Related papers: Entanglement of free-fermion systems, signal proce…
This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…
We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
We consider simple CFT models which contain massless bosons, or massless fermions or a supersymmetric combination of the two, on the strip. We study the deformations of these models by relevant boundary operators. In particular, we work out…
The correlation spectrum of fully developed one-dimensional mappings are studied near and at a weakly intermittent situation. Using a suitable infinite matrix representation, the eigenvalue equation of the Frobenius-Perron operator is…
In entanglement computations for a free scalar field with coupling to background curvature, there is a boundary term in the modular Hamiltonian which must be correctly specified in order to get sensible results. We focus here on the…
We consider a spin-$\frac{1}{2}$ chain with competing nearest and next-nearest neighbor interactions within a transverse magnetic field, which is known to be an equiavelent to the ANNNI model. When studing thermodynamics of the 2D ANNNI…
In a recent paper (arXiv:1905.07348v1), Dyson scheme to deal with density matrix of non-Hermitian Hamiltonians has been used to investigate the entanglement of states of a PT-symmetric bosonic system. They found that von Neumann entropy can…
Association schemes are combinatorial objects that allow us solve problems in several branches of mathematics. They have been used in the study of permutation groups and graphs and also in the design of experiments, coding theory, partition…
Factorization machine (FM) is a prevalent approach to modeling pairwise (second-order) feature interactions when dealing with high-dimensional sparse data. However, on the one hand, FM fails to capture higher-order feature interactions…
Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's…
The present review presents the authors previous results on the topic from the title in a new light. Most of the previous results were obtained using the techniques of antilinear Hilbert-Schmidt mappings of one Hilbert pace into another,…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
Filter bank-based multicarrier (FBMC) systems have attracted increasing attention recently in view of their many advantages over the classical cyclic prefix (CP)-based orthogonal frequency division multiplexing (CP-OFDM) modulation.…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…