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We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
We solve inverse problems from the D-N map for the quantum graph on a finite domain in a square lattice and that on a hexagonal lattice, as well as inverse scattering problems from the S-matrix for a locally perturbed square lattice and a…
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…
Two problems in the search of metric characteristics on weighted undirected graphs with non-negative edge weights are being considered. The first problem: a weighted undirected graph with non-negative edge weight is given. The radius,…
Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an…
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a…
We study the following inverse graph-theoretic problem: how many vertices should a graph have given that it has a specified value of some parameter. We obtain asymptotic for the minimal number of vertices of the graph with the given number…
The graph isomorphism (GI) problem is the computational problem of finding a permutation of vertices of a given graph $G_1$ that transforms $G_1$ to another given graph $G_2$ and preserves the adjacency. In this work, we propose a quantum…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
We analyze the inverse problem of recovering geometric information from the return map induced by a round-trip between a convex core C and an admissible domain. This process defines a discrete dynamical system on the boundary of C governed…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
Anomaly detection is a crucial task in complex distributed systems. A thorough understanding of the requirements and challenges of anomaly detection is pivotal to the security of such systems, especially for real-world deployment. While…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
Topological concepts open many new horizons for photonic devices, from integrated optics to lasers. The complexity of large scale topological devices asks for an effective solution of the inverse problem: how best to engineer the topology…
We determine the optimum topology of quasi-one dimensional nonlinear optical structures using generalized quantum graph models. Quantum graphs are relational graphs endowed with a metric and a multiparticle Hamiltonian acting on the edges,…
We consider weighted, directed graphs with a notion of absorption on the vertices, related to absorbing random walks on graphs. We define a generalized inverse of the graph Laplacian, called the absorption inverse, that reflects both the…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…