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In this paper, we introduce the concept of monotone Gregus-\'Ciri\'c-contraction mappings in weighted digraphs. Then we establish a fixed point theorem for monotone Gregus-\'Ciri\'c-contraction mappings defined in convex weighted digraphs.
This paper treats the global stabilization problem of continuous-time switched affine systems that have rank-deficient convex combinations of their dynamic matrices. For these systems, the already known set of attainable equilibrium points…
Bifurcations are one of the most remarkable features of dynamical systems. Corral et al. [Sci. Rep. 8(11783), 2018] showed the existence of scaling laws describing the transient (finite-time) dynamics in discrete dynamical systems close to…
We study the two-player communication problem of determining whether two vertices $x, y$ are nearby in a graph $G$, with the goal of determining the graph structures that allow the problem to be solved with a constant-cost randomized…
A graph is weakly $2$-colored if the nodes are labeled with colors black and white such that each black node is adjacent to at least one white node and vice versa. In this work we study the distributed computational complexity of weak…
We provide an overview of the state-of-the-art in the area of sequential change-point detection assuming discrete time and known pre- and post-change distributions. The overview spans over all major formulations of the underlying…
The dynamical properties of finite dynamical systems (FDSs) have been investigated in the context of coding theoretic problems, such as network coding and index coding, and in the context of hat games, such as the guessing game and…
At a critical point of a second order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can…
We extend to infinite graphs the matroidal characterization of finite graph duality, that two graphs are dual iff they have complementary spanning trees in some common edge set. The naive infinite analogue of this fails. The key in an…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…
We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes…
In this article we study algorithmic synthesis of the class of stabilizing switching signals for discrete-time switched linear systems proposed in [12]. A weighted digraph is associated in a natural way to a switched system, and the…
This paper investigates the problem of dynamical sampling for graph signals influenced by a constant source term. We consider signals evolving over time according to a linear dynamical system on a graph, where both the initial state and the…
In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we…
Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…
Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of…
The labeling of point features on a map is a well-studied topic. In a static setting, the goal is to find a non-overlapping label placement for (a subset of) point features. In a dynamic setting, the set of point features and their…
Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network…
We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…