相关论文: Making Laplacians commute

Evaluating the similarity of non-rigid shapes with significant partiality is a fundamental task in numerous computer vision applications. Here, we propose a novel axiomatic method to match similar regions across shapes. Matching similar…

In this paper, we consider a distributed model predictive control (MPC) algorithm for coordinated path-following. Relying on the time-critical cooperative path-following framework, which decouples space and time and reduces the coordination…

Combinatorial optimization problem (COP) is difficult to solve because of the massive number of local optimal solutions in his solution space. Various methods have been put forward to smooth the solution space of COPs, including homotopic…

The analytic dilation method was originally used in the context of many body Schr\"odinger operators. In this paper we adapt it to the context of compatible Laplacians on complete manifolds with corners of codimension two. As in the…

This paper studies the problem of distributed formation maneuver control of multi-agent systems via complex Laplacian. We will show how to change the translation, scaling, rotation, and also the shape of formation continuously by only…

Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of…

The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using…

This paper proposes a novel approach for designing channel estimation, beamforming and scheduling jointly for wideband massive multiple input multiple output (MIMO) systems. With the proposed approach, we first quantify the maximum number…

The task of flying in tight formations is challenging for teams of quadrotors because the complex aerodynamic wake interactions can destabilize individual team members as well as the team. Furthermore, these aerodynamic effects are highly…

The community detection problem on multilayer networks have drawn much interest. When the nodal covariates ar also present, few work has been done to integrate information from both sources. To leverage the multilayer networks and the…

Optical proximity correction (OPC) is a vital step to ensure printability in modern VLSI manufacturing. Various OPC approaches based on machine learning have been proposed to pursue performance and efficiency, which are typically…

We show that bulk quantities localized on a minimal surface homologous to a boundary region correspond in the CFT to operators that commute with the modular Hamiltonian associated with the boundary region. If two such minimal surfaces…

In this largely expository note, we discuss the mapping properties of the Laplacian (and other geometric elliptic operators) in spaces with an isolated conical singularity following the approach developed by B.-W. Schulze and collaborators.…

In this paper, we consider a cooperative communication network where multiple low-Earth-orbit (LEO) satellites provide services to multiple ground users (GUs) cooperatively at the same time and on the same frequency. The multi-satellite…

Finding appropriate low dimensional representations of high-dimensional multi-modal data can be challenging, since each modality embodies unique deformations and interferences. In this paper, we address the problem using manifold learning,…

This paper tackles the problem of downlink data transmission in massive multiple-input multiple-output (MIMO) systems where user equipments (UEs) exhibit high spatial correlation and channel estimation is limited by strong pilot…

In this work, we perform a careful study of an special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to…

We consider the standard hypergeometric differential operator $D$ regarded as an operator on the complex plane $C$ and the complex conjugate operator $\overline D$. These operators formally commute and are formally adjoint one to another…

A spectral minimal partition of a manifold is its decomposition into disjoint open sets that minimizes a spectral energy functional. It is known that bipartite spectral minimal partitions coincide with nodal partitions of Courant-sharp…

A proof of the optimality of the eigenfunctions of the Laplace-Beltrami operator (LBO) in representing smooth functions on surfaces is provided and adapted to the field of applied shape and data analysis. It is based on the Courant-Fischer…