Related papers: Primitive operations for the construction and reor…
We study the class of all finite directed graphs up to primitive positive constructability. The resulting order has a unique greatest element, namely the graph $P_1$ with one vertex and no edges. The graph $P_1$ has a unique greatest lower…
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…
At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships and structures. Traditional graph models are often static, lacking dynamic and autonomous behavioral…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of…
Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…
Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
Statisticians and quantitative neuroscientists have actively promoted the use of independence relationships for investigating brain networks, genomic networks, and other measurement technologies. Estimation of these graphs depends on two…
To any inhibition-dominated threshold-linear network (TLN) we can associate a directed graph that captures the pattern of strong and weak inhibition between neurons. Robust motifs are graphs for which the structure of fixed points in the…
Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational…
Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem…
Preservers and additive spanners are sparse (hence cheap to store) subgraphs that preserve the distances between given pairs of nodes exactly or with some small additive error, respectively. Since real-world networks are prone to failures,…
Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures supported on the birth-death plane and endowed with an…
The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, states that any two almost optimal graphs of the same order $n$…
The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
Conditional graph generation tasks involve training a model to generate a graph given a set of input conditions. Many previous studies employ autoregressive models to incrementally generate graph components such as nodes and edges. However,…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…