Related papers: Combinatorial approximations of dynamical systems:…

A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…

We describe a general approach for maximum a posteriori (MAP) inference in a class of discrete-continuous factor graphs commonly encountered in robotics applications. While there are openly available tools providing flexible and easy-to-use…

Low density graphs are considered to be a realistic graph class for modelling road networks. It has advantages over other popular graph classes for road networks, such as planar graphs, bounded highway dimension graphs, and spanners. We…

We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…

Unsupervised representation learning for dynamic graphs has attracted a lot of research attention in recent years. Compared with static graph, the dynamic graph is a comprehensive embodiment of both the intrinsic stable characteristics of…

The domatic number of a graph is the maximum number of vertex disjoint dominating sets that partition the vertex set of the graph. In this paper we consider the fractional variant of this notion. Graphs with fractional domatic number 1 are…

Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…

Chaotic hyperbolic dynamical systems enjoy a surprising degree of rigidity, a fact which is well known in the mathematics community but perhaps less so in theoretical physics circles. Low-dimensional hyperbolic systems are either conjugate…

We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…

Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs.…

Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…

A metrized graph is a compact singular 1-manifold endowed with a metric. A given metrized graph can be modelled by a family of weighted combinatorial graphs. If one chooses a sequence of models from this family such that the vertices become…

We identify the graph data structure, frontiers, operators, an iterative loop structure, and convergence conditions as essential components of graph analytics systems based on the native-graph approach. Using these essential components, we…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

We present a probabilistic framework for modeling structured spatiotemporal dynamics from sparse observations, focusing on cardiac motion. Our approach integrates neural ordinary differential equations (NODEs), graph neural networks (GNNs),…

Scene graphs represent the key components of a scene in a compact and semantically rich way, but are difficult to build during incremental SLAM operation because of the challenges of robustly identifying abstract scene elements and…

Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…

The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of 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…

Understanding the global dynamics of a robot controller, such as identifying attractors and their regions of attraction (RoA), is important for safe deployment and synthesizing more effective hybrid controllers. This paper proposes a…