Related papers: An Adaptive Grid Algorithm for Computing the Homol…
We present a combinatorial proof for the existence of the sign refined grid homology in lens spaces, and a self contained proof that $\partial_{\mathbb{Z}}^2 = 0$. We also present a Sage program that computes $\widehat{\mathrm{GH}}…
In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the…
Group synchronization aims to recover the group elements from their noisy pairwise measurements. It has found many applications in community detection, clock synchronization, and joint alignment problem. This paper focuses on the orthogonal…
We generalize some of the functional (hyper-circle) a posteriori estimates from finite element settings to general graphs or Hilbert space settings. We provide several theoretical results in regard to the generalized a posteriori error…
We consider the problem of adaptation to the margin and to complexity in binary classification. We suggest an exponential weighting aggregation scheme. We use this aggregation procedure to construct classifiers which adapt automatically to…
Semi-supervised clustering problems focus on clustering data with labels. In this paper,we consider the semi-supervised hypergraph problems. We use the hypergraph related tensor to construct an orthogonal constrained optimization model. The…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
Deep learning method is of great importance in solving partial differential equations. In this paper, inspired by the failure-informed idea proposed by Gao et.al. (SIAM Journal on Scientific Computing 45(4)(2023)) and as an improvement, a…
It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across \Omega(n \log n) coset states. One of the only known models…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
Four adaptations of the smoothed aggregation algebraic multigrid (SA-AMG) method are proposed with an eye towards improving the convergence and robustness of the solver in situations when the discretization matrix contains many weak…
Automatic segmentation of an image to identify all meaningful parts is one of the most challenging as well as useful tasks in a number of application areas. This is widely studied. Selective segmentation, less studied, aims to use limited…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
For any undirected graph $G=(V,E)$ and a set $E_W$ of candidate edges with $E\cap E_W=\emptyset$, the $(k,\gamma)$-spectral augmentability problem is to find a set $F$ of $k$ edges from $E_W$ with appropriate weighting, such that the…
In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Numerical solutions of hyperbolic partial differential equations(PDEs) are ubiquitous in science and engineering. Method of lines is a popular approach to discretize PDEs defined in spacetime, where space and time are discretized…
In this work, we propose a novel adaptive grid mapping approach, the Adaptive Patched Grid Map, which enables a situational aware grid based perception for autonomous vehicles. Its structure allows a flexible representation of the…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…