Related papers: Heteroclinic networks in coupled cell systems
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
A hypergraph is a data structure composed of nodes and hyperedges, where each hyperedge is an any-sized subset of nodes. Due to the flexibility in hyperedge size, hypergraphs represent group interactions (e.g., co-authorship by more than…
Heterogeneous, interconnected, systems-level, molecular data have become increasingly available and key in precision medicine. We need to utilize them to better stratify patients into risk groups, discover new biomarkers and targets,…
Millimeter wave (mmWave) links have the potential to offer high data rates and capacity needed in fifth generation (5G) networks, however they have very high penetration and path loss. A solution to this problem is to bring the base station…
Over the last decade, the growing amount of UL and DL mobile data traffic has been characterized by substantial asymmetry and time variations. Dynamic time-division duplex (TDD) has the capability to accommodate to the traffic asymmetry by…
Smooth planar vector fields containing two hyperbolic saddles may possess contours formed by heteroclinic connections between these saddles. We present an overview of the bifurcations of these contours based on papers by J.W. Reyn and A.V.…
Heterogeneous base stations (e.g. picocells, microcells, femtocells and distributed antennas) will become increasingly essential for cellular network capacity and coverage. Up until now, little basic research has been done on the…
The heterogeneous network is a robust data abstraction that can model entities of different types interacting in various ways. Such heterogeneity brings rich semantic information but presents nontrivial challenges in aggregating the…
Hypergraph data, which capture multi-way interactions among entities, are increasingly prevalent in the big data era. Generating new hyperlinks from an observed, usually high-dimensional hypergraph is an important yet challenging task with…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
Cell association in cellular networks is an important aspect that impacts network capacity and eventually quality of experience. The scope of this work is to investigate the different and generalized cell association (CAS) strategies for…
The recent reconstruction of the Drosophila brain provides a neural network of unprecedented size and level of details. In this work, we study the geometrical properties of this system by applying network embedding techniques to the graph…
In this paper we present a computer-assisted procedure for proving the existence of transverse heteroclinic orbits connecting hyperbolic equilibria of polynomial vector fields. The idea is to compute high-order Taylor approximations of…
A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
A coupled cell network is a type of ordinary differential equation $\dot x(t)=f(x(t))$, with structural constraints on the vector field $f$, encoded in a directed graph, whose cells and arrows are labeled by type. The generated dynamics can…
Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domains for practical applications. They also provide a…
For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell…
The application of single-cell molecular profiling coupled with spatial technologies has enabled charting cellular heterogeneity in reference tissues and in disease. This new wave of molecular data has highlighted the expected diversity of…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…