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We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…

Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In $2+1$D, it is well known that the Chern-Simons theory captures all the universal topological data of…

In this paper, we begin constructing a new finite-dimensional topological quantum field theory (TQFT) for three-manifolds, based on group PSL(2,C) and its action on a complex variable by fractional-linear transformations, by providing its…

The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…

Totally equimodular matrices generalize totally unimodular matrices and arise in the context of box-total dual integral polyhedra. This work further explores the parallels between these two classes and introduces foundational building…

We develop a quantum message-passing framework for factor graphs over finite abelian groups. Our starting point is the task of discriminating between a collection of quantum states indexed by the elements of a finite abelian group…

Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected…

Gapped interfaces (and boundaries) of two-dimensional (2D) Abelian topological phases are shown to support a remarkably rich sequence of 1D symmetry-protected topological (SPT) states. We show that such interfaces can provide a physical…

Matrix Product States (MPSs) provide a powerful framework to study and classify gapped quantum phases --symmetry-protected topological (SPT) phases in particular--defined in one dimensional lattices. On the other hand, it is natural to…

Factorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design. Wavelet frames (a.k.a. framelets) are useful in applications such as signal…

Ensemble density functional theory (EDFT) is a promising alternative to time-dependent density functional theory for computing electronic excitation energies. Using coordinate scaling, we prove several fundamental exact conditions in EDFT…

Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional…

Due to the unfavorable scaling of tensor network methods with the refinement parameter M, new approaches are necessary to improve the efficiency of numerical simulations based on such states in particular for gapless, strongly entangled…

In this article, we present a new EEG signal classification framework by integrating the complex-valued and real-valued Convolutional Neural Network(CNN) with discrete Fourier transform (DFT). The proposed neural network architecture…

We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes…

Electronic topological phases of matter, characterized by robust boundary states derived from topologically nontrivial bulk states, are pivotal for next-generation electronic devices. However, understanding their complex quantum phases,…

The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…

The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…

In the landscape of spatio-temporal data analytics, effective trajectory representation learning is paramount. To bridge the gap of learning accurate representations with efficient and flexible mechanisms, we introduce Efflex, a…

Recent vision transformers, large-kernel CNNs and MLPs have attained remarkable successes in broad vision tasks thanks to their effective information fusion in the global scope. However, their efficient deployments, especially on mobile…