Related papers: Transition Graphs of Interacting Hysterons: Struct…

We present a framework for analyzing collections of interacting hysterons through the lens of catastrophe theory. By modeling hysteron dynamics as a gradient system, we show how to construct hysteron transition graphs by characterizing the…

The response, pathways and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically,…

While many materials exhibit a complex, hysteretic response to external driving, there has been a surge of interest in how the complex dynamics of internal materials states can be understood and designed to process and store information. We…

The Preisach model has been useful as a null-model for understanding memory formation in periodically driven disordered systems. In amorphous solids for example, the athermal response to shear is due to localized plastic events (soft…

Many real-world interactions (e.g., researcher collaborations and email communication) occur among multiple entities. These group interactions are naturally modeled as hypergraphs. In graphs, transitivity is helpful to understand the…

Materials which feature bistable elements, hysterons, exhibit memory effects. Often these hysterons are difficult to observe or control directly. Here we introduce a mechanical metamaterial in which slender elements, interacting with…

The response of driven frustrated media stems from interacting hysteretic elements. We derive explicit mappings from networks of hysteretic springs to their abstract representation as interacting hysterons. These maps reveal how the…

Plasticity in amorphous materials, such as glasses, colloids, or granular materials, is mediated by local rearrangements called "soft spots". Experiments and simulations have shown that soft spots are two-state entities interacting via…

Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems. Although their importance is well recognized, a theoretical framework to describe…

Hysterons are elementary units of hysteresis that underlie many complex behaviors of non-equilibrium matter. Because models of interacting hysterons can describe disordered matter, this suggests that artificial systems could respond to…

Bi-stable objects that are pushed between states by an external field are often used as a simple model to study memory formation in disordered materials. Such systems, called hysterons, are typically treated quasistatically. Here, we…

In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of…

Temporal graphs model relationships among entities over time. Recent studies applied temporal graphs to abstract complex systems such as continuous communication among participants of social networks. Often, the amount of data is larger…

Transferring latent structure from one environment or problem to another is a mechanism by which humans and animals generalize with very little data. Inspired by cognitive and neurobiological insights, we propose graph schemas as a…

The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…

Models of coupled binary elements capture memory effects in complex dissipative materials, such as transient responses or sequential computing, when their interactions are chosen appropriately. However, for random interactions, self-loops -…

Although ubiquitous, interactions of groups of individuals (e.g., modern messaging applications, group meetings, or even a parliament discussion) are not yet thoroughly studied. Frequently, single-groups are modeled as critical-mass…

Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not…

Multiplex graphs, characterised by their layered structure, exhibit informative interdependencies within layers that are crucial for understanding complex network dynamics. Quantifying the interaction and shared information among these…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…