Related papers: Topological metric detects hidden order in disorde…
Previous symmetry-based database searches have already revealed ubiquitous band topology in nature, while the destiny of band topology under symmetry-breaking is yet to be studied comprehensively. Here we first develop a framework allowing…
During colony growth, complex interactions regulate the bacterial orientation, leading to the formation of large-scale ordered structures, including topological defects and microdomains. These structures may benefit bacterial strains,…
Topological event detection allows for the distributed computation of homology by focusing on local changes occurring in a network over time. In this paper, a model for the monitoring of topological events in dynamically changing regions…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
We propose a new fast method of measuring distances between large numbers of related high dimensional datasets called the Diffusion Earth Mover's Distance (EMD). We model the datasets as distributions supported on common data graph that is…
Similarity metrics are central in the theory of large networks and graph limits. For bounded-degree graphs, the Benjamini--Schramm metric records the distribution of rooted neighbourhoods, while the stronger colored-neighbourhood metric…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
Networks representing social, biological, technological or other systems are often characterized by higher-order interaction involving any number of nodes. Temporal hypergraphs are given by ordered sequences of hyperedges representing sets…
The Eden cell growth model is a simple discrete stochastic process which produces a "blob" in $\mathbb{R}^d$: start with one cube in the regular grid, and at each time step add a neighboring cube uniformly at random. This process has been…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
How a single fertilized cell gives rise to a complex array of specialized cell types in development is a central question in biology. The cells grow, divide, and acquire differentiated characteristics through poorly understood molecular…
The Extra-Cellular-Matrix (ECM) is a complex interconnected 3D network that provides structural support for the cells and tissues and defines organ architecture key for their healthy functioning. However, the intimate mechanisms by which…
A first principles approach to the theoretical description of the development of biological forms, from a fertilized egg to a functioning embryo, remains a central challenge to applied physics and theoretical biology. Rather than refer to…
Latent world models can contain the state needed for control, yet their terminal-cost interface can expose the planner to the wrong decision-relevant information. In common latent MPC, candidate sequences are ranked by Euclidean distance…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
Networks are a fundamental and flexible way of representing various complex systems. Many domains such as communication, citation, procurement, biology, social media, and transportation can be modeled as a set of entities and their…
Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…
Structural cellular materials in nature, such as wood, trabecular bone, corals, and dentin combine complex biological functions with structural roles, such as skeletal support and impact protection1,2. They feature complex structural…