We would like to acknowledge the support provided by the National Natural Science Foundation of China (No. 62207025), the Humanities and Social Sciences Research Project from the Ministry of Education of China (No. 22YJC190017), and the Fundamental Research Funds for the Central Universities to Yafeng Pan.

The study was conducted at Florida Atlantic University (FAU) and was approved by the FAU Institutional Review Board (IRB).
1. Using Homer3 software (Table of Materials) to perform the pre-processing of the fNIRS hyperscanning data
NOTE: Homer3 is a MATLAB application that analyzes fNIRS data to obtain estimates and maps of brain activation29. Homer3 can be downloaded and installed from the following link (https://openfnirs.org/software/homer/).
<ol>
	<li>Open MATLAB, and navigate to the folder where the raw .nirs files are saved. Select and open the folder.</li>
	<li>Type Homer3 into the command window of MATLAB to launch the Homer3 GUI. Homer3. will detect the .nirs files and ask to convert to .snirf format (a universal file format for storing and sharing NIRS data independently of any specific application-specific file format such as MATLAB) to proceed with the pre-processing of the data.</li>
	<li>After importing the .nirs files into .snirf format in Homer3, click on the Tools option in the Homer3 GUI, and select Edit Processing Stream.</li>
	<li>In the ProcStreamEdit GUI, select the pre-processing steps from the Registry Function column to the Current Processing Stream column by clicking on Add. The included pre-processing steps are as follows:
	<ol>
		<li>Use hmrR_intensity2OD to convert the intensity data to optical density.</li>
		<li>Use hmrR_MotionCorrectWavelet to correct motion artifacts using the appropriate filtering function.</li>
		<li>Use hmrR_OD2conc to convert the OD data to concentration.</li>
		<li>Use hmR_BlockAvg to calculate the Block Average on concentration Data. 
		NOTE: The selection of the pre-processing steps may vary depending on the type of dataset.</li>
	</ol>
	</li>
	<li>To save the current processing stream, click on the Save option, and then exit the ProcStreamEdit GUI.</li>
	<li>To run the pre-processing stream in the main Homer3 GUI, click on the RUN option. After Homer3 finishes running the selected processing stream, it will save the pre-processed time series for each participant in a .mat file format containing Hbo, Hbr, and Hbt for all the channels and events. A folder named homer output will be created by Homer3 in the currently selected folder to store these files.</li>
	<li>A folder named derivatives will be created by Homer3 in the selected folder to store these files. Select the homer folder located in derivatives folder. Choose the .mat file for each brain and export Hbo, Hbr, Hbt. 
	NOTE:&#160;The name of the output folder created by Homer3 is dependent on the Homer3 version.</li>
</ol>
2. Getting started with the LeaderFollowerByPhase toolbox
<ol>
	<li>To analyze the type of interaction that occurs in a hyperscanning recording, use the LeaderFollowerByPhase toolbox, as described in the process shown in Figure 3. In MATLAB, select the .mat files for each brain, and load the Hbo (or Hbr) data of the specific channel and specific event into a one-dimension vector as signal1 and signal2.</li>
	<li>In the MATLAB command line, define the parameters
	<ol>
		<li>lowFreq, highFreq:&#160;Type lowFreq = [low FOI], and highFreq = [high FOI]. The default values are lowFreq = 0.01 Hz, highFreq = 1 Hz. 
		NOTE:&#160;The parameters of the functions lowFreq and highFreq define the frequency of interest (FOI) range. WTC calculates the coherence across the two brains at each time point and frequency. The coherence values are typically averaged within a particular FOI.</li>
		<li>Define the parameter phaseRange; type phaseRange = [range in deg]. 
		NOTE: The default value is phaseRange = 90&#176;. The phase ranges between 0&#176; to 360&#176; due to the circular modulo nature of the phase. The phase ranges are divided according to a range that surrounds four points. In the presented toolbox, a new approach for classifying asymmetric interactions is presented (Figure 4) by examining the coupling directionality using the phase angle values according to the ranges corresponding to lagged synchronization with Signal 1 leading (a range surrounding &#8722;90&#176;) or Signal 2 leading (a range surrounding 90&#176;), Signal 1, Signal 2 in-phase synchronization (a range surrounding 0), and Signal 1, Signal 2 anti-phase synchronization (a range surrounding +180&#176; or &#8722;180&#176;).</li>
		<li>Define the Threshold parameter. Type threshold = [threshold rsq val]. The default value is Threshold = 0. 
		NOTE: The toolbox allows for the specification of a threshold coherence value by specifying the threshold parameter. This allows the researcher to select time points with a specified minimum coherence value. Consequently, only time points with coherence values that are higher than the specified threshold are taken into consideration.</li>
	</ol>
	</li>
	<li>Download the LeaderFollowerByPhase toolbox from the following link (https://www.ariel.ac.il/wp/sns/download/ or https://github.com/Minisharmaa/Leader-Follower-By-Phase).</li>
	<li>Execute the MATLAB function LeaderFollowerByPhase by entering the command cohervalues = LeaderFollowerByPhase(signal1, signal2, lowFreq, highFreq, phaseRange, threshold) into the command line. 
	NOTE: The coherence and phase calculations are performed using the WTC and XWT functions in MATLAB, respectively30.</li>
	<li>Examine the in-phase, Signal 1 leading, Signal 2 leading, and anti-phase synchronization values:
	<ol>
		<li>Inspect the plots in MATLAB. The toolbox generates one figure with four plots.
		<ol>
			<li>Coherence by type of interaction: Inspect the box chart plot on the top-left part of the figure, which shows the R-Squared (Rsq) according to each type of interaction (in-phase, Signal 1 leading, Signal 2 leading, anti-phase). 
			NOTE: For a detailed description of the MATLAB box chart built-in function, see the following link (https://www.mathworks.com/help/matlab/ref/boxchart.html).</li>
			<li>Central indices by type of interaction: Inspect the bar graph on the top-right part of the output figure, which displays the max mean and median according to each type of interaction (in-phase, Signal 1 leading, Signal 2 leading, anti-phase). 
			NOTE: For a detailed description of the MATLAB bar built-in function, see the following link (https://www.mathworks.com/help/matlab/ref/bar.html).</li>
			<li>Coherence over time: Inspect the scatterplot at the bottom-left part of the output figure, which displays the values of coherence and the types of interaction over time. The colored dots represent different types of interaction (black dots represent in-phase synchronization, dark grey dots represent Signal 1 leading, light grey dots represent Signal 2 leading, and purple dots represent anti-phase synchronization). 
			NOTE: The figure shows the dynamics of the interaction: the exchange between the four types of interaction throughout the full-time series. For a detailed description of the MATLAB scatter function, see the following link (https://www.mathworks.com/help/matlab/ref/scatter.html).</li>
			<li>Time percentage: Inspect the pie chart at the bottom right part of the output figure, which displays the division of time according to the different types of interactions. 
			NOTE: For a detailed description of the MATLAB pie function, see the following link (https://www.mathworks.com/help/matlab/ref/pie.html).</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Inspect the output table with the statistic values (i.e., mean, max, median, and standard deviation) for each type of interaction (in-phase synchronization, Signal 1 leading, Signal 2 leading, anti-phase synchronization). The table also presents the percentage of time for which each type of interaction occurred. Each type of interaction appears in a different column.</li>
	<li>Examine the output value in the extracted spreadsheet file (i.e., datatable.xlsx located in the current folder).</li>
</ol>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/65347/65347fig03.jpg" /> 
Figure 3: Overview of the workflow. (A) Mother-child dyads engaged in free play while&#160;hyperscanning fNIRSdata were collected. (B)&#160;Illustration of a mother-child time series.(C) Pre-processing of the time series using Homer3.(D,E) The use of a toolbox to examine different types of interactions, such as in-phase synchronization, anti-phase synchronization, and lagged synchronization. <a href="https://www.jove.com/files/ftp_upload/65347/65347fig03large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/65347/65347fig04.jpg" /> 
Figure 4: Classification of four different types of interactions based on phase. This represents the phase difference of the two neural time series in a 360&#176; modulo. The phase difference can be thought of as a time lag between two values and is measured in degrees and radians or fractions of the wavelength. Here, the 360&#176; modulo is divided into four different ranges depicting four different phases of interaction: (A) Signal 1 leading (a range around 90&#176;, between 45&#176; to 135&#176;), (B) anti-phase synchronization between Signal 1 and Signal 2 (a range around 180&#176; or &#8722;180&#176;, between 135 to &#8722;135&#176;), (C) Signal 2 leading (between &#8722;135&#176; to &#8722;45&#176;), (D) in-phase synchronization (a range around 0, between &#8722;45&#176; to 45&#176;). This division is the default approach (45&#176; around each point); however, the toolbox allows one to configure a different division. While other configurations may not cover all 360&#176;, it may yield a more exact definition of each type of interaction. <a href="https://www.jove.com/files/ftp_upload/65347/65347fig04large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

Revolutionizing fNIRS Studies&amp;#58; A Novel Approach to Neural Coupling

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

One of the most common methods used in fNIRS studies is wavelet transform coherence (WTC), which is a measure of the cross-correlation of two time series as a function of frequency and time10. WTC calculates the coherence and phase lag between two time series using correlational analyses (Supplementary File 1). FNIRS hyperscanning studies have used WTC to estimate IBS in many domains of functioning, including action monitoring12, cooperative and competitive...

In recent years, there has been a shift in the types of studies conducted to understand the neural bases of social behavior1,2. Traditionally, studies in social neuroscience have focused on neural activation in one isolated brain during a socially relevant task. However, advances in neuroimaging technology now allow for the examination of neural activation in the brains of one or more individuals during social interaction as it occurs in &#34;real-life&#34; settings3. In &#34;real-life&#34; settings, individuals are able to move freely, and patterns of brain activation are likely to change as information is exchanged and social partners receive feedback from one another4.
Hyperscanning is a method that assesses this bidirectional information exchange by measuring the brain activity from two or more individuals simultaneously5. An emerging body of research has utilized functional near-infrared spectroscopy (fNIRS), a non-invasive neuroimaging technique that, in comparison to other neuroimaging techniques, is less susceptible to motion artifacts6. Hyperscanning via fNIRS allows for the assessment of inter-brain synchronization (IBS) in real-life settings while the interactive partners move freely and naturally. This is particularly relevant for work with infants and young children, who tend to be quite active. IBS has been reported to reflect mutual understanding between interactive partners, which serves as the foundation for effective social interaction and communication and mediates shared intentionality1,7,8.
Several methods are used to evaluate the IBS of two brains. Such methods include time series correlations, such as cross-correlation and the Pearson correlation coefficient9,10 (see a review by Scholkmann et al.10). Other methods involve evaluating the strength of coupling in the frequency domain. Such methods include phase-locking value (PLV) and phase coherence (see a review by Czeszumski et al.11). One of the most common methods in fNIRS studies uses wavelet transform coherence (WTC)-a measure of the cross-correlation of two time series as a function of frequency and time10.
WTC uses correlational analyses to calculate the coherence and phase lag between two time series in the time-frequency domain. FNIRS hyperscanning studies have used WTC to estimate IBS in many domains of functioning, including action monitoring12, cooperative and competitive behaviour5,13,14,15, imitation16, mother-infant problem solving17, and teaching-learning behavior18,19,20,21. Typically, in hyperscanning studies, cross-brain coherence, as measured by WTC, during an experimental task is compared to cross-brain coherence during a control task. These findings are usually presented with a WTC &#34;hot plot&#34;, which shows the coherence across the two brains at each time point and frequency (see Figure 1).
As suggested by Czesumaski et al.11, WTC has become the standard analytical approach for analyzing fNIRS hyperscanning. WTC analysis is a flexible, &#34;tool-agnostic&#34; method for data visualization and interpretation22. The coherence coefficient heatmap, which provides a narrative form of analysis allowing for the easy identification of periods of synchronous or asynchronous behavior as well as the intensity of brain activity during the completion of a task, is the main advantage of WTC and makes it a strong tool for applied research22. WTC has an advantage over correlation techniques. Correlations are sensitive to the hemodynamic response function&#39;s (HRF) shape, which is thought to differ between individuals (particularly in terms of age) and among different brain areas. In contrast, WTC is unaffected by interregional changes in the (HRF)23. Researchers have used the wavelet approach to study fMRI time series. Zhang et al.24 compared the commonly used functional connectivity metrics, including the Pearson correlation, partial correlation, mutual information, and wavelet coherence transformation (WTC). They carried out classification experiments using large-scale functional connectivity patterns derived from resting-state fMRI data and natural-stimulus fMRI data of video viewing. Their findings indicated that WTC performed best in classification (specificity, sensitivity, and accuracy), implying that WTC is a preferable functional connectivity metric for studying functional brain networks, at least in classification applications24.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/65347/65347fig01.jpg" /> 
Figure 1: Wavelet transform coherence (WTC). WTC shows the coherence and phase angle between two time series as a function of both time (x-axis) and frequency (y-axis). The coherence increase is depicted by the red color in the graph, and the small arrows in the graph show the phase angle of the two time series. The rightward-pointing arrow represents in-phase synchronization; the downward-pointing and upward-pointing arrows represent lagged synchronization; and the leftward-pointing arrow represents anti-phase synchronization30. This figure was adapted from Pan et al.19. <a href="https://www.jove.com/files/ftp_upload/65347/65347fig01large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Recently, Hamilton25 articulated several limitations to the interpretation of cross-brain coherence data in fNIRS hyperscanning studies. One of Hamilton&#39;s primary concerns was that coherence measures (e.g., WTC) only report effects as symmetrical (i.e., two brains are correlated, showing the same pattern of change). However, many social interactions are asymmetric (e.g., information flow between a speaker and a listener) in that two participants may play different roles, and it is not clear that WTC can capture this information. Here, this concern is addressed by a new framework that allows for a straightforward interpretation of the cross-wavelet power by using the cross-wavelet phase&#160;to detect directionality. This framework will also allow examination of how the dynamics of interactions develop and change throughout a task.
While WTC and correlation methods assess functional connectivity, other methods assess effective connectivity, attempting to extract the causal influences of one neural element over another. Transfer entropy is a measure from the field of information theory that describes the transfer between jointly dependent processes26. Another related method is Granger causality analysis (GCA), which has been described as equivalent to transfer entropy26.
In the existing literature of fNIRS hyperscanning studies, Granger causality analysis (GCA) has been widely used to estimate the coupling directionality between fNIRS time series data obtained during a variety of different tasks, such as cooperation5, teaching19, and imitation16. GCA employs vector autoregressive models to assess the directionality of coupling between time series in brain data. Granger causality is based on prediction and precedence: &#34;a variable X is said to &#39;G-cause&#39; variable Y if the past of X contains the information that helps to predict the future of Y over and above information already in the past of Y&#34;27. Accordingly, the G-causality is analyzed in two directions: 1) from subject A to subject B and 2) from subject B to subject A.
While GCA analysis serves as a complementary analysis aimed at determining whether a high coherence value obtained using a WTC function reflects IBS or lagged synchronization (one signal leading the other), it does not allow for the determination of whether anti-phase synchronization has occurred. In traditional neuroimaging studies, in which only one participant is scanned (i.e., the &#34;single-brain&#34; approach), an anti-phase pattern means that the activity in one brain region is increased while the activity in the other brain region is decreased28. In the hyperscanning literature, the presence of anti-phase synchronization may suggest that neural activation is increased in one subject, and at the same time, neural activation is decreased for the other subject. Therefore, there is a need to provide a comprehensive model that can detect the directionality. More specifically, this model will be able to detect anti-phase synchronization (in which the direction of activity in one individual is opposite to that of their partner) in addition to in-phase synchronization and lagged synchronization.
In an attempt to address the concern that WTC shows only symmetrical effects, where both brains show the same pattern of change25, a new approach to identify the type of interaction by examining the phase of synchronization (i.e., in-phase, lagged, or anti-phase) is presented (see Figure 2). To this end, a toolbox using the WTC method to classify the different types of interactions was developed. The types of interactions are classified by using relative phase data from cross-wavelet transform analysis.
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/65347/65347fig02.jpg" /> 
Figure 2: Illustration of the different phase relationships of simple sine waves. (A) When the two signals, Signal 1 (blue lines) and Signal 2&#160;(orange lines), reach their respective maximum, minimum, and zero values at the same time point, they are said to be showing in-phase synchronization32. (B) When one signal reaches its maximum value and the other signal reaches zero value at the same time point, they are said to be showing lagged synchronization (one is leading by 90&#176;)32,33,34. (C) When two time series shift in opposite directions, meaning one signal reaches the maximum and the other reaches the minimum value at the same time point, this is referred to as anti-phase synchronization28. (D-P) In all other phase relationships between two time series, one signal is leading the other. In all positive phases, Signal 2&#160;is leading Signal 1 (e.g., panels E, F, M, and N), whereas in all negative phases, Signal 1 is leading Signal 2 (e.g., panels D, G, H, O, and P). Notably, when the absolute value of the phase is higher, it becomes more distinctive which time series is leading the other (e.g., the leadership is more distinctive in panel J than in panel I, and in panel K, the leadership is more distinctive than in panel L). <a href="https://www.jove.com/files/ftp_upload/65347/65347fig02large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>NIRScout&#160;&#160;</td>
			<td>NIRx Medical Technologies, LLC</td>
			<td>n.a.</td>
			<td>8 sources, 8 detectors</td>
		</tr>
		<tr>
			<td>MATLAB</td>
			<td>The Mathworks, Inc.</td>
			<td>Matlab 2022a</td>
			<td>In this protocol, several toolboxes and buit in MATLAB functions were used: HOMER3 toolbox was used to convert Intensity to OD, to remove motion artifacts through its function hmrMotionCorrectWavelet with default parameters and to convert OD to Conc. Wavelet Toolbox was used to compute WTC.</td>
		</tr>
	</tbody>
</table>

new framework for understanding cross-brain coherence in functional near-infrared spectroscopy (fnirs) hyperscanning studies

Despite the growing body of functional near-infrared spectroscopy (fNIRS) hyperscanning studies, the assessment of coupling between two neural signals using wavelet transform coherence (WTC) seems to ignore the directionality of the interaction. The field is currently lacking a framework that allows researchers to determine whether a high coherence value obtained using a WTC function reflects in-phase synchronization (i.e., neural activation is seen in both members of the dyad at the same time), lagged synchronization (i.e., neural activation is seen in one member of the dyad prior to the other member), or anti-phase synchronization (i.e., neural activation is increased in one member of the dyad and decreased in the other). To address this need, a complementary and more sensitive approach for analyzing the phase coherence of two neural signals is proposed in this work. The toolbox allows investigators to estimate the coupling directionality by classifying the phase angle values obtained using traditional WTC into in-phase synchronization, lagged synchronization, and anti-phase synchronization. The toolbox also allows researchers to assess how the dynamics of interactions develop and change throughout the task. Using this novel WTC approach and the toolbox will advance our understanding of complex social interactions through their uses in fNIRS hyperscanning studies.

Author Spotlight: Unlocking New Insights in fNIRS Studies -  A Novel Framework for Inter-Brain Synchrony Analysis 

New Framework for Understanding Cross-Brain Coherence in Functional Near-Infrared Spectroscopy (fNIRS) Hyperscanning Studies

Many fNIRS studies have focused on coherence to estimate interbrain synchrony, neglecting phase lag information in the WBC hot plot. Here, a more sensitive approach has been presented that estimates coupling directionality, classifying phase angle value as in-phase synchronization, lag phase synchronization, and anti-phase synchronization. Reanalyzing the previous findings using a new proposed framework offers a comprehensive understanding of the nature of the synchronization between participants.Differentiating in-phase synchronization and anti-phase synchronization provides a new level of clarity, enabling the precise interpretation of previous findings. This framework can be applied to various scenarios, such as studying the role of interpersonal synchronization in social behavior, communication, and decision making. Emphasizing the application of craft theory in conjunction with the developed phase toolbox for hyperscanning apneas provides a deeper understanding of the various type of directionalities observed in interaction extending beyond mere coherence.This approach enables the exploration of the information flow from one brain to another brain in hyperscanning setting.

This section demonstrates the types of analyses that can be carried out with the toolbox (which can be downloaded at https://www.ariel.ac.il/wp/sns/download/ or https://github.com/Minisharmaa/Leader-Follower-By-Phase.). For these analyses, fNIRS data collected with a small sample of infant-parent dyads were utilized. Six pairs of mother-infant dyads were tested using a validated behavioral task, the free-play task31, which is as close to a real-life infant-mother interaction as possible. Prior to ...

Watch this Scientific Journal Video about Unlocking New Insights in fNIRS Studies -  A Novel Framework for Inter-Brain Synchrony Analysis at JoVE.com

Wavelet transform coherence (WTC) is a common methodology for assessing the coupling between signals that is used in functional near-infrared spectroscopy (fNIRS) hyperscanning studies. A toolbox for assessing the directionality of the signal interaction is presented in this work.

Despite the growing body of functional near-infrared spectroscopy (fNIRS) hyperscanning studies, the assessment of coupling between two neural signals ...

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1.7K Views.  Ariel University. Many fNIRS studies have focused on coherence to estimate interbrain synchrony, neglecting phase lag information in the WBC hot plot. Here, a more sensitive approach has been presented that estimates coupling directionality, classifying phase angle value as in-phase synchronization, lag phase synchronization, and anti-phase synchronization. Reanalyzing the previous findings using a new proposed framework offers a comprehensive understanding of the nature of the synchronization between particip...

Video: Author Spotlight: Unlocking New Insights in fNIRS Studies -  A Novel Framework for Inter-Brain Synchrony Analysis 

Using Homer3 Software to Perform the Pre-Processing of the fNIRS Hyperscanning Data

To begin open MATLAB, then navigate to the folder where the raw and irs files are saved. Select and open the folder. Type Homer3 into the command window of MATLAB to launch the Homer3 GUI.Homer3 will detect the nirs files and ask to convert them to snirf format to proceed with the pre-processing of the data. After converting the files, click on the Tools option and select Edit Processing Stream. In the process stream edit GUI select the pre-processing steps from the registry function column to the current processing stream column by clicking on Add.Click on the Save option to save the current processing stream and then exit the process stream edit GUI. Click on the RUN option to run the pre-processing stream in the main Homer3 GUI. After Homer3 finishes running the selected processing stream, it will save the pre-processed time series for each participant in a mat file format containing HBO, HBR, and HBT for all the channels and events.A folder named derivatives will be created by Homer3 in the selected folder to store these files. Select the homer folder located in the derivatives folder. Choose the mat file for each brain, and export HBO, HBR, HBT.

Getting Started with the LeaderFollowerByPhase Toolbox

Open the leader follower by phase"toolbox to analyze the type of interaction that occurs in a hyper scanning recording. In MATLAB, select the mat files for each brain and load the HBO or HBR data of the specific channel and event into a one dimension vector as signal one and signal two. In the MATLAB command line, define the parameters of the functions low frequency and high frequency.The default value of low frequency is 0.01 hertz, and high frequency is one hertz. Then define the parameter for phase range, followed by the threshold. The default value of the threshold is zero.Execute the MATLAB function LeaderFollowerByPhase"by entering the command shown on the screen. The toolbox generates one figure with four plots. In MATLAB, inspect the box chart plot, which shows the R squared values for each type of interaction category in phase signal one, leading signal two leading, and antiphase.Then inspect the bar graph on the output figure, which displays the maximum values, mean, and median for all interaction types. The scatterplot displays the values of coherence and the types of interaction over time. The division of time according to different types of interactions.Next, inspect the output table with the statistic values for each type of interaction. The table also presents the percentage of time for which each type of interaction occurred. Finally, examine the output value in the extracted spreadsheet file.The classification analysis was repeated with a threshold of 0.5 on dyad A to explore the influence of changing the minimum threshold values on the classification of the types of interaction within a dyad. The result shows that when a threshold of 0.5 was used, the distribution of the different types of relative phase relationships changed. The percentage of antiphase synchronization increased from 35%to 59%and the percentage of endphase synchronization decreased from 26%to 8%This suggests that antiphase synchronization may be the type of interaction that is more representative of this dyad.