Related papers: Graphical Symplectic Algebra
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
Self-stabilizing algorithms are an important because of their robustness and guaranteed convergence. Starting from any arbitrary state, a self-stabilizing algorithm is guaranteed to converge to a legitimate state.Those algorithms are not…
Recent work at the intersection of formal language theory and graph theory has explored graph grammars for graph modeling. However, existing models and formalisms can only operate on homogeneous (i.e., untyped or unattributed) graphs. We…
Let $k$ be a field. We characterize the group schemes $G$ over $k$, not necessarily affine, such that $\mathsf{D}_{\mathrm{qc}}(B_kG)$ is compactly generated. We also describe the algebraic stacks that have finite cohomological dimension in…
A new family of strongly regular graphs, called the general symplectic graphs $Sp(2\nu, q)$, associated with nonsingular alternate matrices is introduced. Their parameters as strongly regular graphs, their chromatic numbers as well as their…
We introduce the Hierarchical Unified Graph Representation (HUGR): a novel graph based intermediate representation for mixed quantum-classical programs. HUGR's design features high expressivity and extensibility to capture the capabilities…
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…
This thesis provides an extension of the work of Dirk Kreimer and Alain Connes on the Hopf algebra structure of Feynman graphs and renormalization to general graphs. Additionally, an algebraic structure of the asymptotics of formal power…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
Here we give brief account of hermitian symplectic spaces, showing that they are intimately connected to symmetric as well as self-adjoint extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange…
Graph neural networks are attractive for learning properties of atomic structures thanks to their intuitive graph encoding of atoms and bonds. However, conventional encoding does not include angular information, which is critical for…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of…
In this paper we relate a well-known in symplectic geometry compactification of the space of symmetric bilinear forms considered as a chart of the Lagrangian Grassmannian to the specific compactifications of the space of electrical networks…
The purpose of this paper is to shed a new light on classical constructions in enumerative geometry from the view point of derived algebraic geometry. We first prove that the cosection localized virtual cycle of a quasi-smooth derived…
This paper develops an algebraic multigrid preconditioner for the graph Laplacian. The proposed approach uses aggressive coarsening based on the aggregation framework in the setup phase and a polynomial smoother with sufficiently large…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
The recently developed 3D graphic statics (3DGS) lacks a rigorous mathematical definition relating the geometrical and topological properties of the reciprocal polyhedral diagrams as well as a precise method for the geometric construction…