Thematic Einstein Semester 2022

Final conference: Mathematics of complex social systems

September 19-20, 2022

To synthesize the TES’ insights and outcomes, the final conference deepens discussions on four selected issues and gives an insight into student projects that took place throughout the semester. With a set of interdisciplinary sessions, we aim to explore differences and similarities in existing work and to discover gaps and open questions of interest for future research.


The conference takes place online, wherefore the program includes larger breaks. All time slots refer to Berlin time, that is, CEST. If you would like to attend the final conference, please send an email to natasa.conrad AT


Monday, 19.9.22:

Time slot (CEST)

Diffusion and transmission processes

Moderators: Nataša Djurdjevac Conrad, Benjamin Ducke

14:30-15:00 Mark Lake, “Model-based approaches to diffusion and transmission in contemporary archaeology”
15:00-15:30 János Kertész, “Opinion dynamics and algorithmic bias”
15:30-16:00 Peter Grindrod, “The mathematics of very large communities: the interactions within global extreme right wing on Telegram”
16:00-16:30 Panel discussion

System identification and model reduction

Moderator: Stefan Klus

17:00-17:30 Ying-Cheng Lai, “Finding the structure of social networks based on evolutionary game data and beyond”
17:30-18:00 Megan Morrison, “Transitions between peace and systemic war as bifurcations in a signed network dynamical system”
18:00-18:30 Miles Medina, “An empirical nonlinear dynamics approach to analyzing emergent behavior of agent-based models”
18:30-19:00 Panel discussion

Tuesday, 20.9.22:

Time slot (CEST)

Particles and Agents

Moderator: Stefanie Winkelmann

10:00-10:30 Edda Klipp, “Heterogeneity in human-human interaction networks and strategies to combat COVID-19”
10:30-11:00 Adelinde Uhrmacher, “From Systems of Reactions to Continuous-Time Reactive and Deliberative Agents”
11:00-11:30 Christof Schütte, “ABMs with large numbers of agents”
11:30-12:00 Panel discussion
15:00-16:00 TES Data challenge presentations and award ceremony
Moderator: Luzie Helfmann

Structures for agent-based modeling of societal challenges

Moderator: Sarah Wolf

17:00-17:20 Carlo Jaeger,The Hasselmann Program and Multi-Actor-Modeling for the Anthropocene”
17:20-17:40 Joffa Applegate, “The Extended Evolution Framework: A Description and an Exercise for Complex Social Evolution”
17:40-18:00 Madhav Marathe, “A computational theory – graphical dynamical systems”
18:00-18:20 Patrik Jansson, “Domain-Specific Languages for Societal Challenges”
18:20-19:00 Panel discussion

Topic descriptions (abstracts see below)


Diffusion and transmission processes

Processes of diffusion and transmission are fundamental to all social systems. This session will discuss various related methods and topics, from cultural transmission in ancient societies to behavior spreading and opinion dynamics in modern societies. Common themes and challenges emerge from application-dependent differences in underlying principles (simple vs. complex contagions), context (culture vs. behavior) and available data (sparse vs. rich).


System identification and model reduction

In this minisymposium, we will discuss different approaches to learn governing equations and also the underlying network structure from data and how these methods can be applied to complex dynamical systems such as agent-based models or biological systems.


Particles and Agents

This session is about the modeling and simulation of spatial complex systems involving a large number of interacting entities, which are called “particles” in the biochemical context and “agents” in social sciences. We will discuss analogies and differences in the mathematical approaches to analyze these systems in the two contexts.


TES Data Challenge presentations and award ceremony

In the TES Data Challenge students analyzed various data sets from past and present social systems. In this session, a few participants will present their interesting findings, followed by a small award ceremony.


Structures for agent-based modeling of societal challenges

This session asks how mathematics can support agent-based modeling of societal challenges, where systems include multi-layered sets of heterogeneous agents, involved decision making mechanisms, spatially differentiated physical and cultural environments, etc, and relevant concepts, such as cohesion, coordination, transitions, niche construction, sustainability relate to a meso- or macro-level, while models are defined at the micro-level of agents.




Mark Lake (UCL): Model-based approaches to diffusion and transmission in contemporary archaeology

In the early twentieth century the Egyptologist Grafton Elliot Smith proposed that many cultural innovations, such as agriculture and monumental architecture had a single origin, in Egypt, and spread from there around the world.  By the 1960s the advent of radiocarbon dating had rendered such ‘hyperdiffusionist’ thinking untenable, but even so, there remains compelling archaeological evidence for spread of cultural traits at local and regional scale in various parts of the world at various times. Today archaeologists seek more nuanced explanations which differentiate the movement of people and the movement of ideas.  In this short presentation I will survey some of the growing number of mathematical or quasi mathematical models of diffusion and/or transmission that archaeologists are using to help them develop their understanding of past cultural diversity.


Peter Grindrod (University of Oxford): The mathematics of very large communities: the interactions within global extreme right wing on Telegram

The instant messaging platform Telegram has become popular among the far-right movements in the US, the UK, and elsewhere in recent years. These groups use public Telegram channels and group chats to disseminate hate speech, disinformation and conspiracy theories. Recent works revealed that the far-right Telegram network structure is decentralized and formed of several communities divided mostly along the ideological and national lines.Here, we investigated the global associations of the UK far-right network on Telegram  in seeking  understanding the different roles of different channels and their influence relations.We apply a community detection method, based on the clustering of a flow of random walkers, that allows us to uncover the organization of the Telegram network in communities with different roles. We find three types of communities: 1) upstream communities contain mostly group chats that comment on content from channels in the rest of the network;2) core communities contain broadcast channels tightly connected to each other and can be seen as forming echo-chambers; 3) downstream communities contain popular channels that are highly referenced by other channels.

We find that the network is composed of two main sub-networks: one containing mainly channels related to the English speaking far-right movements and one with channels in Russian. We analyze the dynamics of the different communities and the most shared external links in the different types of communities over a period going from 2015 to 2020.  This work illustrates the need to develop methods that work at scale, and embed definitions of influence circularity (echo chambers and so on) exploiting concepts and methods focussing on structure and with options trading efficiencies with focus.


János Kertész (CEU): Opinion dynamics and algorithmic bias

The evolution of opinions on virtual platforms, such as online social networks, is subject to radically different constraints than under traditional circumstances, like in face-to-face communication. By means of personalized, content filtering algorithms, online social platforms target and control the information individuals receive. This is usually done by collecting behavioral data on an individual’s preferences, and then filtering incoming content from the rest of the social network, amounting to a so-called “algorithmic bias”. This new type of socio-technical bias can strongly impact the evolution of behavior, opinions, and norms in a population of individuals, who are often unaware of the role of algorithms in their interactions. Collective social phenomena like “echo chambers”, fragmentation and polarization of opinions, increasingly visible features of the global socio-political landscape, are likely promoted by algorithmic bias mechanisms. We explore the effect of online algorithmic bias on opinion dynamics by using simple models and characterize the bias intensity by the probability by which the platform chooses not to show content to an individual coming from users of the opposite state or opinion. We use theoretical tools of binary-state models, including the approximate master equation framework as well as numerical simulation for realistic settings including empirical social networks. We focus on the majority-vote and the noisy voter models as prototypical opinion-formation rules.  The models show rich behavior with continuous and discontinuous transitions between coexistence-consensus-polarization states, depending on model types, bias intensity and network structure. Our results show that the link between online algorithmic bias and collective social behavior, although nuanced, can be modeled systematically, and highlights the complementary roles of filtering algorithms, rules of interaction, and network structure in the emergence of polarized information spreading. Finally we report about research on French political tweets, where interaction between politicians and people can be represented by a two.layer network. Based on text analysis and community detection we reveal the political landscape and we demonstrate that a simple opinion dynamics model can satisfactorily reproduce the empirical findings.


Adelinde Uhrmacher (University of Rostock): From Systems of Reactions to Continuous-Time Reactive and Deliberative Agents 

The talk will revolve around differences and similarities of two modeling languages for simulation. The rule-based language ML-Rules supports modelers in succinctly expressing models of biochemical reaction systems and cellular systems at multiple levels. ML3 (Modeling Language for Linked Lives) is a language developed for continuous time agent-based modeling in demography. We will discuss application-specific requirements for both languages and the implications for their respective syntax and semantics, to move on to challenges and solutions for efficiently executing the respective models.


Patrik Jansson (Chalmers University): Multi-objective optimisation and exploration of system simulations

When we use mathematical models and complex computer implementations to simulate a system with many parameters, classical optimisation
methods are often not applicable. This presentation describes some of the concepts, challenges, and potential solutions, for exploring the solution space.


Madhav Marathe (University of Virginia): A computational theory – graphical dynamical systems

Graphical Dynamical systems (GDS) are a special type of communicating automata that can be used to model very large socio-technical systems. GDS based “formal simulations” potentially provide a rigorous, useful new setting for a theory of interaction-based computation. The setting is natural for comprehension of distributed systems characterized by interdependent, but separately functioning sub-parts. Massively parallel and grid computing and the associated algorithm design issues, advanced communication systems, biological networks, epidemiological processes, markets, socio-technical systems are examples of such systems.
I will focus on the computational aspects of GDS. The concepts and results shed light on the computational complexity of computing phase space properties of GDS. Applicability of these concepts will be described in the context of large scale socio-technical systems.


Carlo Jaeger (Global Climate Forum): The Hasselmann Program and Multi-Actor-Modeling for the Anthropocene

Klaus Hasselmann earned the Nobel prize in physics 2021 ”for groundbreaking contributions to our understanding of complex physical systems”, jointly with Syukuro Manabe and Giorgio Parisi. In parallel with his work as climate scientist, he started to engage with economics three decades ago because he realized that climate change is deeply connected with how today’s world economy works. In response, he planted the seeds for a research program that he has since pursued with colleagues from the Max Planck Institute of Meteorology, that he directed, and from other institutes, most notably the Global Climate Forum, that he initiated.

A key aspect of the Hasselmann Program is to shed the idea that decision makers need models from climate scientists and from economists in order to implement the optimal strategies identified by those scholars. Instead, it is essential to also model the decision processes influenced by scientific research that in turn influence the global climate as well as the world economy.

To model the relevant decision processes, it is useful to distinguish between multi-agent and multi-actor models. Multi-agent models are a fast-growing family of heterogeneous computer models referring to all kinds of systems, from computer networks to ecosystems, from urban dynamics to chemical reactions, and counting. The climate system, e.g. can be simulated with multi-agent models by representing it as a complex network where the nodes correspond to regional subprocesses treated as agents and the edges correspond to causal links between subprocesses (e.g. the impact of atmospheric and oceanic processes in specific regions of the tropical Atlantic on droughts in the central Amazon).

As for multi-actor models, in the Hasselmann Program they are the subset of multi-agent models that explicitly includes human decision-makers. Actors in this sense are a particular kind of agents, namely us humans with our individual decisions and their intended and unintended consequences, as well as the small and large teams in which we make collective decisions that come with their consequences, too. In the beginning Anthropocene, that we are presently experiencing, multi-actor models are especially important to represent actors on whose decisions the future of the coupled humankind-Earth system depends.

In the Hasselmann Program, the starting point for computer modeling of human actors are the players, aka rational actors, introduced by von Neumann and Morgenstern when they laid the foundations of game theory. Actors of this kind are characterized by (1) possible actions, (2) possible consequences of each combination of actions of all players, (3) expectations of these consequences by each player,  and (4) preferences between these consequences. As von Neumann and Morgenstern knew, such players are different from the representative agent needed for the supply and demand theory of prices. In fact, this difference leads to major research challenges, e.g. when dealing with carbon prices. Bill Nordhaus was right when, as the first economist to receive a Nobel prize explicitly related to climate change, he titled his Nobel lecture “Climate Change: The Ultimate Challenge for Economics“.

Game theory offers a powerful structure for modeling multi-actor systems. Still, that structure has been and still needs to be elaborated much further. A crucial refinement concerns the capability of actors to coordinate themselves through communication networks  – a key capability we humans share with many non-human agents. For computer modeling, the biggest challenge may well be the fact that human beings need and use natural languages for many purposes, including to communicate with each other and to think for themselves. In view of the beginning Anthropocene, a particularly important purpose would and hopefully will be to achieve peaceful coordination in the face of global challenges.

Against this background, an important next step in the development of the Hasselmann Program will be to represent key social norms expressed in natural language, norms that matter when dealing with climate change and other global challenges of the Anthropocene. They will include laws, conventions and other norms along with their histories in the overall co-evolutionary dynamics of the coupled humankind-Earth system. An instructive example is the social norm that inflation should be in the neighborhood of 2% per year. This norm is currently followed by the main central banks, with far-reaching and sometimes problematic effects. An interesting question about social norms relevant for climate change is whether the 2 and 1.5 °C temperature goals declared by the signatories to the Paris accord will lead to a similarly influential social norm – and if so, what might be its effects on global inequality, industrial structure and more.

Last not least, to be able to model realistic transition paths of today’s world economy towards a sustainable future one needs to expand the Hasselmann Program by an adequate representation of the global stocks of different kinds of fixed capital (power plants, buildings, machines, etc.). Remarkably, von Neumann provided the necessary starting point here, too. It consists in the representation of actual and possible production processes using specific fixed capital items (e.g. new computers) while along with their main marketable outputs producing used items of the same kind (e.g. used computers). Fixed capital items as well as other goods can then be treated as agents, just like printers, computers etc. in multi-agent models of computer networks. The managers that decide how to use these agents can then be treated as actors interacting with them as well as with the broader social-ecological systems in which they operate.

Background about the Hasselmann Program and its development so far is to be found at:

MATH+ organizers

Nataša Djurdjevac Conrad (ZIB), Benjamin Ducke (DAI), Stefan Klus (U Surrey), Stefanie Winkelmann (ZIB), Sarah Wolf (FU/GCF)