Catalyzing Collaborations: Modeling the Dynamics of Scientific Collaboration at Conferences

By Emma R. Zajdela

Each year, hundreds of thousands of scientists around the world attend conferences to learn about the latest discoveries in their fields, disseminate their findings, interact with one other, and build their research networks. However, these meetings come at a high cost; the direct monetary price alone is estimated at tens of billions of U.S. dollars annually, in addition to environmental and opportunity costs [2]. One of the most important outcomes of conferences is the creation of new scientific collaborations between people who may otherwise never have met. My research team thus sought to answer the following question: How effective are conferences at forming new scientific collaborations?

To address this query, we developed a model to understand and predict the way in which scientists form collaborations at conferences. In 1996, physicist Serge Galam asked, “Do humans behave like atoms?” [1]. This question inspired us to perceive scientists at a conference like molecules in a solution, where the chemical reaction represents the formation of the collaboration. In this analogy, the conference itself acts as a catalyst in that it accelerates the reaction by changing the potential for collaboration. Such an idea provides the basis for a linear model with the following assumptions:

1. As scientists interact more intensely, their probability of collaborating \(P(t)\) increases with growth rate \(S\).
2. When scientists cease to interact, the probability of collaborating \(P(t)\) declines with decay rate \(W\): \[\frac{dP}{dt}=\underbrace{S\frac{I}{I_\textrm{max}}(1-P)}_\textrm{strengthening}-\underbrace{WP\bigg(1-\frac{I}{I_\textrm{max}}\bigg)}_\textrm{weakening}.\]

The above ordinary differential equation (ODE) has fixed points at \(P=0\) when interaction is absent \((I=0)\) and reaches \(P=1\) when interaction intensity is maximal \((I=I_\textrm{max})\). One can generalize the ODE by introducing the parameters that correspond to a minimum probability \(P_\textrm{min}\) and a maximum probability \(P_\textrm{max}\). This setup ensures that the chance of a pair of scientists collaborating is never null, even when they have not interacted before (i.e., if a third party were to bring them together), and never 100 percent certain, even when they have interacted maximally in the past. 

However, our linear model has a major limitation. When scientists cease to interact, the probability of collaboration relaxes to zero; this result implies that scientists completely forget each other after the conference ends, regardless of their interaction level. To address this issue, we first reformulate the linear model as a potential function

\[\frac{dP}{dt}=-\frac{dV}{dP},\]

where the minus sign implies that stable equilibria occur at minima of the potential \(V(P)\). This potential for the linear model is a quadratic function wherein the stable fixed point rises with increasing values of \(I\). We modify this potential function to account for the effect of memory. When interaction is \(I=0\), the new potential function (see Figure 1) has two stable fixed points at \(P=0\) and at a memory probability \(P=P_\textrm{mem}\), with an unstable fixed point in the middle. The barrier between \(0\) and \(P_\textrm{mem}\) disappears as interaction increases, leaving only a single stable equilibrium. Parameters \(S\) and \(W\) control the respective strengthening and weakening rates at which the fixed points are approached. The exact form of the potential function—which is a piecewise quadratic function—that we used to derive the nonlinear memory model is available in the supplementary information of our resulting paper [4]. 

Defining “Interaction” \(I(t)\) Between Scientists Throughout the Conference 

Consider a pair of scientists \((A,B)\) as the simplest unit of possible collaboration. Suppose they spend time \(T\) together in a room with a group of \(N\) people. As the number of people in the group becomes smaller (or as in the aforementioned chemical analogy, becomes more concentrated), the interaction intensity should get higher. We can define interaction between \(A\) and \(B\) as the total time that \(A\) spent listening to \(B\). By making the convenient (but unrealistic) assumption that all individuals spend an equal amount of time speaking, we note that \(I\) is symmetric \((I_{A,B}=I_{B,A}=I_{AB})\). Thus,

\[I_{AB} \propto \frac{\overbrace{T-T/N}^\textrm{Total time spent listening}}{\underbrace{N-1}_\textrm{# of people to listen to}}=\frac{T}{N},\]

where \(\frac{T}{N}\) is the time that \(A\) spent speaking. We normalize so that when \(N=2\) and \(I_{AB}=T\), 

\[I_{AB}=\frac{2T}{N}.\]

To yield the effective interaction intensity \(I(t)\), we divide by time \(T\):

\[I(t)=\frac{2}{N}.\]

Between sessions, we assume that the interaction \(I_\textrm{min}\) is proportional to the total number of participants, which corresponds to people’s informal interactions at coffee breaks or social events. Figure 2a depicts a typical interaction profile between participants at a conference, and Figure 2b shows the corresponding probabilities for the linear and nonlinear models. An interactive version of Figures 1 and 2 is available online.

Scialog Dataset

To test the model, our group at Northwestern University’s Department of Engineering Sciences and Applied Mathematics partnered with the Research Corporation for Science Advancement (RCSA). RCSA is a nonprofit funding agency that runs the “Scialog” conferences, which stands for “Science Dialog.” These meetings seek to accelerate science’s impact through research, intensive dialog, and community-building activities. They unite 50 to 60 early-career Fellows with roughly 10 senior facilitators for three days. At the end of the conference, the Scialog Fellows form teams of two to four people and write proposals; five to six of these proposals typically receive funding [3]. The Scialog dataset contains detailed records from past conferences, both in-person and virtual, and includes the following information:

1. Each participant’s familiarity with other participants on a scale of 0-3 (0 being “I have never heard of this person” and 3 being “I have collaborated with this person”).
2. The sessions that each participant attended throughout the conference (each conference had three to four small group sessions with three to four people each, and three to four discussion groups with eight to 12 people each).
3. The scientists that collaborated at the end of the conference (i.e., submitted proposals together).

For simplicity in our study, we restricted the data to four in-person conferences that corresponded to the first in each conference series; doing so omitted any effects of scientists who were returning from a previous conference and going to the next in the series. Testing revealed that the nonlinear catalysis model outperforms seven other candidate models and accurately reproduces the collaborations that formed across all conference data. Empirical analysis showed that pairs who collaborated interacted on average 63 percent more during the conference than pairs who did not ultimately collaborate; the results were significant across all tested conference data. We also compared the actual conference group assignments to 2,500 counterfactual scenarios. Results suggest the presence of a causal effect of interaction on collaboration formation, particularly for pairs who co-attended small group sessions. In fact, the probability of collaboration between participants who attended the same small group session is eight times that of participants who were not in the same session. 

This research shows that conference organizers can optimize conference design to catalyze collaborations. In doing so, they might even influence the future direction of science. A more detailed description of the work is available in our corresponding paper [4].

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Emma Zajdela presented this research during a minisymposium at the 2021 SIAM Conference on Applications of Dynamical Systems, which took place virtually last year.

Acknowledgments: This research was funded by the U.S. Department of Agriculture (NACA 58-3022-0-005), the National Science Foundation’s Graduate Research Fellowship Program (DGE-184216), and the Global Impacts Graduate Research Fellowship from Northwestern University’s Buffett Institute for Global Affairs. 

References
[1] Galam, S. (1996). When humans interact like atoms. In Understanding group behavior: Consensual action by small groups (Vol. 1) (pp. 293-312). New York, NY: Psychology Press.
[2] Sarabipour, S., Khan, A., Seah, Y.F.S., Mwakilili, A.D., Mumoki, F.N., Sáez, P.J., … Mestrovic, T. (2021). Changing scientific meetings for the better. Nat. Hum. Behav., 5, 296-300.
[3] Wiener, R.J., & Ronco, S. (2019). Scialog: The catalysis of convergence. ACS Energy Lett., 4-5, 1020-1024.
[4] Zajdela, E.R., Huynh, K., Wen, A.T., Feig, A.L., Wiener, R.J., & Abrams, D.M. (2021). Catalyzing collaborations: Prescribed interactions at conferences determine team formation. Preprint, arXiv:2112.08468.

Emma Zajdela is Ph.D. candidate in applied mathematics at Northwestern University, a National Science Foundation Graduate Research Fellow, and 2020 Buffett Institute Global Impacts Fellow. Her research focuses on the development of mathematical models to understand and predict complex social phenomena with applications to poker games, autonomous vehicles, scientific collaboration at conferences, and fashion trends.