Related papers: Graph Theoretic Framework of Dynamical Systems Thr…
The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying assumption: that the quintessential unit…
Algorithms which compute properties over graphs have always been of interest in computer science, with some of the fundamental algorithms, such as Dijkstra's algorithm, dating back to the 50s. Since the 70s there as been interest in…
We investigate graph transformations, defined using Datalog-like rules based on acyclic conjunctive two-way regular path queries (acyclic C2RPQs), and we study two fundamental static analysis problems: type checking and equivalence of…
This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length $k$ in a graph with $N\geq k$ edges and no loops. Our proof relies on a construction of a number of terminating algorithms that…
The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena.…
Signal processing on directed graphs (digraphs) is problematic, since the graph shift, and thus associated filters, are in general not diagonalizable. Furthermore, the Fourier transform in this case is now obtained from the Jordan…
Hilbert-space fragmentation provides a mechanism for ergodicity breaking in quantum many-body systems even in the absence of disorder, leading to dynamically disconnected sectors and strong memory of initial conditions. However, identifying…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…
This work aims to make it easier for a specialist in one field to find and explore ideas from another field which may be useful in solving a new problem arising in his practice. It presents a methodology which serves to represent the…
A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…
This paper studies the algebraic boundary of the elliptope $\mathcal{E}(G)$ of a graph $G$. In particular, we completely characterize the algebraic boundary of $\mathcal{E}(G)$ when $G$ is cycle completable. In this case, the boundary is a…
We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…
In this paper we introduce the concept of generalized d-graph (admitting cycles) as special dependency-graphs for modelling dynamic programming (DP) problems. We describe the d-graph versions of three famous single-source shortest…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…
We introduce the notion of combinatorial encoding of continuous dynamical systems and suggest the first examples, which are the most interesting and important, namely, the combinatorial encoding of a Bernoulli process with continuous state…
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…