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Understanding the evolutionary stability of cooperation is a central problem in biology, sociology, and economics. There exist only a few known mechanisms that guarantee the existence of cooperation and its robustness to cheating. Here, we…
Much of the structure in social networks has been explained by two seemingly independent network evolution mechanisms: triadic closure and homophily. While it is common to consider these mechanisms separately or in the frame of a static…
In this work we present a strategic network formation model predicting the emergence of multigroup structures. Individuals decide to form or remove links based on the benefits and costs those connections carry; we focus on bilateral consent…
In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a class of…
Necessary conditions for asymptotic stability and stabilizability of subsets for dynamical and control systems are obtained. The main necessary condition is homotopical and is in turn used to obtain a homological one. A certain extension is…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
The space of stability conditions on a triangulated category is naturally partitioned into subsets $U(A)$ of stability conditions with a given heart $A$. If $A$ has finite length and $n$ simple objects then $U(A)$ has a simple geometry,…
Collective behavior is commonly attributed to direct interactions among system components. Using a minimal stochastic model, we show that higher-order collective structure can instead emerge from shared stochastic environments, even in the…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
Spatial structure and species interactions jointly shape the dynamics and biodiversity of ecological systems, yet most theoretical models either neglect spatial heterogeneity or sacrifice analytical tractability. Here, we provide a unified…
The abundance of data about social relationships allows the human behavior to be analyzed as any other natural phenomenon. Here we focus on balance theory, stating that social actors tend to avoid establishing cycles with an odd number of…
In two earlier papers we derived congruence formats with regard to transition system specifications for weak semantics on the basis of a decomposition method for modal formulas. The idea is that a congruence format for a semantics must…
Social balance theory describes allowable and forbidden configurations of the topologies of signed directed social appraisal networks. In this paper, we propose two discrete-time dynamical systems that explain how an appraisal network…
Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
This paper is motivated by recent developments in group stability, high dimensional expansion, local testability of error correcting codes and topological property testing. In Part I, we formulate and motivate three stability problems: 1.…
Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt…
We present a geometric formulation of classical Cosserat elasticity in which the coframe and rotational connection are treated as independent variational fields. In contrast to conventional metric-based approaches, this formulation makes…
Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must…
Social mobilization often fails not for a lack of collective interest, but because of fierce competition between rival movements for the same limited pool of participants. We generalize the classic threshold model of collective behavior to…