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This paper develops a framework for identification, estimation, and inference on the causal mechanisms driving endogenous social network formation. Identification is challenging because of unobserved confounders and reverse causality;…
Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In…
Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical)…
Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary timescales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of…
Complex distribution networks are pervasive in biology. Examples include nutrient transport in the slime mold \emph{Physarum polycephalum} as well as mammalian and plant venation. Adaptive rules are believed to guide development of these…
Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood…
A model of an evolving network of interacting molecular species is shown to exhibit repeated rounds of crashes in which several species get rapidly depopulated, followed by recoveries. The network inevitably self-organizes into an…
Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
Maintaining a sustainable socio-ecological state of a river delta requires delivery of material and energy fluxes to its body and coastal zone in a way that avoids malnourishment that would compromise system integrity. We present a…
A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal…
Link prediction systems (e.g. recommender systems) typically use graph topology as one of their main sources of information. However, automorphisms and related properties of graphs beget inherent limits in predictability. We calculate hard…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs,…
We posit that autoregressive flow models are well-suited to performing a range of causal inference tasks - ranging from causal discovery to making interventional and counterfactual predictions. In particular, we exploit the fact that…
The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
Many complex networks depend upon biological entities for their preservation. Such entities, from human cognition to evolution, must first encode and then replicate those networks under marked resource constraints. Networks that survive are…
Emergent patterns in complex systems are related to many intriguing phenomena in modern science and philosophy. Several conceptions such as weak, strong and robust emergence have been proposed to emphasize different epistemological and…