Abstract
This article presents a new tool that provides a methodological context to observe and analyze, both qualitatively and quantitatively, manifestations of abductive reasoning in empirical research. Abduction is a form of a complex reasoning carried out to make sense of surprising or ambiguous phenomena or fill the gaps in our beliefs. Despite the ubiquity of abduction in professional and everyday problem-solving processes, little empirical research was dedicated to investigate this type of reasoning, and most of them focused on products of abduction—abductive hypotheses. Our instrument,
Aim of the Study
In this article, we describe a new methodological tool, called
Introduction
Abductive Reasoning
Abductive reasoning serves the purpose of making sense of surprising, ambiguous, or otherwise puzzling phenomena in order to fill the gaps in our beliefs, maintaining or restoring their coherence (Thagard, 2000; Thagard & Shelley, 1997). This type of reasoning is ubiquitous in both professional contexts such as scientific research, forensic investigation, clinical diagnose, and everyday ones such as natural language understanding, empathy, and theory of mind (Hobbs, 2006; Ottens et al., 1995; see, e.g., Magnani, 2009). Surprisingly enough, it is also quite mysterious. There is widespread agreement that the essence of abduction is captured by the schema proposed by Peirce (CP, 5.189): The surprising fact, C, is observed. But if A were true, C would be a matter of course. Hence, there is reason to suspect that A is true.
Another source worth referring to is also Tavory and Timmermans (2014). The authors’ interest in abduction is on a methodological level rather than an object level as they are concerned with abduction as a qualitative data analysis approach, not accounting for abductive reasoning per se. Nevertheless, their understanding of what abduction consists in is very much in line with ours—a concise witness to that is their “Synopsis of abductive analysis” (Tavory & Timmermans, 2014, pp. 131–132).
Known Measures of Abductive Reasoning
According to our experience, finding a task capable of evaluating abductive reasoning in empirical research is a challenge. An example of a method that enables a researcher to analyze the process of abductive reasoning in both quantitative and qualitative approaches was used by Oh (2008). In his research, empirical data referring to the process of learning were analyzed based on the framework provided by the abductive inquiry model. According to that model, abductive reasoning consists of four phases: ◦ Exploration ◦ Examination ◦ Selection ◦ Explanation
Oh investigated abductive inquiry as a method that could be used as a helping aid for teachers of earth science. Abductive method appeared to be an effective way to teach scientific reasoning in case of both older and younger students and promoted understanding of complicated phenomena. After analyzing the process of learning by abductive inquiry, Oh described what exactly had happened during each phase of the model. During the exploration phase, participants investigated earth scientific phenomena with provided data and transformed them into problems that could be explained abductively. The examination phase needed activation and an expansion of background knowledge to find rules for abductive inference and then some hypotheses were generated (thus, these two phases cover three first parts of the Vertue & Hague, 2008, model). Selection consisted of evaluating hypotheses empirically and/or theoretically and then choosing the most plausible ones. The final, exploration phase resulted in causal and narrative explanations using previously selected hypotheses.
A study referring to those two phases was conducted by Donelly et al. (1990). They used a measure designed to assess clinical problem-solving. It consisted of three tasks requiring the listing of possible diagnoses that should be tested, starting from the most to the least promising. The second part of the task required a description of the way of testing generated hypotheses. In this study, responses were judged by experts only in terms of their accuracy. Despite that limitation, it seems that further qualitative analyses of data could also be possible.
However, most measures of abductive reasoning seem to limit possible analyses of data to the quantitative approach and relate only to a single phase of the process. For instance, a task used by Mirza (2015) to assess the effects of abductive reasoning training referred only to the ability of generating hypotheses. A method was profiled to the expertise area of the participants (
Similarly, a task requiring a hypothesis to be generated was used by Kwon, Lee, Shin, and Jeong (2009) in the research aimed at investigating the learning-related changes in brain activation induced by the training of hypotheses generation skills. The authors assumed that the process of formulating hypotheses consists of six steps: ◦ Observing a situation ◦ Generating a causal question ◦ Analyzing the question ◦ Representing experienced phenomena ◦ Causing representation ◦ Constructing hypotheses
A training task was designed for academic students and required the generation of biological hypotheses (exemplary task question: “Why is the monkey covered with white fur?”). The evaluation system was limited to the final step of formulating hypotheses, that is, they were evaluated by counting the number of explanations included in each of them. This model differs substantially to the ones proposed by Vertue and Haig (2008) and Oh (2008).
A slightly different version of a method to evaluate the hypothesis generation ability, adjusted to abilities of primary school students, was used in a project carried out by Kwon et al. (2006). The task required generating hypotheses that could explain a swing situation relating to a simple pendulum motion.
Another method, a task not only to study generating hypotheses but also understanding them, was used by Lee (2012). The author assumed that hypothesis-understanding refers to the process when a reasoner accepts new hypotheses as causal explanations in their cognitive structure by way of temporal or logical order. It does not explore suitable explicans proposed by the subject as is done in the hypothesis-generating process (Kwon et al., 2009). However, this complex method did not appear to be useful in the case of the goals of our study.
A different type of the task, requiring not generating but testing hypotheses, was used in a study by Lawson and colleagues (2000). The task was a modified version of Lawson’s (1978) Classroom Test of Scientific Reasoning. It was assumed that a measure required abilities to identify and control characteristics, combinations, thinking in categories of probability, proportions, and correlations. Each item required making prediction or responding to a question and explaining how the answer was obtained. An exemplary test position could be to plan experiments to test a certain hypothesis and decide what result of the test would enable a rejection of the hypothesis. Only items with both a correct answer and an adequate explanation were judged to be correct.
All the tasks mentioned above required specific knowledge. However, abductive reasoning also might be measured by a task based on abstract content. Russo and Meloy (2002) evaluated hypothesis generation and hypothesis testing with the use of the Wason’s “2-4-6” task (Wason, 1960). In the standard version of the “2-4-6” task, subjects are instructed to discover the rule-generating sequences of three numbers by inventing number triples and then receive immediate feedback. The rule is “ascending numbers.” The roles of hypothesis generation and testing in the task were investigated by tracing the discovery process. It appeared that the process consisted of an initial phase of major hypothesis shifts to identify the essence of the correct rule, and a phase of smaller hypothesis refinements (Russo & Meloy, 2002).
It can be concluded that methods used in empirical research to assess abductive reasoning refer to a particular model of abduction or just to the hypothesis generating or testing phase. As a consequence, they are not usually associated with abductive reasoning by authors at all. The presented tasks require a rather specific knowledge and are set in a professional or abstract context. Variables assessed by the measures are usually limited to the correctness of the hypotheses (depending on the opinion of experts) and the broadness (understood as taking into account different aspects of the situation). The findings of the review indicated a major methodological loophole in the case of the process of abductive reasoning, especially in terms of the possible variability caused by individual differences between participants. In our research, we addressed this gap.
As we interpret abduction as a reasoning process consisting of two intertwined components, generation and evaluation of hypotheses, a complex task allowing both of them to be addressed was the one we needed. One important constraint was that the context of a task should be close to common, real-life problems. However, in spite of informal content and the structure of the task, the method should maintain requirements of standardization so as to enable further comparative analyses. Last but not least, the measure had to provide the possibility to conduct not only quantitative but also qualitative analyses as we aimed to investigate potential different ways of performing abductive problem-solving. To summarize, the task we needed should satisfy the following conditions: enable two phases to be measured: hypothesis generation and testing, offer the possibility to assess both process and products of abduction, be set in a context close to a real-life problem, be a standardized measure, and provide data that can be analyzed both qualitatively and quantitatively.
Further on, we present the final version of the task and summarize the process of constructing the measure regarding the accepted criteria of abductive reasoning.
Method: Find Out Task
To construct the measure of abductive reasoning that would meet our requirements, the following procedure was applied: choosing the most suitable model of abductive reasoning, defining constructional requirements of the task (conceptual and methodological), researching the relevant literature in search of existing methods, creating primary sketches of the task (more than 40 sketches were taken into consideration), developing a chosen project, a pilot study to test the preliminary project of the task, a constructional pilot study to develop the final project of the task, and an exploratory pilot study to analyze the data that the task enables a researcher to gather.
During the process of constructing the task, 12 versions of the method were created—most digital, a few in a paper-pencil format and one that can be conducted as spoken communication. Most of them were updated, and corrected versions of the previous ones and presenting all of them would exceed the limit allowed for this article. In case of any interest in alternative tools, we encourage the reader to contact the authors of the paper directly.
To facilitate the understanding of the task, we start by presenting the final and chosen version of the method. Only then major modifications that have been introduced to the tool are described.
General Procedure
The test should be conducted individually in laboratory settings with the use of computer equipment. The task is performed with the use of Google Docs—a text document and a chat window. The participant is seated in a separated room in front of a computer. The person conducting the experiment is in a room next door so as to provide the participant with more comfortable conditions of work but, at the same time, be able to help in case of any questions regarding the procedure or any technical difficulties. First, the subject is acquainted with a tool and encouraged to ask any questions. Then, the person conducting the experiment leaves the room and communication starts to be mediated via the chat window. Schematic representation of the task is presented below (Figure 1).

Find Out: a schematic representation.
The first message (appearing in the chat window) is sent to encourage the participant to start the task and show the proper way of communicating (online). The procedure consists of three stages, each with a time limit, which are presented one by one. The participant starts the next stage only after completing the former part of the task. Instructions are delivered gradually, for each stage separately so as to encourage the participant to perform only the task required at a certain stage. Each piece of instructional information or reply sent to the participant is highly standardized. The person conducting the experiment is equipped with a list of specially prepared information and copy it over to the major body of the task in a timely manner or when it is necessary. There is also a specially prepared FAQ document with issues and solutions that appeared in the pilot studies and may be problematic. The conductors of the experiment must complete training under the supervision of more experienced researchers before they can start conducting the test.
Research is carried out in Polish, but for the needs of the article, we have translated the instructions and sample performances of one participant to enable readers to have a better understanding of the task. Google Docs with translated instructions and sample performances for each stage of the task can be found online Supplementary Materials. A scheme of the procedure of the investigation is presented in Table 1.
The Procedure: A Schematic Representation.
Part 1: Warm-up
The first stage of the task requires formulating hypotheses. It takes 20 min and starts with sending a message encouraging the subject to start the task and suggests the proper way of communicating (only via chat). In the Online Supplementary Materials, you can see this particular stage (Find Out Stage 1).
At this moment of the procedure, the story is presented. The content of the story is highly inspired by a story from the On a winter’s night police stopped a car for a routine control. The driver turned out to be a famous celebrity (his identity is now known to the journalists). He had two bottles of mulled wine with him. He told the police that he had bought the wine 40 minutes before from the Christmas market held in the city centere—more specifically, from the stand of the manufacturer of regional specialties, including good-quality mulled wine. The man claimed that he had been going to visit his friends and he had bought the wine as a gift for them. However, it turned out that one of bottles was half empty and a distinct odor of mulled wine was present in the car. The driver admitted that he had succumbed to temptation and had drunk half of the bottle of the wine by himself. The police officers gave him a breathalyzer test and read its result. Subsequently, they had a conversation with the man. Immediately after, the driver drove off. The police officers consulted each other, got into their car and took off in the direction of the city centere.
Some major modifications were introduced to the original story in order to provide many possible variants of a viable explanation at different levels of solving the problem. After 20 min, the person conducting the experiment reminds the participant that the time is up and she or he can only finish the sentence. The next stage then begins. An example of one participant’s performance (Subject 1) after the first stage can be found in Online Supplementary Materials (Example: Find Out Stage 1).
Part 2: Cooperation
The second stage lasts 30 min. It requires not only generating but also testing previously generated hypotheses and new ideas. Now, the subject works on already devised explanations but is allowed to ask yes–no questions to
A blank template for the second stage of the task (
Part 3: Final report for the editor in chief
At the third stage, the subject is asked to consider all of the information gathered up to that point and write down the most plausible explanation or explanations of what has happened. What is more, the participant has to provide justifications for each explanation. The explanation, along with its justifications, has to be written in a two-column table. This stage ends after 15 min, and this is the end of the whole task.
The template can be found in the Online Supplementary Materials (
The final version of the task is based on some basic assumptions (presented above) on the proper methodological context that enables the observation of expressions of abductive reasoning in a context close to real-life conditions and the results of two pilot studies. In order to make it clear why some methodological, procedural, or structural decisions on the task were accepted, the most significant findings of two pilot studies are briefly described below.
Pilot Study Number 1: Testing Preliminary Version of the Task
The major goal of the first study was to investigate whether a task built on a mystery story can act as an adequate methodological context to investigate abductive reasoning in terms of the hypotheses generation phase. It was expected that this measure would enable individual differences among participants to be observed. If so, the next step would be to develop the procedure in the direction that enables not only a hypothesis generation phase to be evaluated but also a testing phase. Forty-five undergraduate students (33 women, 11 men, 1 preferred not to answer) aged 18–22 (
Each story includes several aspects that are underspecified and need to be accounted for. For example, in Story Number 1, it is not known what the result of the breathalyzer test was, what the content of a conversation between the driver and police officers was, and what had really happened that the bottle was half empty. In order to direct the process of formulating explanations, each story ended with a question:
What has happened and did anyone break the law? Both stories used in the first pilot study are presented in Online Supplementary Materials (
At that point of our research, we thought that an additional request (i.e., “whether anyone broke the law”) would not only help to better understand the requirements of the task but also to facilitate generating ideas involving different aspects of the situation. Participants were tested in two groups, but each person worked individually. There was no time limit as we wanted to assess how long it would take to complete the test. The instructions included the suggestion that the performance of the task should take no more than 30 min, but participants were informed that anyone who would prefer to work longer would be given the opportunity to do so.
Ten participants shared their opinions on the task. It could be concluded that the participants enjoyed solving the task and that the instructions were clear enough (no comment suggested otherwise). However, the idea to ask about breaking the law did not prove itself as facilitation. Instead, some participants reported feeling incompetent to judge any legal issues. As a result, we have decided to delete the additional question from further versions of the task. It appeared that the first story (about a driver and the police) enabled us to gather observations that demonstrated more individual differences than the second story (about coworkers), which was probably too sketchy and therefore inspired the subjects to create similarly sketchy explanations. The next versions of the task were based on the modification of the first but not the second story.
Further modifications introduced to the task were chosen to accomplish two partially disparate goals: to optimize the chance of observing individual differences and to standardize the context of their appearance to reduce the risk of confounding factors, which could impair the objectivity of future studies on the individual differences in abductive reasoning.
Pilot Study Number 2: Constructing the Final Version of the Task
After analyzing and reconsidering the results of the first pilot study, some decisions were made on the preliminary scheme of the task. The next step was a constructive pilot study conducted to accomplish two major goals: to define the final form of the experimental task and to decide on the details of the procedure of the testing routine. At this stage, the task was being modified just after the people conducting the experiment had received sufficient feedback to improve the method. As a consequence, 12 versions of the task were empirically tested and evaluated. Nineteen subjects (aged 24–69) participated in the study. The group of participants was varied enough to show a wide diversity of performances and enabled us to receive diverse feedback. Each version of the task was performed by one, two, or three participants.
The following major modifications were introduced during this stage: changing the format of the medium from an analog paper-pencil task to a computerized task. Although the analog version of the task is still available on request and can be useful in some cases (please contact authors in case of interest), the digital version enabled us to shorten the time needed to complete the task and improved the process of gathering and analyzing the data.
Modifications of the structure of the task
The final version of the task contains not only the notepad where hypotheses are written but also a place where participants can make additional notes—the scratch pad. Participants claimed that it helped them to structuralize their thoughts and moved the task closer to the real-life conditions of solving a problem.
Modifications of the instructions
In the final version, instructions are presented step-by-step, each part immediately before the corresponding stage of the task. At first, complete instructions for the whole task overall and for each stage of the task separately were delivered at once, just at the beginning of the procedure. However, the volume of information appeared to be too extensive to be effectively processed and remembered by participants. Moreover, some participants started to perform latter stages of the task ahead of time. The content of the instructions has been refined many times so as to make them as precise as possible but with no loss of clarity. In order to assure standardization of the interaction between the subject and the researcher, a model of communication has been designed. This model applied not only to the necessary information but also to situations that may occur.
Modifications of the procedure
The chosen version of the procedure is set in time-restricted conditions: up to 20 min for the first stage, 30 min for the second, and 15 min for the third. These limits appeared to be a reasonable compromise between the risk of cognitive fatigue and a need to assess performance that is really a reflection of a cognitive competence in abductive reasoning, not only a mental speed or verbal fluency. What is more, the time limit seems to be closer to real-life conditions than limiting the number of questions or actions that can be performed during the task and saves the possibility of analyzing two important indicators of individual differences: the number of questions asked by the participant and the dynamics of questioning.
Modifications of the story line to make the task easier and less formal
When starting the second pilot study, we believed that placing the task in the context of a detective story would help to create a ludic atmosphere. As a consequence, the higher level of the participants’ engagement and, at the same time, lower level of stress associated with an experimental condition of the assignment were expected. The participants played the role of a detective seeking an explanation for what had happened in a presented enigmatic story. However, the convention of a detective story appeared to be problematic. Interviews with participants of the study revealed that some of them were misled by the background story and had searched for an explanation in a strictly directed way—they were looking for a serious crime, perceived as much more representative for this context than a traffic offence. Some other subjects reported feeling incompetent in the face of a task perceived by them as requiring specific forensic knowledge and procedures. What is more, this task condition caused emotional arousal that could influence further observations. To avoid these difficulties, some modifications to the story line were introduced. Subsequent versions of the task were set in a context, which was less connected with a professional expertise. The role to play was no longer a detective but an investigative journalist working for a news service, not a police department. However, the task was still to explain the same enigmatic situation. This informal working condition enabled us to avoid previous limitations.
Modifications of the content of the task
The content of the target story has been modified most frequently out of all aspects of the task. The initial version was the one used in the first pilot study, which is found in the Online Supplementary Materials (
Exemplary changes involved the removal of the misleading question, previously placed just after the story (i.e., “What has happened and did anyone break the law?”), clarifications and specifications of some facts from the story, adding some new information. The intention was to optimize the story as a trigger of abductive reasoning. The mystery had to be pronounced but, at the same time, more than one divergent way of solving it should be possible.
Changes in possible answers to subjects’ questions
At the starting point, possible responses to questions asked by participants during the second stage (called cooperation), designed to evaluate hypotheses testing phase, were as follows:
Pilot Study Number 3: Evaluation of the Task, Exploratory Analyses
The aims of the third pilot study were to evaluate the task and explore what characteristics of the process and the products of abductive reasoning could be identified and evaluated with
Observations
The
Samples of Qualitative Analyses
Searching for the methodological framework compatible with the primary goals of the project and enabling us to conduct exploratory qualitative research has so far directed us to the grounded theory approach and qualitative content analysis. This section of the article contains samples of the analyses that we have managed to conduct so far (some of them are still being continued). However, as a sufficiently attentive presentation of those analyses would highly exceed the acceptable limit of this article, we are currently working on a separate article presenting the results of qualitative analyses. At this point, we would only like to provide readers with a sense of the methodological possibilities of the task. Please bear in mind that the presented samples do not exhaust all the possibilities of conducting qualitative analyses of the data provided with the framework of
The content of hypotheses: fragments and gap fillers
We conducted multilevel analyses on the formal characteristics of the content of participants’ responses. It appeared that the content of the responses could be categorized into
Analyses revealed that basic events described in the story (understood as fragments that can be further explained in the process of filling in the gaps) can be perceived as answers to the question “What has happened?” Other fragments and gap fillers (if delivered in the content of the story or not) answer not only the aforementioned questions of “when and why” but also the questions “who, (with) what, where, what happened, and how.” It should be emphasized that fillers addressing the problem “why and how” are usually used to specify only what has happened. It can be concluded that events and fillers correspond to seven gold forensic questions (see, Gross, 1908) that should be asked by a policeman during the process of a criminal investigation: “What (has happened), who, (with) what, where, when, how, and why.”
The distinction of
A problem-space coverage
The aforementioned distinction helped to create a coding system referring to the dimension of
Analyses led us to the conclusion that
Two independent variables referring to the
There are some perspectives of qualitative analyses that we have taken into consideration but, as both the research and analyses are still in progress, the results cannot be presented yet: the correctness of the effects and the process of abducting (e.g., hypotheses, questions, justifications, modifications), the manner of organizing the content of information which appeared to fit the distinction proposed by Bruner (1986, 1991) between a paradigmatic and narrative mode of cognition, types of gap fillers, and strategies of solving the abductive problem which can only be identified after comparing the three stages of the task (the work is still in progress).
Conclusions
The
On the basis of described pilot studies, we believe that
What seems to be a reasonable doubt is whether the requirements and laboratory context of the task provide conditions that enable a process of abductive reasoning that is close enough to real-life conditions to be observed. Although our tool seems to be much closer to that requirement than other known measures of the same phenomenon, we still cannot claim that the ecological accuracy of the measure is optimal.
What can be considered an asset of the method is that it provides a framework to conduct further empirical research of both a qualitative and quantitative nature. We plan to take advantage of some possibilities and are currently working on an article presenting the results of qualitative analyses of the data. Further analyses are still being conducted in order to work out a satisfying assessment system that could serve in a future investigation focused at looking for the cognitive and personality correlates of the individual differences in performing abductive reasoning.
Supplemental Material
Supplemental Material, Example__Find_Out_Chat_window_ - Find Out A New Method to Study Abductive Reasoning in Empirical Research
Supplemental Material, Example__Find_Out_Chat_window_ for Find Out A New Method to Study Abductive Reasoning in Empirical Research by Dorota Żelechowska, Natalia Żyluk and Mariusz Urbański in International Journal of Qualitative Methods
Supplemental Material
Supplemental Material, Example__Find_Out_Stage_1 - Find Out A New Method to Study Abductive Reasoning in Empirical Research
Supplemental Material, Example__Find_Out_Stage_1 for Find Out A New Method to Study Abductive Reasoning in Empirical Research by Dorota Żelechowska, Natalia Żyluk and Mariusz Urbański in International Journal of Qualitative Methods
Supplemental Material
Supplemental Material, Example__Find_Out_Stage_2 - Find Out A New Method to Study Abductive Reasoning in Empirical Research
Supplemental Material, Example__Find_Out_Stage_2 for Find Out A New Method to Study Abductive Reasoning in Empirical Research by Dorota Żelechowska, Natalia Żyluk and Mariusz Urbański in International Journal of Qualitative Methods
Supplemental Material
Supplemental Material, Example__Find_Out_Stage_3 - Find Out A New Method to Study Abductive Reasoning in Empirical Research
Supplemental Material, Example__Find_Out_Stage_3 for Find Out A New Method to Study Abductive Reasoning in Empirical Research by Dorota Żelechowska, Natalia Żyluk and Mariusz Urbański in International Journal of Qualitative Methods
Supplemental Material
Supplemental Material, Find_Out_Pilot_Study_1__Stories - Find Out A New Method to Study Abductive Reasoning in Empirical Research
Supplemental Material, Find_Out_Pilot_Study_1__Stories for Find Out A New Method to Study Abductive Reasoning in Empirical Research by Dorota Żelechowska, Natalia Żyluk and Mariusz Urbański in International Journal of Qualitative Methods
Supplemental Material
Supplemental Material, Find_Out_Stage_1 - Find Out A New Method to Study Abductive Reasoning in Empirical Research
Supplemental Material, Find_Out_Stage_1 for Find Out A New Method to Study Abductive Reasoning in Empirical Research by Dorota Żelechowska, Natalia Żyluk and Mariusz Urbański in International Journal of Qualitative Methods
Supplemental Material
Supplemental Material, Find_Out_Stage_2 - Find Out A New Method to Study Abductive Reasoning in Empirical Research
Supplemental Material, Find_Out_Stage_2 for Find Out A New Method to Study Abductive Reasoning in Empirical Research by Dorota Żelechowska, Natalia Żyluk and Mariusz Urbański in International Journal of Qualitative Methods
Supplemental Material
Supplemental Material, Find_Out_Stage_3 - Find Out A New Method to Study Abductive Reasoning in Empirical Research
Supplemental Material, Find_Out_Stage_3 for Find Out A New Method to Study Abductive Reasoning in Empirical Research by Dorota Żelechowska, Natalia Żyluk and Mariusz Urbański in International Journal of Qualitative Methods
Footnotes
Acknowledgments
The authors would like to thank former students of the Faculty of Psychology and Cognitive Science, Dajana Bieganowska and Kinga Antonik-Jończyk, for their help during the process of conducting the research.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Science Centre, Poland (DEC-2013/10/E/HS1/00172).
Supplemental Material
The supplemental material for this article is available online.
References
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
