system.
Game concepts could also be used as searching criteria to find appropriate benchmark games for AI agents. Many AI techniques are not suitable or applicable to certain games types, such as algorithms dedicated to deterministic games versus agents dedicated to stochastic games with hidden information. This applicability problem can be more specific, mainly when the techniques are based on some specific heuristics or functions such as knowledge designed for some specific game goals. The search for good benchmarks can be timeconsuming and would be much easier with the use of game concepts showing the properties of games in a recommender system. Identifying smaller subsets of games that give near equal information about an agent compared to the full set has been previously investigated for the GVGAI framework [78]. By comparing the concepts present within the Ludii game corpus, we can achieve a similar means of creating a smaller game subset that still provides maximal concept coverage.

VI. CONCLUSION
This paper refines the notion of game concepts to General Board Game Playing. Such concepts are defined using common terms which are understood by game players and designers. These concepts can be identified automatically for games in Ludii thanks to the ludeme representation, and are associated with any level of game abstraction. Game concepts provide several interesting research possibilities, including the creation of a portfolio agent via agent or heuristic selection, transfer learning between games, explainability of AI techniques and strategies, Game Generation, Game Reconstruction and Game Recommendation.
Future work over the next few years will primarily involve identifying more game concepts and implementing their detection within the Ludii system, as well as investigating the research directions proposed in this paper. In the long term, the ludeme philosophy used to represent games could be extended to other domains, such as protein folding, physics simulations or chemical reactions, by adapting the notion of ludemes to conceptual units of each of these topics. Consequently, concepts specific to these fields could be identified and detected by similar techniques, providing a human understandable explanation for any technique applied in these fields.