相关论文: Polyphase equiangular tight frames and abelian gen…

Exhaustive study of topological semimetal phases of matter in equilibriated electonic systems and myriad extensions has built upon the foundations laid by earlier introduction and study of the Weyl semimetal, with broad applications in…

The signature is a canonical representation of a multidimensional path over an interval. However, it treats all historical information uniformly, offering no intrinsic mechanism for contextualising the relevance of the past. To address…

Over-complete systems of vectors, or in short, frames, play the role of analog codes in many areas of communication and signal processing. To name a few, spreading sequences for code-division multiple access (CDMA), over-complete…

In this paper, we propose an extended plane wave framework to make the electronic structure calculations of the twisted bilayer 2D material systems practically feasible. Based on the foundation in [Y. Zhou, H. Chen, A. Zhou, J. Comput.…

The effective field theory (EFT) framework is a precise approximation procedure when the inherent assumptions of a large-scale separation between the Standard Model (SM) and new interactions alongside perturbativity are realised.…

We present a generic approach that allows us to develop a fully polynomial-time approximation scheme (FTPAS) for minimizing nonlinear functions over the integer points in a rational polyhedron in fixed dimension. The approach combines the…

Effective Field Theory (EFT) provides a powerful framework to exploit a separation of scales in order to perform systematically improvable, model-independent calculations. We apply this method to strongly interacting quantum systems with…

This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…

We consider a toy model of a 3-dimensional topological quantum gravity. In this model, a contribution of a given 3-manifold is given by the partition function of an abelian Topological Quantum Field Theory (TQFT), with a topological…

The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the…

Equivariant tree models are statistical models used in the reconstruction of phylogenetic trees from genetic data. Here equivariant refers to a symmetry group imposed on the root distribution and on the transition matrices in the model. We…

Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left…

In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame…

The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's…

In this paper, we present a new approach of creating PTAS to the TSP problems by defining a bounded-curvature surface embedded spaces. Using this definition we prove: - A bounded-curvature surface embedded spaces TSP admits to a PTAS. -…

Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…

We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M…

This work proposes a geometric insight into equivariant message passing on Riemannian manifolds. As previously proposed, numerical features on Riemannian manifolds are represented as coordinate-independent feature fields on the manifold. To…

We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed…

We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show…