相关论文: Graph kinematics of discrete physical objects: bey…
It is proposed that a complete understanding of two-dimensional quantum gravity and its emergence in random matrix models requires fully embracing {\it both} Wigner (statistics) and 't Hooft (geometry). Using non-perturbative definitions of…
Learning data-efficient object dynamics models for robotic manipulation remains challenging, especially for deformable objects. A popular approach is to model objects as sets of 3D particles and learn their motion using graph neural…
Particle physics models where there are large hidden extra dimensions are currently on the focus of an intense activity. The main reason is that these large extra dimensions may come with a TeV scale for quantum gravity (or string theory)…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Let ${\cal G}=(G,w)$ be a weighted simple finite connected graph, that is, let $G$ be a simple finite connected graph endowed with a function $w$ from the set of the edges of $G$ to the set of real numbers. For any subgraph $G'$ of $G$, we…
The use in the action integral of a volume element of the form $\Phi d^{D}x$ where $\Phi$ is a metric independent measure can give new interesting results in all types of known generally coordinate invariant theories: (1) 4-D theories of…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with pressure-driven flows, incorporates a convex energy…
Graph-structured data arise ubiquitously in many application domains. A fundamental problem is to quantify their similarities. Graph kernels are often used for this purpose, which decompose graphs into substructures and compare these…
For each positive integer $n$, let $G_n$ be the graph of integer partitions of $n$, where two partitions are adjacent if one is obtained from the other by an elementary transfer of a cell in the Ferrers diagram, followed by reordering.…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
A consistent quantum theory of gravity has remained elusive ever since the emergence of General Relativity and Quantum Field Theory. Attempts to date have not yielded a candidate that is either free from problematic theoretical…
Treewidth is a well-known graph invariant with multiple interesting applications in combinatorics. On the practical side, many NP-complete problems are polynomial-time (sometimes even linear-time) solvable on graphs of bounded treewidth. On…
In this paper we describe a physical problem, based on electromagnetic fields, whose topological constraints are higher dimensional versions of Kirchhoff's laws, involving $2-$ simplicial complexes embedded in $\mathbb{R} ^3$ rather than…
The Perron value $\rho(T)$ of a rooted tree $T$ has a central role in the study of the algebraic connectivity and characteristic set, and it can be considered a weight of spectral nature for $T$. A different, combinatorial weight notion for…
In the Metric Dimension problem, one asks for a minimum-size set $R$ of vertices such that for any pair of vertices of the graph, there is a vertex from $R$ whose two distances to the vertices of the pair are distinct. This problem has…
The problem of realizing finite metric spaces in terms of weighted graphs has many applications. For example, the mathematical and computational properties of metrics that can be realized by trees have been well-studied and such research…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
We introduce the tree distance, a new distance measure on graphs. The tree distance can be computed in polynomial time with standard methods from convex optimization. It is based on the notion of fractional isomorphism, a characterization…
We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and…