Related papers: Heteroclinic networks in coupled cell systems
Complex tables with multi-level headers, merged cells and heterogeneous layouts pose persistent challenges for LLMs in both understanding and reasoning. Existing approaches typically rely on table linearization or normalized grid modeling.…
We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of its incoming and outgoing directions exclude even the…
For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant under the network adjacency matrix. The complete lattice of synchrony subspaces of an $n$-cell regular network can be seen as an…
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…
Accurate early congestion prediction can prevent unpleasant surprises at the routing stage, playing a crucial character in assisting designers to iterate faster in VLSI design cycles. In this paper, we introduce a novel strategy to fully…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…
Network embedding in heterogeneous information networks (HINs) is a challenging task, due to complications of different node types and rich relationships between nodes. As a result, conventional network embedding techniques cannot work on…
Network embedding has recently attracted lots of attentions in data mining. Existing network embedding methods mainly focus on networks with pairwise relationships. In real world, however, the relationships among data points could go beyond…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
Recent advances in single cell sequencing and multi-omics techniques have significantly improved our understanding of biological phenomena and our capacity to model them. Despite combined capture of data modalities showing similar progress,…
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…
Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by…
A two-tier heterogeneous cellular network (HCN) with intra-tier and inter-tier dependence is studied. The macro cell deployment follows a Poisson point process (PPP) and two different clustered point processes are used to model the…
Temporal heterogeneous information network (temporal HIN) embedding, aiming to represent various types of nodes of different timestamps into low dimensional spaces while preserving structural and semantic information, is of vital importance…
Cell differentiation in multicellular organisms is a complex process whose mechanism can be understood by a reductionist approach, in which the individual processes that control the generation of different cell types are identified.…
We classify simple heteroclinic networks for a $\Gamma$-equivariant system in ${\mathbb R}^4$ with finite $\Gamma \subset {\rm O}(4)$, proceeding as follows: we define a graph associated with a given $\Gamma \subset {\rm O}(n)$ and identify…
Heterogeneous small cell networks with overlay femtocells and macrocell is a promising solution for future heterogeneous wireless cellular communications. However, great resilience is needed in heterogeneous small cells in case of…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…
Drug combinations are frequently used for the treatment of cancer patients in order to increase efficacy, decrease adverse side effects, or overcome drug resistance. Given the enormous number of drug combinations, it is cost- and…
Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…