Related papers: Hypergraph Diffusions and Resolvents for Norm-Base…
This paper develops analityc methods for investigating uniform hypergraphs. Its starting point is the spectral theory of 2-graphs, in particular, the largest and the smallest eigenvalues of 2-graphs. On the one hand, this simple setup is…
The analogy to heat diffusion has enhanced our understanding of information flow in graphs and inspired the development of Graph Neural Networks (GNNs). However, most diffusion-based GNNs emulate passive heat diffusion, which still suffers…
Collaborative filtering is a critical technique in recommender systems. It has been increasingly viewed as a conditional generative task for user feedback data, where newly developed diffusion model shows great potential. However, existing…
While Graph Neural Networks (GNNs) have recently become the de facto standard for modeling relational data, they impose a strong assumption on the availability of the node or edge features of the graph. In many real-world applications,…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a…
Image retrieval based on deep convolutional features has demonstrated state-of-the-art performance in popular benchmarks. In this paper, we present a unified solution to address deep convolutional feature aggregation and image re-ranking by…
Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This process was recently extended to hypergraphs. We introduce a variant of…
We develop a novel framework for modeling diffusion on complex networks by constructing Laplacian-like operators based on walks around a graph. Our approach introduces a parametric family of walk-based Laplacians that naturally incorporate…
For a connected weighted hypergraph, we give a randomized almost-linear-time solver for the Poisson problem for the cut-based hypergraph Laplacian in the natural input size $P=\sum_{e\in E}|e|$, the sum of hyperedge sizes. For every fixed…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
We study distributed optimization of finite-degree polynomial Laplacian spectral objectives under fixed topology and a global weight budget, targeting the collective behavior of the entire spectrum rather than a few extremal eigenvalues. By…
In this paper we provide nearly linear time algorithms for several problems closely associated with the classic Perron-Frobenius theorem, including computing Perron vectors, i.e. entrywise non-negative eigenvectors of non-negative matrices,…
We consider the problem of dominating set-based virtual backbone used for routing in asymmetric wireless ad-hoc networks. These networks have non-uniform transmission ranges and are modeled using the well-established disk graphs. The…
Graph generative models have broad applications in biology, chemistry and social science. However, modelling and understanding the generative process of graphs is challenging due to the discrete and high-dimensional nature of graphs, as…
Flood prediction is critical for emergency planning and response to mitigate human and economic losses. Traditional physics-based hydrodynamic models generate high-resolution flood maps using numerical methods requiring fine-grid…
High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
The Lagrangian of a hypergraph is a crucial tool for studying hypergraph extremal problems. Though Lagrangians of some special structure hypergraphs have closed-form solutions, it is a challenging problem to compute the Lagrangian of a…