相关论文: Electrical varieties as vertex integrable statisti…
The identification of distribution network topology and parameters is a critical problem that lays the foundation for improving network efficiency, enhancing reliability, and increasing its capacity to host distributed energy resources.…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
The response matrix of a resistor network is the linear map from the potential at the boundary vertices to the net current at the boundary vertices. For circular planar resistor networks, Curtis, Ingerman, and Morrow have given a necessary…
We present a connection between two seemingly disparate fields: VC-theory and graph theory. This connection yields natural correspondences between fundamental concepts in VC-theory, such as shattering and VC-dimension, and well-studied…
On a non-compact, smooth, connected, boundaryless, complete Riemannian manifold $(M,g)$, one can define its ideal boundary by rays (or equivalently, Busemann functions). From the viewpoint of Mather theory, boundary elements could be…
We introduce a novel machine learning based framework for discovering integrable models. Our approach first employs a synchronized ensemble of neural networks to find high-precision numerical solution to the Yang-Baxter equation within a…
We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the…
Ensemble models of graphs are one of the most important theoretical tools to study complex networks. Among them, exponential random graphs (ERGs) have proven to be very useful in the analysis of social networks. In this paper we develop a…
Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting…
We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form…
Let $\grad$, $\curl$, and $\dv$ be the graph-theoretic analogues of the gradient, curl, and divergence operators from multivariate calculus. The graph Laplacian $-\dv \grad$ gives rise to the celebrated Laplacian matrix, while the matrix…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…
Assortativity, i.e. the tendency of a vertex to bond with another based on their similarity, such as degree, is an important network characteristic that is well-known to be relevant for the network's robustness against attacks. Commonly it…
Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation,…
We develop the theory of torsional rigidity -- a quantity routinely considered for Dirichlet Laplacians on bounded planar domains -- for Laplacians on metric graphs with at least one Dirichlet vertex. Using a variational characterization…
We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses $U_q\big(\mathfrak{sl}(2)\big)$ invariance due to the choice of open boundary conditions imposed. An…
We present a method based on graph theory for evaluation of the inelastic propensity rules for molecules exhibiting complete destructive quantum interference in their elastic transmission. The method uses an extended adjacency matrix…
A key challenge in network science is the detection of communities, which are sets of nodes in a network that are densely connected internally but sparsely connected to the rest of the network. A fundamental result in community detection is…