Thematic Einstein Semester

Einstein lecture series

April 28 – September 8, 2022

Experienced visiting and local researchers shall present recent work on mathematics of complex social systems in a regular series of talks throughout the summer semester.

The Einstein lecture series is part of the Thematic Einstein Semester “The Mathematics of Complex Social Systems: Past, Present, and Future”.

Organizational detail

The Einstein lecture series takes place as an online event (exception: 05.05. hybrid event with live part at Zuse Institute Berlin in Berlin-Dahlem).

Content

Mason Porter (UCLA): Opinion Dynamics and Spreading Models on Social Networks

From the spreading of diseases and memes to the development of opinions and social influence, dynamical processes are affected significantly by the networks on which they occur. In this talk, I’ll review recent work by my collaborators and me on social influence and opinion models on networks. I’ll discuss several types of models — including threshold models of social contagions, voter models that coevolve with network structure, and bounded-confidence models with continuous opinions — and present how such processes are affected by the networks on which they occur. I’ll also connect these models to phenomena such as opinion polarization and the development of echo chambers in online social networks.

Grigorios A. Pavliotis (Imperial College London): Interacting multiagent models in the social sciences: collective behaviour, phase transitions and inference

Several mathematical models in the Social Sciences that have been developed in recent years are based on interacting multiagent systems. Often, such systems can be described using interacting diffusion processes. Examples include models for sychronization (the noisy Kuramoto model), systemic risk (the Desai-Zwanzig model), and opinion formation (the noisy Hagselmann-Krause model). For such models, the emergence of collective behaviour, e.g. synchronization and consensus formation, can be interpreted as a disorder-order phase transition between, e.g. a uniform and a clustered/localized state. Such a phase transition can be studied rigorously in the mean field/thermodynamic limit that is described by the McKean-Vlasov equation. In this talk we will present recent results on the rigorous analysis of phase transitions for such systems on their impact on their dynamical properties. Furthermore, we present inference methodologies, for learning parameters in the mean field model from observations of sufficiently long single trajectories of the interacting particle system.  The effect of phase transitions on this inference problem is elucidated and the development of diagnostic tools for predicting phase transitions is discussed.

Ramon Grima (University of Edinburgh): Agent-based models of stochastic gene expression in growing cell populations

The random nature of gene expression is well established experimentally. Mathematical modelling provides a means of understanding the factors leading to the observed stochasticity. Most modelling of stochastic gene expression is based on the two state (or telegraph) model. It is nowadays routine to fit the mRNA distributions given by this model to experimental distributions for cellular mRNA estimated from population snapshot data. This leads to an inference of the transcriptional parameters, i.e. the transcription rate and the promoter switching rates. However this procedure is inherently flawed because fluctuations in cellular RNA (and protein) reflects many processes downstream of transcription. To counteract these issues, we have recently developed realistic agent-based models of cellular RNA/protein that include a considerable number of salient features of single-cell biology, such as cell division, replication, mRNA maturation, dosage compensation, cell size control and growth-dependent transcription. I will discuss the construction of these models, how their solution can be approximated analytically and then used to infer parameters using single cell data collected over several generations or from population snapshots.

John Harlim (Pennsylvania State University): Machine learning of missing dynamical systems

In the talk, I will discuss a general closure framework to compensate for the model error arising from missing dynamical systems. The proposed framework reformulates the model error problem into a supervised learning task to estimate a very high-dimensional closure model, deduced from the Mori-Zwanzig representation of a projected dynamical system with projection operator chosen based on Takens embedding theory. Besides theoretical convergence, this connection provides a systematic framework for closure modeling using available machine learning algorithms. I will demonstrate numerical results using a kernel-based linear estimator as well as neural network-based nonlinear estimators. If time permits, I will also discuss error bounds and mathematical conditions that allow for the estimated model to reproduce the underlying stationary statistics, such as one-point statistical moments and auto-correlation functions, in learning Ito diffusions.

Mauro Maggioni (Johns Hopkins University): Learning Interaction laws in particle- and agent-based systems

Interacting agent-based systems are ubiquitous in science, from modeling of particles in Physics to prey-predator and colony models in Biology, to opinion dynamics in economics and social sciences. Oftentimes the laws of interactions between the agents are quite simple, for example they depend only on pairwise interactions, and only on pairwise distance in each interaction. We consider the following inference problem for a system of interacting particles or agents: given only observed trajectories of the agents in the system, can we learn what the laws of interactions are? We would like to do this without assuming any particular form for the interaction laws, i.e. they might be “any” function of pairwise distances. We consider this problem both the mean-field limit (i.e. the number of particles going to infinity) and in the case of a finite number of agents, with an increasing number of observations, albeit in this talk we will mostly focus on the latter case. We cast this as an inverse problem, and present a solution in the simplest yet interesting case where the interaction is governed by an (unknown) function of pairwise distances. We discuss when this problem is well-posed, we construct estimators for the interaction kernels with provably good statistically and computational properties, and discuss extensions to second-order systems, more general interaction kernels, and stochastic systems. We measure empirically the performance of our techniques on various examples, that include extensions to agent systems with different types of agents, second-order systems, and families of systems with parametric interaction kernels. We also conduct numerical experiments to test the large time behavior of these systems, especially in the cases where they exhibit emergent behavior. The above is based on multiple joint works with F. Lu, J.Miller, S. Tang, and M. Zhong.

Jeremy Gibbons (University of Oxford): Algorithm Design by Calculation

Where do algorithms come from? Sometimes they require a flash of insight, a creative spark. But often, they do not: sometimes the algorithm falls out naturally from a problem specification and straightforward program transformations. In this case, just “doing the obvious thing” suffices, and one need not wait for inspiration to strike; one can just start calculating – in the same way that we do not need inspiration for solving a division problem, but can calculate a solution. I will show some examples of algorithm design by calculation, in a functional programming setting. This talk is based on the book “Algorithm Design with Haskell” (CUP, 2020) by Richard Bird and myself.

Ulrik Brandes (ETH Zürich): On Social Space, Graph Embeddings, and Network Positions

The way in which complex systems are represented determines the methods that can be applied in their analysis. Over the past century, the development of social network analysis has benefitted tremendously from graph representations. So much so, that social networks are often introduced as graphs. Similarly, representations for multivariate networks, multilayer networks, or higher-order networks make use of generalizations such as multigraphs, hypergraphs, and so on. The transfer of methods originally formulated as graph problems is not necessarily straightforward, however, and generalizations are motivated more often by formal analogy than the original conceptual foundation, if there ever was one. I will argue that the concept of network positions provides a unifying framework for a mathematical treatment of social networks that is aligned with substantive theory.

Gert Jan Hofstede (Wageningen University): Artificial Sociality to grasp complex social systems 

When modelling social systems, we face the complication that what we can measure, and therefore use for quantitative models, may not coincide with what matters to us. We are socialized to internalize unwritten rules of behaviour. Artificial Sociality relies on generic social science for filling in human motives. This is in fact a realization that we humans are children of our evolution, with evolved tendencies for “eusocial” behaviour. We live in a world of groups, where affiliation, status and power are paramount. The lecture will give pointers as to how we can use artificial sociality for making sense of complex social systems.

Juan A. Barcelo (Universitat Autònoma de Barcelona): PREDICTION OF THE PAST IN THE PRESENT. Learning, classification and explanation in archaeology through theories, techniques and technologies of computational intelligence.

Almost 100 years after the first application of formal and quantitative methods to understand the past, archaeology is facing new ways to explain what might have happened in the past. It is not just a matter of new computational methods to organize an ever-increasing amount of data, but of a complete rethinking of the very idea of “explanation”. In this presentation, I introduce some computational methods such as Bayesian networks, but I also intend to offer a different way of approaching our reconstructions of the past, emphasizing the idea of causality and how to build causal models. Some examples of ceramic classification, site prediction and settlement models will also be presented.

Frank Schweitzer (ETH Zürich): Beyond dyadic networks: From interaction data to emerging group relations

Social network analysis already presupposes a network to analyze. But no network is given, a fact that is mostly overlooked or ignored. It breaks down into several conceptual problems which need to be understood. Firstly, networks need to be constructed from available data. How do we define a link? How do we distinguish meaningful interactions from random encounters? How do undirected interactions translate into directed, weighed and signed social relations? Secondly, the resulting network topology cannot be understood without dynamics. Is a network created by incremental growth, or by merging existing groups? How is extensive network growth related to internal dynamic processes like rewiring, or densification? Should disconnected components be ignored in the network analysis? Thirdly, the network approach requires to decompose all interactions into dyadic interactions between two agents. How can group influences be considered? What is the feedback of the dynamics on the network, for instance consensus formation, on the dynamics of the network? How do higher order structures impact the network? In my talk I will address these conceptual challenges using examples from human and animal social systems.

Maja Schlüter (Stockholm University): The potentials of social-ecological modelling for addressing sustainability challenges

Environmental problems are complex and characterized by interdependence between human behaviour and biophysical processes. Making sense of and identifying possible actions towards sustainability in the context of complex causality and social-ecological feedbacks is challenging. In my talk, I will discuss how dynamic modelling, in particular dynamical systems and agent-based modelling, can serve as tool to negotiate different understandings of complex problems, to explore emergent phenomena and investigate path-dependencies and social-ecological feedbacks.  I will build on several examples of collaborative model building and analysis of poverty traps, the collapse of the Baltic cod in Sweden and sustainable fisheries management in Mexico to discuss the different roles models and modelling can play in support of sustainability, such as supporting integrative analysis that bridges the social and ecological, and serving as thinking tool and means for theorizing. 

Miranda J. Lubbers (Universitat Autònoma de Barcelona): A network science approach to social cohesion

The growing inequality, diversity, and polarization of contemporary societies make it urgent to understand what binds societies together and how these bonds can be strengthened. Surprisingly, however, the societal cohesion literature has almost entirely ignored one of its core dimensions up until recently: relationships (Schiefer & Van der Noll, 2017; Dragolov et al., 2016). Social scientists often exclusively study individual indicators (typically of ideational cohesion, e.g., social and institutional trust, solidarity with other social groups), and predict them with individual and national attributes. Yet, people do not live in a social void or are solely informed about society by the evening news. In this talk, I discuss the methods that have been used so far for studying the cohesion of societal networks, their benefits, and drawbacks. Then, I present a new methodology to estimating network social cohesion for entire societies, which I implement in the ERC Advanced Grant project “A network science approach to social cohesion”. The method hybridizes the Network Scale-Up Method (cf. McCormick et al., 2010) with personal network analysis and simulation to estimate the composition and structure of societal networks and their relation with ideational cohesion. I present preliminary data from Spain in the talk to gauge its viability.