Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety potential applications, particular optics and photonics. However, experimental realization is notoriously difficult. Recently, Zhong et al. [Q. Zhong, J. Kou, \ifmmode \mbox{\c{S}}\else \c{S}\fi{}. K. \"Ozdemir, R. El-Ganainy, Phys. Rev. Lett. 125, 203602 (2020)] ...

This paper presents a tensor decomposition (TD) based reduced-order model of the hierarchical deep-learning neural networks (HiDeNN). The proposed HiDeNN-TD method keeps advantages both HiDeNN and TD methods. automatic mesh adaptivity makes more accurate than finite element (FEM) conventional proper generalized (PGD) TD, using fraction FEM degrees freedom. work focuses on theoretical foundation...

Hybrid Planning combines Hierarchical Task Network (HTN) planning with concepts known from Partial-Order Causal-Link (POCL) planning. We introduce novel heuristics for Hybrid Planning that estimate the number of necessary modifications to turn a partial plan into a solution. These estimates are based on the task decomposition graph that contains all decompositions of the abstract tasks in the p...

We present an algorithm for simulating diffuse interreflection in scenes composed of highly tessellated objects. The method is a higher order extension of the face cluster radiosity technique. It combines face clustering, multiresolution visibility, vector radiosity, and higher order bases with a modified progressive shooting iteration to rapidly produce visually continuous solutions with limit...

Existing approaches for evaluating word order in machine translation work with metrics computed directly over a permutation of word positions in system output relative to a reference translation. However, every permutation factorizes into a permutation tree (PET) built of primal permutations, i.e., atomic units that do not factorize any further. In this paper we explore the idea that permutatio...