Related papers: Graph theory approach to exceptional points in wav…
We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in this respect, namely quad-graphs, the cellular…
The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros…
Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…
We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing…
The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high…
Geometrically decorated two-dimensional (2D) discrete surfaces can be more effective than conventional smooth reflectors in managing wave radiation. Constructive non-specular wave scattering permits the scattering angle to be other than…
Exceptional points (EPs), singularities in non-Hermitian systems where eigenvalues and eigenstates coalesce, exhibit a dramatically enhanced response to perturbations compared to Hermitian degeneracies. This makes them exceptional…
We consider the scattering theory for the Schr\"odinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves…
We analyze graphs attaining the extreme values of various spectral indices in the class of all simple connected graphs, as well as in the class of graphs which are not complete multipartite graphs. We also present results on density of…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number.…
We present a new method for the control of waves based on inverse multiple scattering theory. Conceived as a generalization of the concept of metagrating, we call metaclusters to a finite set of scatterers whose position and properties are…
This paper studies the problem of detecting anomalous graphs using a machine learning model trained on only normal graphs, which has many applications in molecule, biology, and social network data analysis. We present a self-discriminative…
Detecting anomalies in a temporal sequence of graphs can be applied is areas such as the detection of accidents in transport networks and cyber attacks in computer networks. Existing methods for detecting abnormal graphs can suffer from…
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…
The challenges of graph stream algorithms are twofold. First, each edge needs to be processed only once, and second, it needs to work on highly constrained memory. Diffusion degree is a measure of node centrality that can be calculated (for…
Two damped coupled oscillators have been used to demonstrate the occurrence of exceptional points in a purely classical system. The implementation was achieved with electronic circuits in the kHz-range. The experimental results perfectly…
This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…
We study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs. A frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators…
We introduce and analyse ensembles of 2-regular random graphs with a tuneable distribution of short cycles. The phenomenology of these graphs depends critically on the scaling of the ensembles' control parameters relative to the number of…