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Many living and non-living complex systems can be modeled and understood as collective systems made of heterogeneous components that self-organize and generate nontrivial morphological structures and behaviors. This chapter presents a brief…

In biological systems, the growth of cells, tissues, and organs is influenced by mechanical cues. Locally, cell growth leads to a mechanically heterogeneous environment as cells pull and push their neighbors in a cell network. Despite this…

We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity,…

The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or…

Efforts to improve the adversarial robustness of convolutional neural networks have primarily focused on developing more effective adversarial training methods. In contrast, little attention was devoted to analyzing the role of…

Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is…

We investigate the interplay between pre-stress and mechanical properties in random elastic networks. To do this in a controlled fashion, we introduce an algorithm for creating random freestanding frames that support exactly one state of…

Combinatorial mechanical metamaterials feature spatially textured soft modes that yield exotic and useful mechanical properties. While a single soft mode often can be rationally designed by following a set of tiling rules for the building…

The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we…

Avalanches are rapid cascades of rearrangements driven by cooperative flipping of hysteretic local elements. Here we show that flipping dynamics and race conditions -- where multiple elements become unstable simultaneously -- give rise to…

In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological…

Mechanical metamaterials, whose unique mechanical properties stem from their structural design rather than material constituents, are gaining popularity in engineering applications. In particular, recent advances in self-assembly techniques…

On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these…

Soils and sediments are soft, amorphous materials with complex microstructures and mechanical properties, that are also building blocks for industrial materials such as concrete. These Earth-mediated materials evolve under prolonged…

A common trait of complex systems is that they can be represented by means of a network of interacting parts. It is, in fact, the network organisation (more than the parts) what largely conditions most higher-level properties, which are not…

From atomic crystals to bird flocks, most forms of order are captured by the concept of spontaneous symmetry breaking. This paradigm was challenged by the discovery of topological order, in materials where the number of accessible states is…

Unravelling current complex food systems is relevant for their adjustment and redesign under the current changing climate conditions. Redesign may be necessitated by migration of people and changes of locations of major agri-food…

To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…

Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness…

Metamaterials are artificially engineered structures that manipulate electromagnetic waves, having optical properties absent in natural materials. Recently, machine learning for the inverse design of metamaterials has drawn attention.…