Related papers: Topological portraits of multiscale coordination d…
A novel viewpoint, i.e., adaptive synchronization, is proposed to explore collective rhythm observed in many complex, self-organizing systems. We show that a simple adaptive coupling is able to tip arrays of oscillators towards collective…
Understanding the dynamical behavior of complex systems is of exceptional relevance in everyday life, from biology to economy. In order to describe the dynamical organization of complex systems, existing methods require the knowledge of the…
Graphs serve as powerful tools for modeling pairwise interactions in diverse fields such as biology, material science, and social networks. However, they inherently overlook interactions involving more than two entities. Simplicial…
Robust online multi-person tracking requires the correct associations of online detection responses with existing trajectories. We address this problem by developing a novel appearance modeling approach to provide accurate appearance…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
Topological representations are rapidly becoming a popular way to capture and encode higher-order interactions in complex systems. They have found applications in disciplines as different as cancer genomics, brain function, and…
A coupled map lattice whose topology changes at each time step is studied. We show that the transversal dynamics of the synchronization manifold can be analyzed by the introduction of effective dynamical quantities. These quantities are…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
Effective human-robot teaming is crucial for the practical deployment of robots in human workspaces. However, optimizing joint human-robot plans remains a challenge due to the difficulty of modeling individualized human capabilities and…
We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the…
Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key mathematical techniques include persistent homology and the…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…
The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter. The global nature of topological ordering makes these phases robust and hence promising for applications. However, the…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
The interaction topology among the constituents of a complex network plays a crucial role in the network's evolutionary mechanisms and functional behaviors. However, some network topologies are usually unknown or uncertain. Meanwhile,…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…