The Hadwiger–Nelson problem concerns the chromatic number of these graphs.An intersection graph is a graph in which each vertex is associated with a set and in which vertices are connected by edges whenever the corresponding sets have a nonempty intersection. When the sets are geometric objects,...
Opinion formation cannot be modeled solely as an ideological deduction from a set of principles; rather, repeated social interactions and logic constraints among statements are consequential in the construct of belief systems. We address three basic ques
In the inspector there are a number of variables. The first one is named "Convex", it sets if the convex hull of the points should be calculated or if the polygon should be used as-is. Using the convex hull is faster when applying the changes to the graph, but with a non-convex po...
The Δ-hull number of G is the minimum cardinality of a set S such that 〈S〉Δ=V(G) and is denoted by hΔ(G). The Δ-interval function and the associated Δ-convexity were introduced by Mulder in [25]. In [24], the Δ-convex sets, where they were called Δ-closed sets, ...
Cancer subtypes identification is one of the critical steps toward advancing personalized anti-cancerous therapies. Accumulation of a massive amount of multi-platform omics data measured across the same set of samples provides an opportunity to look into
choice() # sets of closed switches in unsafe power flows >>> tl.draw(closed_switches) New configuration must be one of the safe flows, and must be realized with least switch operations. We put a score (edge weight) on a new switch status if it is inconsistent with the current status,...
However, in practice, the types of cost functions and constraints allowed by the communication format are usually restricted to functions that facilitate the dispatch problem’s solution (e.g. (4)). In contrast, the actual costs and constraints (2b) may be strongly non-convex. Therefore, the...
Zhang, Convex sets in graphs. Congr. Numer. 136, 19–32 (1999) MathSciNet MATH Google Scholar G. Chartrand, P. Zhang, On the chromatic dimension of a graph. Congr. Numer. 145, 97–108 (2000) MathSciNet MATH Google Scholar G. Chartrand, P. Zhang, The theory and applications of...
architecture and not necessarily on the fully distributed architecture. Instead of clients communicating with the same server, we split the load among multiple servers. Fig. 1 The graph federated learning architecture Full size image With this architecture, we associate a convex optimization problem ...
Machine learning plays an increasingly important role in many areas of chemistry and materials science, being used to predict materials properties, accelerate simulations, design new structures, and predict synthesis routes of new materials. Graph neural networks (GNNs) are one of the fastest growing ...