相关论文: Orthonormal integrators based on Householder and G…

We present examples of Lax-integrable multi-dimensional systems of partial differential equations with higher local symmetries. We also consider Lagrangian deformations of these equations and construct variational bivectors on them.

The strict relation between some class of multiboson hamiltonian systems and the corresponding class of orthogonal polynomials is established. The correspondence is used effectively to integrate the systems. As an explicit example we…

We provide efficient algorithms to compute convergents of quadratic irrationals. We show that for square roots, provided Galois' refinement of Lagrange's theorem holds, certain decimations of the sequence of convergents are signed Chebyshev…

In the past three years, many researchers have proven and/or employed some Wirtinger-type integral inequalities to establish less conservative stability criteria for delayed continu\-ous-time systems. In this present paper, we will…

The subject of simulating internal organs is a valuable and important topic of research to multiple fields from medical analysis to education and training. This paper presents a solution that utilizes a graphical technique in combination…

A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…

In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear…

We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the fast variables and have a computational cost determined by…

We propose a linearly implicit structure-preserving numerical method for semilinear Hamiltonian systems with polynomial nonlinearities, combining Kahan's method and exponential integrator. This approach efficiently balances computational…

The introduction of Transformers architecture has brought about significant breakthroughs in Deep Learning (DL), particularly within Natural Language Processing (NLP). Since their inception, Transformers have outperformed many traditional…

In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. We demonstrate that these two algorithms have an exponential speedup over their…

We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref. [1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\bar z$ are sampled. In contrast to the…

The analogous quaternionic polynomials of a class of bivariate orthogonal polynomials (arXiv: 1502.07256, 2014) introduced. The ladder operators for these quaternionic polynomials also studied. For the quaternionic case, the ladder…

Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…

Deformable Image Registration (DIR) plays a significant role in quantifying deformation in medical data. Recent Deep Learning methods have shown promising accuracy and speedup for registering a pair of medical images. However, in 4D (3D +…

FPGAs provide a flexible and efficient platform to accelerate rapidly-changing algorithms for computer vision. The majority of existing work focuses on accelerating image classification, while other fundamental vision problems, including…

In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…

Implicit Neural Representations (INRs) have emerged and shown their benefits over discrete representations in recent years. However, fitting an INR to the given observations usually requires optimization with gradient descent from scratch,…

We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this…