相关论文: Making Laplacians commute

The problem of formulating a correct notion of Laplacian on compact quantum groups (CQGs) has long been recognized as both fundamental and nontrivial. Existing constructions typically rely on selecting a specific first-order differential…

As a key enabler for massive machine-type communications (mMTC), spatial multiplexing relies on massive multiple-input multiple-output (mMIMO) technology to serve the massive number of user equipments (UEs). To exploit spatial multiplexing,…

Combinatorial optimization problems (COPs) are an important research topic in various fields. In recent times, there have been many attempts to solve COPs using deep learning-based approaches. We propose a novel neural network model that…

We present a new clustering algorithm that is based on searching for natural gaps in the components of the lowest energy eigenvectors of the Laplacian of a graph. In comparing the performance of the proposed method with a set of other…

This paper introduces a Koopman-enhanced distributed switched model predictive control (SMPC) framework for safe and scalable navigation of quadrotor unmanned aerial vehicles (UAVs) in dynamic environments with moving obstacles. The…

In this work, we consider the spatial search for a general marked state on graphs by continuous time quantum walks. As a simplest case, we compute the amplitude expression of the search for the multi-vertex uniform superposition state on…

A spatially correlated broadcast setting with M antennas at the base station and M users (each with a single antenna) is considered. We assume that the users have perfect channel information about their links and the base station has only…

We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the single-particle eigenstates are related to discrete orthogonal…

Improving charge carrier mobilities in organic semiconductors is a challenging task that has hitherto primarily been tackled by empirical structural tuning of promising core compounds. Knowledge-based methods can greatly accelerate such…

In the following, we give an explicit construction of a Laplacian on the Minkowski curve, with energy forms that bear the geometric characteristic of the structure. The spectrum of the Laplacian is obtained by means of spectral decimation.

One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a radically new…

Dynamical Systems (DS) are fundamental to the modeling and understanding time evolving phenomena, and have application in physics, biology and control. As determining an analytical description of the dynamics is often difficult, data-driven…

This paper proposes continuum deformation as a strategy for controlling the collective motion of a multiple quadcopter system (MQS) carrying a common payload. Continuum deformation allows expansion and contraction of inter-agent distances…

Signed networks allow to model positive and negative relationships. We analyze existing extensions of spectral clustering to signed networks. It turns out that existing approaches do not recover the ground truth clustering in several…

In this paper we offer a computational approach to the spectral function for a finite family of commuting operators, and give applications. Motivated by questions in wavelets and in signal processing, we study a problem about spectral…

Since the year 2000, adaptive optics (AO) has seen the emergence of a variety of new concepts addressing particular science needs; multiconjugate adaptive optics (MCAO) is one of them. By correcting the atmospheric turbulence in 3D using…

For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…

We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…

In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…

We consider a Laplacian on periodic discrete graphs. Its spectrum consists of a finite number of bands. In a class of periodic 1-forms, i.e., functions defined on edges of the periodic graph, we introduce a subclass of minimal forms with a…